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INAUGURAL FUNCTION OF

Prof. S. MINAKSHI SUNDARAM

MEMORIAL SOCIETY

andandandand

One Day Seminar on CHALLENGES IN CURRENT

MATHEMATICS RESEARCH on

22nd October, 2010

SOUVENIR

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Department of Mathematics

National Institute of Technology

Warangal, 506004

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COMMITTEES

Advisory Committee:

Prof. P.V. Arunachalam

Prof. V. Vani Prasada Rao

Prof. T.K.V. Iyengar

Sri P.V.S.S.S.R. Somayajulu

Smt K. Girija Sarma

Organizing Committee

Patron : Director, NITW Chief Advisor : Prof T.K.V. Iyengar Organizing Secretary : Prof. Y.N. Reddy Treasurer : Dr. D. Srinivasacharya

Reception Committee : Prof. G.R.K. Acharya Dr. N. Srinivasacharyulu Transportation Committee : Dr. D. Dutta Dr. P. Muthu Accommodation Committee : Dr. KNSK Viswanadham Dr. JVR Murthy Hospitality/Catering Committee : Dr. D. Srinivasacharya Registration Committee : Ms. J. Pranitha Souvenir / Certificates Committee : Dr. D. Srinivasacharya Dr. R. S. Selva Raj Stage / Seminar Hall Committee : Dr. H.P. Rani Help Desk : Dr. A. Benerji Babu

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From the desk of Organizing Secretary

Since ancient times, Mathematics is recognized as an essential and basic tool which plays a

vital role in problem solving. Industrialization and Computerization in the present Hi-Tech world

is progressing at a great speed by the sincere efforts of various scientists who are aiming at a better

society. With the invention of super computer, the scientific community has been experiencing

rapid developments in the areas of their respective fields of research. The diversified growth in

various fields is quite amazing and this is essentially due to the self less and thought provoking

pure research that was carried out by our fathers and fore fathers in 18th, 19th and 20th centuries.

Prof. S. Minakshi Sundaram was an outstanding Mathematician of 20th century whose

Research work of 1940’s was so great that it influenced the refinement of the famous Atiyah --

Singer – Index Theorem, one of the greatest theorems of 20th century.

Some admirers and proud students of late Prof. Meenakshi Sundaram joined together

recently and with a view to perpetuate the memory of their teacher and researcher par excellence,

for the posterity, have formed the society by name Prof. S Meenakshi Sundaram Memorial

Society. It is an honour for us here that Prof. T.K.V. Iyengar, an illustrious student of Prof. S.

Meenakshi Sundaram during 1962-64 who is serving our department/institute actively sine 1967,

was chosen to be the Secretary of the Society.

The members of the Department of Mathematics thought of having the Historic Inaugural

Function of the Society followed by a One day Seminar on CHALLENGES IN CURRENT

MATHEMATICS RESEARCH here at NIT, Warangal. We thank the Society for accepting our

invitation to have the Inaugural function here.

The deliberations at the Function and the Seminar, I am sure, will influence not only the

delegates attending the Seminar but also our P.G. Students and Research Scholars in shaping their

careers. I wish the Delegates a fruitful interaction in the function.

Y.N. Reddy

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PROFILE OF THE DEPARTMENT

The Department of Mathematics has been in existence since the inception of the College in 1959.

UG Programmes : The Department offers basic courses in Mathematics for B.Tech.

PG Programmes: At post-graduate level, the department offers well-designed diverse courses for

all Programmes of M.Tech. M.C.A., M.B.A. and M.Sc. Tech (Engg. Physics) and also offers

Global Electives for all PG and Ph.D. Programmes.

M.Sc. – 2-year (Four Semester) PG Programmes: The department offers Two 2-year (Four

Semester) PG programmes namely: M. Sc (Applied Mathematics) programme and M. Sc.

(Mathematics and Scientific Computing) (on self-financing basis) programme. In addition to the

regular class room instruction and laboratory course in each semester, seminar and project work

are integral parts of both the courses. They inculcate a spirit of practical application of

Mathematical Concepts and also instill enthusiasm for research activity. Special emphasis is laid

on promoting team spirit and improving the oral communication skills of the students. Admission

to both these programmes is through a National Level Entrance Test.

M.Sc. (Applied Mathematics) – 2 year Programme: This industrially oriented M.Sc. (Applied

Mathematics) course, initially sponsored by UNESCO, was started in the year 1970 with an initial

intake of 6 students and later raised to 10 students in open category and 3 seats for SC/ST

reservation. Now the number of seats are increased to 40.

M.Sc. (Mathematics and Scientific Computing) – 2 year Programme: In the context of

changing needs of the software industry, the Department is offering a Computer Oriented

Mathematics course – M.Sc. (Mathematics and Scientific Computing). This course is offered from

the year 2001 onwards, with a judicious combination of essential Mathematics, Applied

Mathematics and Computer courses.

Ph.D. Programme : The Department offers Ph.D programme in Mathematics on regular basis and

also under Quality Improvement Programme (QIP).

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The admissions for regular Ph.D. programme are made through advertisement by the institute in

every semester.

The admissions for the Ph.D. programme under Q.I.P. are made by the AICTE by an

advertisement in leading news papers every year.

Research Profile : The Department since its inception in 1959 is known to be an active research

center in Applied Mathematics.

Number of Ph.Ds awarded : 52

Number of candidates working for their Ph.D. : 21

Research Projects : The Department has successfully completed 20 research projects funded by

various organizations like MHRD, AICTE, UGC, CSIR and DST etc.

Conferences Organized by The Department : The Department has successfully organized

several conferences like 13th congress of APSMS in 2004, 44th congress of ISTAM in 1999, 5th

congress of APSMS in 1993 and 23rd congress of ISTAM in 1978, six seminars in mathematics

and 10 workshops/ summer schools.

Computational Laboratory: The Department has a full-fledged computational laboratory to meet

the requirements of the M.Sc. students, research scholars and the faculty.

Departmental Library: The Department has a well-stocked library for immediate reference of the

staff and students.

Alumni : The Alumni of the M.Sc. course are occupying distinguished positions such as the

members of the faculty at IITs, NITs, Software Industries in India and abroad and consultants to

World Bank projects.

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Mathematics Association: All the students and faculty of the Department are members of The

Mathematics association. This association organizes several academic and co curricular programs

like Quiz, Debate, Talent tests etc.

Faculty Members of the Department

S. No

Name of the faculty Designation. Field of Specialization

1. Dr. T.K.V. Iyengar, Ph.D. Professor Fluid Mechanics

2. Dr. G.R.K. Acharya, Ph.D. Professor Bio Fluid Mechanics

3. Dr. Y.N. Reddy,Ph.D. Professor & Head Numerical Analysis

4. Dr. N. Srinivasa Charyulu, Ph.D. Associate Professor Numerical Methods

5. Dr. K.N.S.K. Viswanadham, Ph.D. Associate Professor Numerical Analysis

6. Dr. J.V. Ramana Murthy, Ph.D. Associate Professor Fluid Mechanics

7. Dr. Debashis Dutta, Ph.D. Associate Professor Operations Research

8. Dr. D. Srinivasacharya, Ph.D. Associate Professor Fluid Mechanics

9. Ms. J. Pranitha, M.Sc. (Ph.D.) Assistant Professor Computational Fluid Dynamics

10. Dr. R. S. Selva Raj, Ph.D. Assistant Professor Coding Thoery

11. Dr. H.P. Rani, Ph.D. Assistant Professor Computational Fluid Dynamics

12 Dr. P. Muthu, Ph.D. Assistant Professor Bio Fluid Mechanics

13 Dr. A. Benarji Babu, Ph.D. Assistant Professor Fluid Mechanics

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Prof. S. MINAKSHI SUNDARAM - A BRIEF PROFILE

Prof. P. V. ARUNACHALAM, Retd. Prof. of Mathematics, S.V.U., Tirupathi

Former Vice Chancellor, Dravidian University, Kuppam

Subramiah Minakshisundaram was born on 12th October 1913 in Trichur, Kerala State, of India.

He studied in C.R.C.High School, Perambur, Madras State from 3rd Class to Sixth during 1919 to

1929 when he passed S.S.L.C. He had constantly topped in Mathematics having shown a marked

aptitude for the subject..

Collegiate Education: Studied Intermediate in Pachiyappa's College, Madras from 1929 to 1931.

Higher Education: Studied B.A. Hons. Mathematics from Loyola College, Madras from 1931 to

1934 and secured First Class First. Got his M.A. Degree in Mathematics of the Madras University

on payment of a token sum as was the custom in some universities in India , those days.

Research Work after M.A. : His teachers were the well known Prof.K.Anand Rau and Prof. R.

Vaidyanathaswamy . For a few years he worked under R.Vaidyanathaswamy. After studying the

books " Mathoden der Mathematics Physik " of Prof. Richard Courant and Prof.Lichtenstein, then

Prof.Razaiuddin Siddiqui author of Lectures on Quantum Mechanics and former Professor of

Osmania University and who worked under Prof. Werner Heisenberg of Germany he published a

few papers in Non-Linear Parabolic Equations.

His thesis was entitled "Fourier Ansatz and Non- Linear Parabolic Equations." Some of his papers

were published in the Proceedings of the Indian Academy of Sciences while most of them

appeared in the Journal of the Indian Mathematical Society. The thesis as a whole was published

by the Madras University in their Journal.

In the year 1940 he was awarded the D.Sc. in Mathematics of the Madras University, its

distinguished alumnus, the much coveted degree of those days of a reputed university. For some

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time he was Research Fellow, Department of Mathematics of the Madras University on a meager

sum.

For a long time he was without any financial assistance and during that period he eked out his

livelihood by private tuitions . Dr.P.K.Menon, Director , Joint Cipher Bureau, New Delhi mention

that the active Mathematician of Madras that he was in those days and the name he made for

himself in mathematical circles of Madras. He was and active member and was primarily

responsible for organising a mainature Mathematics Club at Madras , of which

Prof.C.T.Rajagopal, Prof.K.Chandrasekharan, Prof.K.G.Ramanathan and few others were active

participants. His work attracted the attention of stalwarts in the field of Partial Differential

Equations at that time, one of them being Dr.Richard Courant , Professor Emeritus , Courant

Institute of Mathematical Sciences, New York University. The report on his thesis was excellent

and it was praised very much. His thesis was adjudged to be one of the best thesis for the year

1940 and awarded the Narsinga Rao Medal and also he was awarded the Ramanujam Medal.

Prof.Minakshisundaram could not secure a job in those difficult days in spite of his academic

distinctions. Late Prof.Narsinga Rao promised him the job of a Tutor in Mathematics at the

Annamalia University, Annamalainagar when he was the Head of the Department of Mathematics

there. But in 1943 , when the Department of Mathematical Physics was started by the University at

the initiative of late Dr. C.R.Reddy, an eminent educationist, and under the Headship of

Prof.Nagendra Nath, Minakshisundaram was offered the post of Lecturer in the Department of

Mathematical Physics by Dr.. C.R.Reddy who was very much impressed with his academic

achievements.Thus he joined the Andhra University Department of Mathematical Physics as

lecturer in the year 1943.

From 1943 to 1946 he worked as Lecturer in the Department of Mathematical Physics in the

Andhra University. In 1946 he was invited by the Director , Dr.Aydelotte, to be a Member of the

School of Mathematics of the Institute of Advanced Study, Princeton, New Jersey, USA. He was

there from 1946 to 1948. Meanwhile the Andhra University Authorities promoted him to

Readership in the Department of Mathematical Physics. He worked as Reader in the Department

from 1946 to 1950. Late Prof.A.Narsinga Rao was then Head of the Department of Mathematical

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Physics having come over from Annamalai University at the invitation of late Dr.C.R.Reddy, Vice

Chancellor.

Returning from the Institute of Advanced Study, Princeton, in 1948, he rejoined duty as Reader in

the Department of Mathematical Physics, Andhra University and continued in the post till he

became Professor and Head of the Department of Mathematical Physics in the year 1951, after the

post became vacant due to the retirement of Prof.A.Narsinga Rao in the year 1950.

A significant event in Prof.Minakshisundaram"s career as a Mathematician during 1950 was the

invitation to the International Symposium on Differential Equations, Stillwater, Oaklahoma, USA.

His participation in the deliberations of the International Congress of Mathematics held at

Cambridge, Massachussets, USA , at invitation of the congress. He was the Head of the

Department of Mathematical Physics from 1951 to 1962.During this period he worked hard in

bringing the reputation of the Department of Mathematical Physics to limelight and a measure of

respectability for the students of the department elsewhere in learned Institutions of the world.

In 1958 He was invited on an Educational Tour to USA. as a member of the General Education

Team. He was also invited to the International Congress of Mathematicians, Edinburgh, to deliver

lecture. This lecture was well received and praised. Dr.M.H.Stone visited the Department of

Mathematical Physics and was the guest of honor at a valedictory function of the Departmental

Association. It was all due to the personality of Prof.S.Minakshisundaram as a reputed

Mathematician. A couple of his students misunderstood him as the path to modern research is

difficult. He used to point out his achievemnts as coming from his own hard work and in this none

was his guide.

In a sense late Prof.K.Ananda Rau and Prof.R.Vaidanathaswamy appeared to be his guides in

disguise when he was confronted with difficulties in his mathematical labors.

In the year 1951, he participated in a summer seminar organized at the Tata Institute of

Fundamental Research,Bombay along with his students, now Prof.P.Sambasiva Rao of the

Department of Engineering Mathematics of the Andhra University, at the invitation of

Prof.K.Chandrasekharan.During that period there was close collaboration between the two eminent

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Mathematicians which resulted in their book " Typical Means " seeing the light of day. It was very

well received by Mathematicians the world over. It is a source book for further work which the

authors have taken pains to compose.

He was very social and had many friends in all ranks of the University Staff and elsewhere. There

was none who did not know Prof.Minakshisundaram for generations and generations of students,

colleagues and administrative personnel. In a sense he was an idealist, and often at times used to

live in a world of his own, always dreamy and always thoughtful, thinking over some problem

mathematical or otherwise. Mrs.Minakshisundaram had to take a lot of pains to remind him of his

food and other small human requirements of daily life. He had an eye for talent and ability and

wherever it was found he used to enslave himself for them. Most of the young talented students

were his great friends and he used to derive aesthetic pleasure in their company. He trained a

number of students for various examinations and many of them now occupy positions of

responsibility in various walks of life.

In 1967 SMS was invited to the Indian Institute Of Advanced Studies in Simla.He was very

happy.He never felt happy just teaching and the academic value of the subject was not his forte.In

the wonderful surroundings,atmosphere of the foot hills of the Himalayan rangehe could work

peacefully and with verve.The last work of his life began.He was once again invited by the then

Vice Chancellor Prof. K.R.Srinivasa Iyengar to be the first Director and later Principal of the Post

Graduate Center of the Andhra university at Guntur. As Prof.S.Minakshisundaram had a soft

corner for Andhra University he relinquished his post at Simla and rejoined the University.

He occupied himself both day and night in organising the Center in various ways which shortened

his life as is seen from his premature death through heart disease due to overwork. He had a severe

heart attack at Guntur and had to retire prematurely from service of the University much to his

regret and those of his admirers. While at Guntur he was offered a Research Professorship in

Mathematics at the Institute for Fluid Dynamics and Applied Mathematics, College Park,

University of Maryland, USA on a very high salary and attractive terms in recognition of his

unusual talents and abilities. Unfortunately, he could not avail himself of the opportunity because

of his bad health at that time. His name was proposed for the post of President of the Indian

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Mathematical Society, a unique academic honor, but we could not see him function as President of

the Society.

He was also selected as Research professor in Mathematics under the U.G.C. scheme for Retired

Professors in India. But even this opportunity was denied by cruel Fate which took away his

precious life quite unexpectedly. He had a panoramic plan of publishing a number of books on

advanced mathematics and it should be mentioned that his premature death was a great loss to

Indian Mathematics.

BOOKS PUBLISHED.

1. TYPICAL MEANS S.Minakshisundaram and K.Chandrasekharan . Oxford University Press-

Bombay 1952-Fundamental Research Monograms.

2. Lectures on Functional Analysis and Applications. Lectures delivered in I.I.T. Madras, 1965.

3. Composite Mathematics Text in Telugu for students of the VIII Class , Government of Andhra

Pradesh Publication and Editor, 1968.

4. SPECTRAL THEORY OF DIFFERENTIAL OPERATORS-HEAT EQUATION. Under

Security for possible publication in the Higher Mathematics Series of the Von Nostrand Company,

U.S.A.

POSITIONS HELD IN ANDHRA UNIVERSITY.

1. Joined the Faculty as Lecturer in 1943 of the Mathematical Physics Department.

2. Reader in the Mathematical Physics Department from 1946 to 1950.

3. Professor and Head of Mathematical Physics Department from 1951 to 1961.

4. Warden of the University Hostels in 1957 and again 1962.

5. Librarian of the University Library from 1960 to 1961.

6. In Charge Registrar of the Andhra University in 1961.

7. Research Professor in Indian Institute of Advanced Studies, Simla 1966 to 1967.

8. First Special Officer , Post Graduate Center, Guntur, 1967 to 1968. 9. He organized the Indian

Mathematical Society Conference at Andhra University in 1961.

10. He gave Special Lectures Seminars during his distinguished career at And University

from 1948 to 1966.

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Prof. S. M. S – A GURU PAR EXCELLENCE

Prof. V. VANI PRASADA RAO

Président, SMS

We are very happy to bring out this Souvenir on the occasion of the inaugural function of the

activities of Prof. S. Minakshisundaram Memorial Society, in collaboration with the National

Institute of Technology, Warangal.

I studied B Sc (Hons) Mathematical Physics under Prof. S. Minakshisundaram, fondly known as

Prof SMS, in Andhra University during the period 1950-53. They were the formative years of my

life and it was my privilege, honour and good fortune to be groomed by a Guru who was a

professor of exceptionally high calibre. He has set an example in many aspects of my life which I

follow even now.

When I was in the final year of the B Sc (Hons) course, he wanted me to teach a junior student

who was weak in a subject during the summer holidays. He used to sometimes visit these tuitions

and sit behind the student to ensure that he was following my teaching. That was the type of

dedication and commitment he showed towards his students.

Prof. SMS was not just a teacher, but also a great GURU who was deeply interested in his students'

overall well-being. He was a mentor and well-wisher. He always extended a helping hand to his

students and guided them in their careers well after they left the University.

For some reason known to him alone he kept a mental note of me even after my leaving that

department. After completion of M Sc (Statistics) from Andhra University, I joined Indian

Statistical Institute, Calcutta for the Statisticians Training Course. A month after my joining, I

received a telegram from Prof. SMS offering me a job without my applying for it. It was a great

surprise not only to me but to all my friends. I was overjoyed and left the Institute with the

permission of the then Head of the Indian Statistical Institute, Prof C. R. Rao Garu. I joined

Andhra University as a faculty member in the department of Mathematical Physics. Later some

people asked me whether I was related to Prof.SMS. I used to reply in the affirmative “Yes, ours is

a Guru-Shishya relationship”.

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Like his affection for his students, his love for his subject was unparalleled. His efforts to make

Mathematics interesting were continuous and creative. As students in the coastal town of

Vishakhapatnam we used to go for evening walks with Prof SMS on the beach. He used to unravel

certain Mathematical concepts outside of the classroom.

During one year Andhra University conducted a science exhibition and the Department of

Mathematical Physics had to contribute their exhibits as well. The students were wondering and a

bit skeptical as to what could be interesting in a dry subject like Mathematics for the average

visitor. But under the inspiration and guidance of Prof SMS we prepared shapes of various

mathematical objects, charts of interesting mathematical problems and solutions which a layman

could easily understand and at the same time appreciate the wonders of mathematics. During that

year the Department’s exhibits attracted a large number of crowds.

Prof SMS was a dedicated Guru who produced a number of students of high calibre who have

occupied and continue to hold positions of responsibility in various walks of life in India and

abroad. Some are in Academics working as professors in different Universities in USA and other

countries, some are in colleges and Institutes of high repute like the IITs, CITs, IIMs, ISI and

ISRO. Some are in leading organizations in the IT industry, some others in All India Services, the

Defense Services like the Army Navy etc. It is a great tribute and blessing by the Guru that one of

his students has risen to the level of Nobel Laureate.

Prof. SMS commands high respect not only in academic fields and his students and has many

admirers in all circles of life. In his address to the International Congress of Mathematics 2010

held in Hyderabad, the Honourable Chief Minister of Andhra Pradesh applauded four

mathematicians namely Prof C R Rao, Prof Minakshisundaram, Prof Chandrasekharan and Prof

K.G. Ramanathan for their remarkable and outstanding contributions to Mathematics.

Prof SMS is an ideal Acharya - a person who has dedicated his life to learning and research and

who had special warmth for his students and helped them in every way. It is my good fortune and

honour to have a GURU like him.

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MY CONTACT WITH PROF. S. MINAKSHISUNDARAM

AND ANDHRA UNIVERSITY

Prof. M. RAJAGOPALAN,

Tennessee State University,

Nashville, TN 37201

I joined BSC (HONS.) Mathematical Physics 3rd year in Andhra University in 1947. At

that time, I was only 15 years old. Prof. S. Minakshisundaram was on leave that year and was

visiting member of the Institute for Advanced Studies in Princeton U.S.A. Of course, everyone

knew that a membership in that institute is given to only those who are very strong in their fields.

When he came back the next year, I was ready to learn what he had to say in my 4th (Hons.) and 5th

(Hons.). How I got prepared in my 3rd (Hons.) to absorb what I learned later from Prof. S.M.S. is

worthwhile saying. I learned Analysis in my 3rd year Hons. Under Prof. T.Vijayaraghavan. Prof.

Vijayaraghavan was an outstanding mathematician and there are mathematical objects called

“Vijayaraghavan Numbers” in mathematical literature just like we have Einstein’s relativity. He

was responsible for my learning “correct thinking” or so called “rigor” in mathematics. The way I

learned that “rigor” in mathematics is when Prof. Vijayaraghavan gave me a “zero” in the final

examination in analysis at the end of 3rd year honors. My classmates laughed at me when I got this

“zero” and I was also embarrassed when I got “zero” in the examination from Prof.

Vijayaraghavan. That was the only zero I got in any examination in my entire life. I went to Prof.

Vijayaraghavan and demanded an explanation why I got a “zero” in the final examination on

analysis. He patiently showed me all my mistakes in my answers and then I completely understood

what “rigor” is and also the fact that the backbone of good mathematics is “rigor”. Then I

requested Prof. Vijayaraghavan to help me read the book on “Analysis” written by A. Ramanathan

and that professor was very kind with me and helped in my learning that book rigorously. I have

done more than 200 problems from that book and when Prof. S.M.S. came to teach my class I was

really prepared. Prof. S.M.S. taught Riemann integration, Fourier series, Potential theory and I

grasped almost all of the details. Prof. S.M.S. could see that I understood what he taught and he

was more enthused and exhibited many nuances in the courses which helped me in my research

and also in my teaching later on. In the future years as a professor of mathematics when I had to

teach Calculus I and II, I never needed to look into a book to prepare for the classes. I just think of

what Prof. S.M.S. taught me and the ideas flow from me to my students easily and smoothly. The

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training given to me by Prof. S.M.S. and Prof. T. Vijayaraghavan was so good that in the final

examination on analysis at the end of my honors course when a problem appeared on the test, the

like of which I have never seen before in my life, I calmly analyzed the problem and got the

answer! When I came out of that examination hall and when I compared the performance of my

classmates with mine I found out I was the only one who solved that problem on the test.

Prof. S. Minakshisundaram had a great liking to me since he is a very good mathematician.

He found out that I have a good mathematical talent. A proverb in Tamil says “ Pambin kalai

pambe ariyum” (A snake knows all about the legs of snakes). Prof. Minakshisundaram offered me

Junior Government of India Research Scholarship to come to Andhra University and work with

him on mathematics. At that time he taught me Hilbert Space, which was analysis, but he showed

me that analysis becomes easier if I get a geometrical picture in the background. With that concept

of having a picture in mind to study theorems as Prof. Minakshisundarm taught me, I got the

ability to study numerous mathematical subjects by myself with no help from others. Luckily, the

library of Andhra University had a wonderful collection of books and mathematical journals that

dealt with Banach Spaces, Differential Equations, Modern Algebra, Potential Theory, Harmonic

Analysis, Duality in LCA Groups etc. Many of these subjects are not taught in undergraduate or

even honors courses in India. Prof. S. Minakshisundaram enjoyed talking to me on H* algebras. As

a result, I published two papers in the Journal of Indian Math Society. These papers were included

in a book on Banach Algebras authored by C.E. Rickart and that helped me to get a research

assistantship in Yale University in 1960. But the background I gained in Andhra University in

Mathematics was so powerful that I finished my PhD thesis in Yale University essentially by Sep.

1962 just in two years of joining Yale. That was not common for university students to finish PhD

in two years time. It was because of Andhra University having outstanding faculty in Mathematics

in the early 60’s and it was one of the strongest Departments in Mathematics and I think that I was

lucky to be a student in such a good school. Dr. Minakshisundaram’s strength in mathematics can

be understood from the fact that many mathematicians all over the world worked on a problem

called “Minakshisundaram Coefficients Problem”; Dr. V. Patodi of TATA Institute became well

known by solving that problem.

Prof. S. Minakshisundaram was interested among other things in so called “Divergent

series”. That is where summability methods play a role. Research was done on summability

methods throughout India in the 50’s. Prof. S. Minakshisundaram introduced me to this field also.

17

His view on the subject was very interesting. His views on the divergent series and summability

culminated in a book called typical means jointly authored with K. Chandrasekharan of TATA

Institute. I could not take full advantage of his presentation of that subject because I left Andhra

University soon to be a lecturer in mathematics in Banaras Hindu University. Before I left Andhra

University for good to become a Lecturer in Mathematics in BHU (Benaras Hindu University), I

was given Senior Govt. of India Scholarship by Prof. S. Minakshisundaram. So, I was allowed to

be a member of the faculty club in Andhra University. Prof. Minakshisundaram was also a member

of that faculty club and I had opportunity to see Prof. SMS in a different angle. He came to the

club in lungi (that is my memory today). He used to chat with a select few members in that club

and one of them was the Registrar K.V.S.Gopalaswamy of Andhra University. He had a lot of

power. . Prof. Minakshisundaram sometimes played Bridge in that club with me. He used to cut

jokes then. One day he was cutting jokes at the administration of Andhra University since the

hostel bills were going constantly up and the students started complaining about it. Prof.SMS cut

jokes at the mismanagement of the hostel by the administration including the Registrar. So, the

Registrar replied powerfully. He made Prof. Minakshisundaram the warden of the hostel next year.

Indirectly he challenged Prof. SMS to show that he can administer the hostel better than others. In

those days the Andhra University hostel was laughing stock to all students, faculty and others.

Food was horrible. Many students got accommodation in the so called “Sheds” which were

crowded with10 to 12 students in a room. Those rooms were also leaking. The students used to say

that if someone can survive a one year stay in that hostel he will get the capacity to survive even in

the Sahara desert. One good side of the hostel, just the names of the buildings, which I remember

were Ashoka Vardhana, Sadharama Saadhana, Vinaya Vihara and Viveka Vinayasa. Prof SMS

became the warden of the hostel though he did not want it. Everybody thought that Prof SMS

cannot do much to improve the conditions of the hostel.

But Prof SMS was made of sterner stuff. Otherwise, how can he be so famous in

Mathematics and produce so many good students and become a visiting member of the Institute of

the Advance Studies in Princeton, USA. He was seen going around on errands in hostel with a

lungi at odd times. No body could tell where and when he will appear in the hostel. How did he

manage to check the account books surprisingly? It is known only to him. To spring a surprise,

when food and other materials were stolen from the hostel is an interesting story that he loved to

talk about. The net result was, due to his constant and dedicated vigil, the hostel bills came down

18

by ½ of what it was before. His prestige which was already high went up higher. The

administration requested him to continue as a warden of the hostel after his term as a warden ended

in 1 year.

But smilingly he said “no” to that request, with his constant companion in his hand. Who

was that constant companion of Prof SMS that he held in his hands. (That is “Cigarette”). He was

so addicted to Cigarette that someone remarked that he may even leave doing his Mathematics but

not his Cigarette. Many people told him to stop that habit of smoking. Prof SMS agreed on

principle. But effectively, he could not stop smoking. At one time, he was hospitalized and then

under Doctor’s advice, he stopped smoking. Everyone was surprised. But that did not last for long

duration. He again started smoking. This time, it became fatal. That Cigarette cut his life short. It is

a pity that such a great talent fall a prey to small temptations like smoking. It is a deep loss to the

community.

It is only in the fitness of things that we should have memorials to such great people of

India like Prof SMS, so that the next generation could cherish our talents and feel proud of our

community.

19

TITBITS ON MATHEMATICS

Prof. M. RAJAGOPALAN

Tennessee State University,

Nashville (TN) 37209 USA

I am thankful for the invitation from SMS society to give this talk. Originally I thought of

giving a talk on my recent research work on shift operators on c x c0 which is going to be

published in 2011. However I was suggested to choose a topic that could be easily understood. So I

changed my talk to the present one. Many people in the audience may feel that this talk is

elementary and not deep. I request their pardon and patience.

Recently, I was reading some articles in archaeology revealing the history of Hindus and

their achievements. I found it interesting. Yes, History and achievement of Hindus though that

word is very carefully avoided and not used in political circles. Recent archaeological discoveries

place the Hindu culture as existing for 50,000 years. .

The following books are worth reading in this connection.

1. George Fuwerstein, Subash Kak and David Frawley; In search of the cradle of civilization

(New Light on Ancient India); Motilal BanarsiDass publishers; pvt. Ltd; Delhi (2008)

2. D.Frawley; Yoga and Ayurveda; Self Healing and Self Realization; Twin lakes (WI) Lotus

press

3. B.B.Lal; The Earliest Civilization of South Asia; New Delhi Aryan books international

(1997)

4. T.R.N.Rao and S.Kak; Computing Science in Ancient India, Lafayette (LA) ; USL press (

1998) also Delhi, Munshiram Mohanlal ( 2000)

5. INDIA’S CONTRIBUTION TO WORLD THOUGHT AND CULTURE; First Edn 1970.

Now available from:

Vivekananda Kendra Prakash Trust;

No 5, Singarachary Street; Triplicane,

Chennai -5 (600 005)

20

And also from:

R.S.Narayana Swamy;

43 Ramanujam Street, T.Nagar,

Chennai -17 (600 017)

Phone (044) 2434 5665.

These studies reveal the great depths of Hindu culture of which we should be proud. For

example, the early cultural period of Hindus called rock art period is dated as around 40000 BC.

The Indus Saraswati tradition is dated around 8000 BC to 1300 BC. Writing in India is found as

early as 3300 BC or earlier. New biological evidence shows that Hindus lived in the Indian

subcontinent for more than 50000 Years.

The earliest textual source is the RIGVEDA. It contains astronomical references going

back up to 5000 BC and even earlier. The Hindus used the Saptarishi calendar which goes back up

to 6676 BC. So Hindu history is very old and has many achievements though that is not taught in

schools. Let us see some aspects of the Hindu achievements related to mathematics.

Ancient Mathematics

Numbers are the base of mathematics. Place value of a number is the root of understanding

and doing calculations with numbers. The place value system was discovered first by the Hindus.

It was already in use in 5th century A.D in India and is found in the Hindu religious books called

Siddhanthas and also in Yajurveda samhita (see page 47 of the book 5) mentioned above namely,

India’s contribution to world thought and culture, Vivekananda ROCK MEMORIAL

COMMITTEE.

Yajurveda Samhita gives names to all the numbers 1, 10,102,103, 104, 105, 106, 107, 108,

109, 1010, 1011 and 1012. The Westerners, Arabs, Egyptians or Mesopotamians do not have different

names for each of these powers 1, 10,102-----1012. For example in English 10 is ten. 102 is hundred

.103 is thousand. The names ten, hundred, thousand are different. But 104 is ten thousand and there

is no separate name in English for 104 ; just as 103 is thousand and not ten hundred . In Sanskrit 10

is dasa, 102 is sata,103 is sahastra, 104 is ayuta., 105 is niyuta ,106 is Prayuta, 107 is Arbuda , 108 (

nyarbuda), 109 (samudra) , 1010(madhya) , 1011 ( anta) , and 1012 (pararda) .

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The westerners used the complicated Roman numeral system and hence their progress in

mathematics was not as rapid as that of Hindus for some time. In eighth century AD a Hindu

astronomer visited the court of the king Abbasid Caliph in middle east and taught the Arabs the

place value system of numbers and the Hindu numerals 0,1,2,3,4,5,6,7,8,and 9. The Europeans

learnt the place value system of numbers later on from the Arabs and since then the development

of mathematics in Europe was rapid.

Geometry:

It is generally believed that Pythagoras was the first to discover what is now known as

Pythagoras theorem. But Katyayana Sulba Sutra contains the statement and proof of Pythagoras

theorem. It was written in 700 BC about two hundred years before Pythagoras. Hindus used a lot

of geometry in the construction of the altar to perform their yagnas. Pascal studied binomial

theorem and he explained that theorem in a geometrical way by writing the numbers in the form of

a triangle. In mathematical literature it is called Pascal triangle.

PINGALA wrote his book Chandas Sutra which studies binomial theorem in 3rd century

BC and he called that Pascal triangle as Meru prasta. So Pascal triangle was known to Hindus long

before the Europeans (SEE PAGE 49 OF THE BOOK 5 MENTIONED ABOVE). The number π

that comes in the study of circles was given the correct value up to 4 decimal places by Aryabhatta.

The Gregory series which was used at one time to calculate the value of π was known to

mathematicians of Kerala before the Europeans.

Geometry and temple architecture and Sun’s rays

There is temple in the town Sringeri in Karnataka state for Goddess SARADAMBAL

established by the famous Hindu saint ADI SANKARACHARYA. Inside that temple, there is a

smaller temple for the God VIDYA SANKAR. There is a hall with twelve pillars in that temple of

Vidya Sankar. The pillars are named after the twelve months of the year following Sanskrit names

of the months namely Mesha , vrishabha , Mituna , Karkata , Simha , Kanya , Tulam , Vrischchika

, Dhanus , Makara ,Kumbha and Meena . The pillars are so arranged geometrically that the sun’s

rays falls on each month only on that pillar which bears the same name of that month.

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Playing with Numbers:

In India many authors have found interesting properties of numbers. The famous anecdote

of such property of numbers is related to Sri S. Ramanujan who surprised the famous G.H. Hardy

of England by telling that 1729 can be written as sum of two cubes in two different ways and is the

smallest such number. D. Kaprekar of Maharashtra State has written a lot of such interesting and

simple properties of numbers.

Here is a sample: Take four integers from 0 to 9 write them as a four digit number by

writing them side by side in descending order. Now reverse that order and subtract the smaller

from the higher, repeat the above steps beginning from the result of subtraction. If we keep on

repeating this process we end up in '0” or the four digits 7, 6, 4,1, in some order. (It will be nice to

find a proof of this). Note that if you start from the digits 7,6,4,1 and go through the above

process you get back the same digits in one step.

Hindu Religious Prayer and Mathematics:

The following chess problem was hotly discussed in Europe in eighteenth century. The

problem is to move the knight in such a way that it travels to all squares on the chessboard without

landing on the same square twice. It is fun to know that this difficult problem is solved by a prayer

to the Goddess Lakshmi.

The prayer to Goddess Lakshmi consists of two slokas as follows:

RA MAA VA RAA BHI TAA PAA SAA

NII RA JO DA RA PAA DYA HI |

NA YAA SA MAA BHA YAA BHAA MAA

SAA VA NAA TAA PA MAS YA TU ||

RA JO BHI DYA TU YAA TAA YAA (h)

VA RA PAA MAA MA MAA VA NII |

SA SAA RA RAA BHA SYA HI TAA

BHAA SAA PAA PA DYA MAA NA NAA ||

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Meaning: May the Goddess Lakshmi the wife of Vishnu with navel as beautiful as lotus who was

born in milky ocean dispel all my mental distress. May her shining face dispel my ignorance and

sins.

How does a prayer to Lakshmi solve a chess problem tried vehemently by many in Europe

in 18th century? Here is how:

1. Take a Chess Board

2. Write the words in first sloka on each square in on chessboard keeping the same order

3. Look at the words of second sloka and follow it as below

4. Put a knight on the square that says “RA” in the chessboard

5. Now moves the knight to that square in the chessboard that follows same letter”RA” in the

second verse. Note that this letter is “JO”. So move knight to square JO

6. From square “JO” of chessboard move Knight to the square which has the same word as

the one following “JO” in second verse that the word is BHI. So move Knight to square

“BHI”

7. Repeat the above pattern. Now you see Goddess Lakshmi showers her grace on you to

solve the chess Problem

Note: The late PROF, M. VENKATARAMAN USED TO TELL SLOKAS WHICH ARE

PRAYERS TO GOD RANGANATHA OF SRIRANGAM THAT ALSO SOLVES THE ABOVE

CHESS PROBLEM.

Mantras, Puja, and Mathematics:

The so called Prayer to Goddess Lakshmi above is for fun. But such things where a mantra

or puja gave mathematical results have occurred in real life.

(a) The famous S.Ramanujan wrote to his uncle that he does his puja in morning and in

night the Goddess “Namakkal devatai” (who is Lakshmi) appears in his dream and reveals all the

mathematical results for which he became famous throughout the world.

(b) Sadguru Sri Gnanananda established an asram in the south Indian village called

Tapovanam and he gave Sanyasa diksha to many people. One of his disciples was named by him

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as Sri Trivenigiri Swamigal. After leaving Andhra University in 1957. I joined Banaras Hindu

University as a Lecturer in Mathematics; Sri Trivenigiri Swamigal was in Sankara Madam in

Hanuman ghat in Benaras at that time. Of course I had contact with him earlier around 1942, but I

lost that contact for a long time till I met him again in 1957. I approached him and requested to

give me mantropadesa. He gave me some mantras. He told me that they are powerful. I asked him

how powerful they were; he said if I repeat those mantras so many times I will get a lot of

knowledge. I asked him” Can I solve outstanding mathematical problems by doing that japam”?

He said “YES” emphatically.

Later I went to USA as Prof.of Mathematics in Memphis State University in 1972. I had

very light teaching load and so I wanted to spend time on Research. I read many mathematical

papers and found that one problem called “SCARBOROUGH-STONE” problem was open for

about 20 years in spite of serious attempts to solve it by Russians, Polish, Americans, etc. I tried to

solve it. It was hard. I then remembered my Guru's words about the mantra. I did that japam

vehemently with faith in my Guru. Lo! I got solution to that problem. That made me well known

and I got invitations to talk in International conferences, in Germany, Japan, Canada, etc. From

that time I continue to do my Japam with faith in my Guru and so far I have published about 85

Papers in Journals of high repute throughout the World.

Hindu society rose to great heights in Research in the past and even now there are many

Hindu scientists of outstanding caliber. It will be worthwhile writing articles on Hindu

mathematicians.

There are many books on History of mathematics and we find lives of many European

mathematicians in those books. That gives prestige to Europe. Hindus should do the same namely

write and / or run conferences and propagate the contributions to mathematics of Hindus. Of

course there is a good amount of literature on one Hindu mathematician namely Sri S.Ramanujan.

It will be nice to know about other good Hindu mathematicians too.

I am happy to note that the SMS society is making efforts to publicize the contributions of

the great mathematician Prof. S.MINAKSHISUNDARAM. I wish success to their efforts.

25

SCIENTIFIC UNDERSTANDING OF CONSCIOUSNESS -

CONCEPTS FROM INDIAN PHILOSOPHY

HARI SYAMALA DEVI

murty_hari@yahoo.com

Abstract

Consciousness and its relation to the physical body were thoroughly analyzed in ancient

times by Indian sages. Indian philosophy, the store and product of their wisdom, contains many

concepts which can lead to scientific answers to some of the questions that brain scientists and

modern consciousness researchers are struggling with. Today’s trend among modern scientists is

to study the human brain using quantum theory. Concepts in Indian philosophy can be helpful in

this approach. In Indian philosophical literature, thought is often described as being very fast and

one that never comes to stop. Properties of thought described here are very similar to those of

faster-than-light objects, known as tachyons in modern physics. A theory based on the concept

that mind consists of superluminal objects will make it possible to describe mental processes and

interaction of mind with ordinary matter, using the terminology of mathematics and physics and

quantum mechanics in particular.

On this occasion of honoring the memory of Late Professor S. Minakshi Sundaram, I

should point out that theories of linear and non-linear partial differential equations, integral

equations, eigenfunctions of boundary value problems, Fourier analysis, and Hilbert spaces are the

main ingredients of quantum formalism and the contributions by the Late professor (whom we

used to call Master-garu or Mastaru) in all the above areas are invaluable and only too well-known.

1. Introduction

Consciousness and its relation to the physical body were thoroughly analyzed in the Indian

philosophy of ancient times. This philosophy contains many concepts which can lead to scientific

answers to some of the questions that brain scientists and modern consciousness researchers are

concerned with. In particular, we will discuss this philosophy’s proposition that mind is faster than

matter (hence faster than energy and light) and how this proposition sheds light on questions such

as “is monism or dualism, which theory can better explain consciousness scientifically”, “is

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dualism necessarily unscientific?”, “How does a living brain create subjective experience?”, “is

quantum mechanics necessary to explain consciousness in a brain?”. In Indian philosophical

literature thought is often described as being very fast and one that never comes to stop

(interestingly, according to today’s physics, a faster-than-light object, known as tachyon, cannot be

brought to rest.) If mind indeed consists of superluminal objects then it may be possible to

describe its properties and processes and its interaction with ordinary matter in the terminology of

mathematics and physics and quantum mechanics in particular.

We will use the brain-computer analogy to present some ideas from the ancient Indian

Philosophy which helps modern researchers to find scientific explanation of how the physical brain

and the mind work together and how subjective experience occurs in the brain. Indian Philosophy

is often considered to be a mystery and incomprehensible probably because it was all written long

time ago and in Sanskrit, a language not spoken today and also because consciousness is discussed

here in the context of spiritual progress. Contrary to such myths, this literature’s analyses are

objective and concerned with understanding reality and perception of reality rather than with faith

and what one should believe in. In recent days, some quantum physicists think that this ancient

knowledge includes concepts which resonate with findings in quantum physics.

2. Consciousness, Free Will, Mind, and Matter in Indian Philosophy

This philosophy makes a distinction between free will and all other aspects of what we call

consciousness of humans and other living beings in modern terminology. All aspects other than

free will, such as desires, logical thought, remembering, emotions, experiences, imagination and so

on, are all seen as involving a certain memory, and can be amenable to scientific explanation but

not free will. Briefly, this philosophy’s view of consciousness is as follows:

The physical body of a living being is like a piece of hardware. It is made up of matter.

Every living being, human or animal, or any living organism (possibly excluding some primitive

forms of life), has an accumulation of experiences and therefore an accumulation of information,

in other words a memory (called Manas in this literature)1, which we will call mind in this paper.

In this sense, mind is like a computer memory containing data and programs. Just like a computer's

1 In the Sankhya branch of Vedanta, four aspects of the mind are defined: Chitta, Manas, Buddhi, and Ahamkara. In this article, we refer to all of them together as Manas because our focus is only that they are all contained in a memory.

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hardware and software do not know what they are doing, their own existence, and the meaning of

their memory contents, both the body and the mind of a living being also do not really know

anything but there is a certain Consciousness (with big C in front, to convey that it is not part from

the mind mentioned above) that "knows". Consciousness is like the computer operator, as it were,

and the one who "really knows" everything that is part of the living being’s activity. Although a

computer does not really know or understand anything it does, once it is equipped with stored

information (both data and programs) and mechanisms to store, retrieve, and process information,

it is able to exhibit or simulate many "intelligent" behaviors such as learning, planning, and pattern

recognition. Machines which do not have these memory mechanisms cannot exhibit such

"intelligent" behaviors. Hence machine intelligence is based on memory mechanisms and we may

say that an artificially intelligent machine is “intelligent” but not “conscious”, where by

“intelligent” we mean the ability to store, retrieve, and process information. On the other hand,

human beings (and probably other living beings) are not only “intelligent” like the “intelligent

machines” in the sense that they perform various functions in life using the physical brain (similar

to hardware) and the information stored in the brain (similar to software) but they are “conscious”

as well; they know what they are doing at least when awake. Indian philosophy emphasizes that

there is “Consciousness”, different from and independent of any living being’s memory and its

contents and mechanisms. Moreover, intelligence in living beings, unlike in computers, is not

merely a material process but is a process of interaction between ordinary matter of the physical

body and some stored information made up of faster-than-light matter. A living being’s

experiences and emotions are responses of this faster-than-light software to the sensory inputs. The

difference between a living being and a lifeless stone is that the living being has the necessary

faster-than-light information to create experience whereas neither the stone nor the computer have

it. The stone’s inability to create experience is perceived by us as lack of self-awareness. The

philosophy makes a distinction between “information” and “Consciousness”; the former produces

experience in response to external inputs just like a computer’s software while “Consciousness” is

the ability to “really know” and “choose”.

As already said, what we call consciousness in modern terminology is divided into two

components: one is free will and the other is mind, the source of “intelligence” explained above.

Free will is independent of all causes; it is the ability to decide consciously and independent of any

reason from the past and without expecting anything in the future. Manifestation of free will is not

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an unconscious nondeterministic random occurrence. Free will is independent of space and time;

its existence does not depend upon any memory, and it is not bound by any rules or logic. It is said

to be nishkarana meaning that it is not the effect of any cause. (After all, it is free; it would not be

free if it depends upon anything else for anything!) Therefore its existence cannot be described nor

its occurrence be predicted by means of a formula expressed in terms of space and time using some

language such as physics, mathematics, quantum mechanics, or computer science or any other

science! (Note that every language consists of a certain set of symbols and rules to manipulate

those symbols). Existence of such free will needs to be taken as a postulate in any theory that tries

to explain subjective experience.

Free will is not merely the ability to choose one alternative from many potential

alternatives; no doubt free will can do that. When free will does so, this choice indeed cannot be

described by quantum theory or any other physics or even any other science because free will does

not yield itself to space and time descriptions. Actually, decision making programs in our

computers can also make decisions and choices. These programs do so based on the memory

contents of the computer. When the program runs and makes a decision, it does so all by itself

without requiring intervention by the computer operator (the free will)! In fact, the purpose of

creating the program is that it accomplishes the intended task without our doing it ourselves and

without our intervention! Yet, the program is not free because the operator can and is free to

intervene anytime while the program is running. To understand what free will means in Indian

philosophy let us consider an example. When I go to New York, nobody forces me to go or not to

go. I go because I want to go. We think that it is free will but not necessarily in the context of this

article! I go to New York for a reason; to see a friend already known to me, or to buy something,

or to have a good time. There is something in it for me. There is a cause for the action which

is already a content of my brain's memory. On the other hand, free will has no cause, its decisions

do not depend upon any causes or any memory contents. Well, then one may wonder whether

such a free will ever exists. I hope that the small story in the Appendix gives an example of

manifestation of free will and how free will is beyond causality.

One may say that the above approach to consciousness is similar to the first type of

approach that Chalmers criticizes (1995) as one that altogether avoids the “hard problem” by

assuming that free will is outside the domain of science. However, to insist that everything we

experience must have scientific explanation involves assuming the opposite, namely, that nothing

29

exists beyond space and time; in my opinion, the opposite assumption is just as valid or as invalid

as the original assumption that something does exist independent of space and time. In spite of

asserting that free will is independent of space and time and not bound by logic, Indian philosophy

can contribute to scientific knowledge of how experience occurs in our brains and we will try to

describe this contribution in what follows. The mind, excluding free will is called Manas. Manas

keeps accumulating more and more contents as life goes on. Manas is a sense like other senses:

sight, touch, hearing, smell and taste; it is the sense of memory and logic. Manas is said to be

sukshma meaning subtle (like “soft” in the word software) as opposed to the physical body which

is sthula (like hardware) meaning perceivable directly by physical processes of seeing, touching,

hearing, smelling and tasting or indirectly by physical means. Manas is different from the body in

that neither of the two can be transformed into the other unlike for example, matter and energy

which do transform into each other in specific situations. In this literature, Isavasyopanishad for

example (Swami 1990; p 139), mind is often described as being faster than matter (hence faster

than energy, that is, light) and that mind never comes to rest (Mukherjee 2002). Hence the

assertion that the body and the mind cannot be transformed into each other is valid according to the

theory of relativity. But it is possible for the body and the mind to interact with each other

producing more mind and changes in the body. Interestingly, after failures of experiments to

create tachyons in bubble chambers, Feinberg (1970) conjectured that tachyons probably cannot be

produced from matter but that it is possible that tachyons do interact with matter; thus his view is

consistent with the above view of mind and matter although he never associated tachyons with

mind.

If mind indeed consists of faster-than-light objects, then it is possible to describe its

properties and processes in the terminology of mathematics and physics and quantum mechanics in

particular. It may be possible subsequently, even to verify the theory using biological experiments.

Using Bohmian Mechanics, in an earlier paper (Hari 2008), it is shown that a zero energy tachyon

can do what an Eccles’s psychon would do, that is, trigger exocytosis simultaneously across a

whole dendritic tree by interacting with vesicles in multiple and “collapsing” their two-state

quantum wave functions into the state that promotes exocytosis.

Although physicists (other than a few who believe in tachyons) usually tend to avoid

tachyons in their work, it is interesting that Fred Alan Wolf (2008) recently stated some quantum

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field theoretical concepts associating tachyons to mind. In the past, there has been at least one

theoretical physicist, Late Regis Dutheil, a quantum physicist, a consciousness researcher, who

proposed a model in which mind is a field of tachyonic or superluminal matter2.

Some Rationale for Dualism:

A Representation of Information is different From Information itself

Chalmers (1995) points out that there is no convention followed by researchers as to the use

of the word “consciousness” and that “as things stand, those who talk about consciousness are

frequently talking past each other”. The same statement applies to the word “information” because

“information” is used often without a precise definition assuming that the reader should know its

meaning because it is such an easy word. There are a number of phrases floating around:

“physical information”, “classical information”, “quantum information”, all of which represent a

physical quality such as energy. In the context of the “hard problem” or “explaining

consciousness”, one has to understand “information” as Searle (1980) explains: the living brain

and mind deal with meanings. In this context, Shannon’s definition of information does not apply

because it is irrelevant to meaning or experience.

In the previous section we said that a lifeless stone does not have memory mechanisms to receive

inputs and generate responses and that this lack of ability to react is what we perceive as lack of

self-awareness. Hence one may ask: why then is a computer which does have memory

mechanisms and which produces apparently intelligent responses, not self-aware? That is because

the computer carries only a REPRESENTATION of information but not any "real information" or

“phenomenal information” (Chalmers 1995) which only exists in the programmer's head. Still,

amazingly, once a REPRESENTATION of a piece of information is entered into the computer, it

can add, subtract, or a draw a picture of it, and so on; it can do almost anything that a person can

do with that piece of information and behaves as though it knows the information without "really

knowing" it. So, there is a certain "real information" present in human beings and probably in all

living beings that is not yet found in a computer digital or quantum.

2 Dutheil, M.D. considered that the mind, though of tachyonic nature, belongs to the true fundamental universe and that our world is merely a subluminal holographic projection. He taught physics and biophysics at "Poitiers" Faculty of Medicine. He dedicated himself to research in fundamental physics from 1973 on. He was the author of "Superluminous Man" & "Superluminous Medicine". He was a joint Director in "Louis de Broglie" Physics Foundation in Paris. (Evellyn Elsaesser Valarino 1997)

31

The same meaning may be conveyed by different words in different languages. Hence the

meaning is different from any of the words which are used to convey the meaning. Meaning exists

only in the brain but not in the words nor in the paper on which the words are written. Sometimes

language is not even used to communicate information. For example, a right signal flashing from a

car is an indication to others that the car is about to make a right turn. Thus the same piece of

information can be conveyed in many ways and the means of communication always uses a

representation. The representation may be in the form of words, sounds, electrical signals, and so

on. A language is a mapping of information into words (symbols) which become sound energy

when pronounced, and particles of matter when written on a paper, and become electrical energy

when transmitted over a telephone line. Yet information exists only in the brain and is different

from the language or signals that are used for its communication just like water is different from its

container without which it cannot be taken from place to place. We are so accustomed to using

material representations to store or communicate our thoughts because we cannot help it, that we

do not even recognize the fact that information and its mapping are different.

In a digital computer or even in a quantum computer, we know that the meaning is not

generated within the computer but the programmer assigns the meaning to strings of bits and bytes

or qubits, all of which are in their turn, mapped to the states of some specific hardware units in the

computer. Thus the computer carries only a mapping of information that is within the

programmer’s brain but does not actually contain the meaning. So when we talk about information

(data and algorithms) contained in a computer, we are referring to the mapping contained in the

computer, of a certain phenomenal information which is really outside the computer. If the

computer is broken, we can still run the software on another computer provided we have saved a

copy of the software on a storage device such as a CD (compact disc). The point is that software

exists independent of any computer hardware although the software existence and features can be

recognized only when it executes on a piece of hardware by receiving some inputs and producing

some outputs.

It is not that reductionists (those who argue that consciousness is a state of matter) think

that a computer knows the meaning of its memory contents but they believe that the biological

32

matter in a living brain somehow creates the meaning although any matter outside the brain does

not. However, they have yet to prove what they believe.

Indian Philosophy is dualistic in the sense that it asserts that just like in the computer, the

living brain’s software, namely, the mind is also “real information” and it is not a form of matter or

a material energy field; it consists of tachyonic matter, and cannot be created from ordinary matter

all by itself. (However, mind interacting with matter can produce more mind; see the next

section.) According to this philosophy, the physical body and mind of a living being are two

different components in the sense that one cannot be transformed into the other unlike matter and

energy which do transform into the other in some situations. However, body and mind do interact.

Life is the process of interaction between the body and the mind (in the computer analogy, this

interaction is similar to execution of software). Life begins when mind starts interacting with the

body and lasts as long as the interaction continues. At death, the body is no longer able to support

the interaction (just like a computer with defective hardware does not support software execution).

The reincarnation principle of eastern religions, Hinduism and Buddhism for example, states that a

living being’s mind does not cease to exist when the being dies but survives and that the surviving

mind can start interaction with another body if a suitable body is found; in other words, take a new

life. This can now be seen as nothing more than an inference from the computer analogy: a

computer with broken hardware cannot run a piece of software which if saved on a CD, can be

entered into another computer and made to run again! Needless to say that it is only an analogy

and the principle itself is not yet proved by modern science.

Indian Philosophy is known mostly as monism because it explains elaborately that

Consciousness alone appears as the various forms in the universe, mind, matter, and all. The well

known example given is that Consciousness is like gold and all objects in the universe are like

jewels made out of gold. Since the philosophy also claims that this fact can be realized by only

spiritual means beyond the mind and beyond all external means, the monistic part doe not conflict

the dualistic part described above.

Desires, Purposes, Goals, Causality, and Free Will

A chess playing program may play chess very intelligently but it does not care a bit about

winning or losing like one of those enlightened sages! The program is neither happy when it wins

33

nor sad when it loses because to begin with, it does not ever have a desire to win the game! An

emotion occurs as a response to fulfillment or non-fulfillment of some desire or the anticipation of

fulfillment or non-fulfillment of something that we want or need; obviously, lifeless objects do not

have desires or needs. In our daily life, actions of human beings are often initiated by desires,

purposes, needs, and goals, which are closely associated with future states of the living being.

(Activities of other living beings have purposes too.) The search for an appropriate course of

action and the action itself depend upon some information about a future state; for example, if I

want to go to New York I will take a bus to New York but not to Philadelphia. Therefore, the

change from my present state depends upon information regarding a future state3. This state of

affairs seemingly violates the causality principle of classical physics that a cause should always

precede its effect. It seems to also violate the relativistic causality principle which limits causes to

the past light cone of the effect, and which is based on the principle that causal influences cannot

travel faster than the speed of light. Hence, if actions of living beings take place because of

information about some future states as said above, then an interesting and yet-to-be-answered

question is “Are such actions consistent with the principle of causality of either classical or

relativistic physics, and if not, how does one justify them?” One can argue that this is a non-

existent question and there is no causality violation because the goal state information is already

present in the brain. Note that the goal state in my present IMAGINATION is not the same as the

future physical state of my body because I am not in New York yet. The imagined goal is a

mapping of the future physical state (different from the present physical state, else no action

happens), into my present memory. So, the present memory does depend on a not yet realized

physical state. One may formulate the question alternatively: how does the brain create in its

present memory, a mapping of a future physical state of the body of which the brain is also a part?

It is true that the computer’s memory also has the goal state’s (the win state’s) information which

is made use of by the chess playing program but the required mapping is already entered into the

computer’s memory by the programmer; the computer cannot create it by itself. On the other

hand, the brain creates the goal by itself.

3 See Stapp (2008) for example, “Intentions are formulated in terms of a projected (into the future) body-world

schema: they are expressed in terms of an image of how the body in its environment is intended to be at a slightly future time. (Thus, for example, the tennis player imagines how he will strike the ball, or where the ball he is about to hit will land in his opponent’s court)."

34

Of course, free will may play the most important part in initiating an action by choosing the

purpose of the action. For example, free will may choose either to go or not to go on vacation; free

will may also decide whether to go to New York or London. Once the choice is made, say

London, it becomes the desire to go to London (and a content of the brain’s memory). The

appropriate action starts with buying a flight ticket to London and depends upon the information of

the future state of being in London. Indian philosophy makes a distinction between desires or

purposes and free will as follows: Note that we said above that free will “may choose” the desire

or purpose and not “chooses” the desire or purpose because the desire or purpose of a given action

may itself be the result of other desire/s or purpose/s and not necessarily the choice of free will.

For example, suppose one chooses to go on vacation (call the desire W) because he/she wants to

have fun by being away from home. Then W is the effect of the cause consisting of two desires:

W1 = wanting to have fun and W2 = wanting to be away from home together. Since both desires

W1 and W2 are already in the memory, W is a result of a past state of the brain but not a direct

creation of free will. One can now see that given any action, it is difficult to judge whether the

action is initiated by free will or some desires or purposes already existing in the memory. The

distinction between desires or purposes and free will is that the former are contents of a certain

memory (the mind) whereas the latter is not. Indian philosophy views desire as essential to the

creation and maintenance of life in this world (Swami 1990: p 139); like any other content of the

mind it is different from both lifeless matter and free will.

Ever since the birth of quantum mechanics (QM) physicists believed observer’s

consciousness to play a role in some quantum events (the collapse of the wave-function). Some

physicists even hope that QM will be able to explain how free will occurs in the brain because QM

is non-deterministic in the sense that it predicts probabilities of results of measurements but not the

precise results. Beck and Eccles (1992) used QM to suggest that consciousness could be

nonmaterial but nevertheless it can control matter. They proposed an explicit role for

consciousness in one of the brain’s biological processes, the exocytosis, a basic unitary activity of

the cerebral cortex. The scientific community’s interest in using quantum theories to explain how

the brain works is increasing. In the quantum physics literature, there is extensive debate about the

compatibility of quantum non-locality with the causality aspect of relativity physics. For now,

most physicists seem to agree that quantum physics is consistent with what some of them call the

weak causality principle (Cramer, 1980). This principle states that a controllable message cannot

35

be sent backwards in time in any reference frame. It is possible that an explanation of the

apparently peculiar causality of desires and purposes may be found using quantum physics since

there have been instances of apparent causality violations and their explanations in this literature.

Actually, Wolf (1998) believes that occurrence of an experience (not necessarily related to

purposes and desires), implies violation of causality by the brain. While proposing a quantum

physical resolution of (Libet et al.1979) delay-and-antedating paradox, Wolf explains how “Pairs

of causality-violating events must occur in the brain in order that a single experience in

consciousness occurs”.

It is our daily experience that prior to taking an action, one first thinks about what one wants

(called volition, passion, desire, etc.) and then how to get it (reasoning). In this context, the paper

“Causality and Tachyons in Relativity” written by Caldirola and Recami (1980) is particularly

interesting. In the section with title ‘Can a Tachyonic Observer Inform Us about Our Future?’ of

this paper, the authors conclude that a tachyonic observer can convey to an ordinary observer the

effects on a future event E of the anti-signals (negative-energy signals) sent by himself to E so as

to physically influence E. Hence the tachyonic observer seems to be our mind doing the job of the

how-to-get-it reasoning mentioned above.

The Physical Brain Creates Mind Not All By Itself but With the Help of

an Already Existing Mind

In the case of a lifeless computer, we know that programs can learn; they can even discover

new formulas and theories from the data input to them. When a computer program learns, actually

it creates in its memory new contents as patterns of states of its memory cells. The new

information that the program is said to have discovered is obtained only by the programmer’s

assigning meaning to the computer’s output consisting of numbers and letters (a certain language)

corresponding to the newly created memory contents. The meaning to any language once again, is

in the heads of programmers but not in the symbols of the language itself. So, the computer does

not know the meaning of the new formulae it has created but the meaning is known only to the

programmer or user. Another point to note here is that to create even such new patterns of memory

cells though not new information itself, a certain piece of software is required to be present and

complete execution in the computer; a machine which has no software or which cannot execute

36

software cannot learn; today’s engineers and computer scientists would say that such a machine

cannot exhibit “intelligence”.

As to the living brain, it starts learning from the moment it is born. Even if it does not learn

new techniques of how to respond to situations, it constantly interacts with the environment and

stores the experience and thereby creates new memory. Brain scientists do recognize formation of

neuron patterns indicating creation of new memories. To be able to create new patterns of physical

memory, similarly to the computer, the brain should already have some mind (brain’s software)

prior to interacting with its environment and it does according to today’s brain science. Hence

both reductionists and dualists would accept that the living brain (physical brain with mind) creates

more mind upon interaction with the environment. Yet unlike the computer, nobody from outside

assigns or can assign meaning to newly created neuron patterns but the living brain does it by

itself. Reductionists claim that the meaning is a property of biological matter unlike the electronic

circuits in the computer but they have yet to prove their claim scientifically. On the other hand,

dualists think that mind is not a property of biological matter but have not yet attempted any

scientific explanation of how such mind is created.

By claiming that mind is made up of tachyonic matter, Indian Philosophy suggests a possible

approach to a scientific explanation of why meaning, experience, and “real information” exist in a

living brain but not in the computer or any physical means of storage or communication and how

mind interacting with brain’s matter can create more mind.

Summary

Ancient Indian Philosophy makes a distinction between free will and all other aspects of

consciousness which involve memory; we referred to the latter as mind in this paper. In this

literature, it is often stated that mind is faster than all senses (including sight) hence faster than

light and that it never comes to rest. It is often stated that mind is a memory where all

experiences, emotions, desires, etc. are stored. Mind is subtle unlike the physical body. When

interpreted in the terminology of modern physics, the implication is that at least part of what we

call mind is made of tachyonic matter. The proposal that the memory aspect of the mind is made

up of tachyons provides a mathematical means to explain how brain creates mind and how mind

acts upon the brain. It may be possible to verify this proposal experimentally as suggested by Hari

(2008). To explain the views of Indian Philosophy on matter, mind and Consciousness, we

37

compared the brain and its mind to the hardware and software of a computer, Consciousness being

the computer operator as it were, and completely outside the computer and in control of it.

Appendix

What is Free Will?

Once upon a time, there was a very religious person who spoke nothing but truth all his

life. Let us call him Truth Speaker. One day, he was sitting in a grove and doing meditation with

closed eyes. Suddenly, he heard the sound of running foot steps. On opening his eyes, he saw a

scared man running for his life. The man stopped when he saw Truth Speaker, and said with a

gasping breath “I am being chased by robbers. I am running for my life. I cannot run any more. I

will behind the bushes over here. Please do not reveal my where-about to anybody”. So saying,

the man ran and hid behind the bushes without even waiting for Truth Speaker to reply. Truth

speaker went back to meditation. A few minutes later, he again heard thundering foot steps and

opened his eyes. He saw some armed men running. When they saw Truth Speaker, they too

stopped and said “We are looking for a man whom we saw come this way. Did you see anybody

running past you a short while ago? If so, do you know which way he went?” Truth Speaker

thought that he should never tell a lie. So, he pointed to the robbers the bush where the scared man

was hiding. The robbers then caught the man and killed him. After some days, Truth Speaker died

but was taken to hell instead of to heaven. There, Truth Speaker asked the ruler of hell (a

personification of justice according to Hindu Religion) why he was brought to hell instead of to

heaven where he should have been on account of speaking nothing but truth all his life. The ruler

of hell replied “You spoke truth alright but by telling a lie you could have saved the life of the man

being chased by robbers. You did not have a tiny bit of compassion. You were carried away by

your arrogance of sticking to your principle and your selfishness to go to heaven. That is why you

deserve hell.” The point in the story is not at all whether Truth Speaker went to heaven or hell

after death nor whether there is a heaven or hell. The point is a person’s ability to see when to

speak truth and when not. Truth Speaker was following a rule which firmly stuck inside his head

and his mode of thinking was that of a machine which was programmed to tell truth and therefore

never lie. On the other hand, imagine that in the story, Truth Speaker told the robbers that he did

not see anybody around earlier that day and they were only the people that he saw until then. In

this case, his mind did not execute like a machine, a memorized instruction expected to be carried

out. Nor did it care for a future benefit, namely going to heaven. Thus the action of lying was

38

directed neither by the past nor by a future goal. One may argue that to save the life of the stranger

is the reason for lying in the alternative version of the story. True; however, this reason is created

by his free will instantaneously on the spot because until that moment, “speak truth” was the rule

stored in his memory with no conditions under which it can be violated. This ability to violate a

rule of the past but not because of already established goals, and act on one’s own is a self-starter

or spontaneous and is the true free will. This ability refuses to be told what to do and refuses to be

told by somebody or something else; it is above and beyond all causality.

References

Beck Friedrich and Eccles John C. Quantum aspects of brain activity and the role of consciousness. Proc. Natl. Acad. Sci. USA, 1992; 89: 11357-11361.

Caldirola P and Recami E. Causality and Tachyons in Relativity. Italian Studies in the Philosophy of Science. D.Reidel Publishing Company 1980; 249-298

Cramer J G. Generalized absorber theory and the Einstein-Podolsky-Rosen paradox. Physical Review D 1980; 22: 362-376. Chalmers David J. Facing Up to the Problem of Consciousness. Journal of Consciousness Studies 1995; 2(3): 200-19.

Feinberg G. : Particles that go Faster than Light. Scientific American February 1970; 69-77

Hari S. Eccles’s Psychons could be zero-energy tachyons. Neuro Quantology June 2008; 6 (2):152-160.

Libet B. Wright, E.W., Feinstein, B., and Pearl, D. K. Subjective referral of the timing for a conscious sensory experience. Brain 1979; 102-193.

Mukherjee B D. The Essence of Bhagavad Gita, Chapter 6, verse 34. Academic Publishers, Kolkata (2002); 167-169.

Searle John R. : Minds, brains, and programs. Behavioral and Brain Sciences, 1980; 3: 417-457.

Swami Rama. Wisdom of the ancient sages: Mundaka Upanishad. Himalayan International Institute of Yoga, Science, and philosophy of U.S.A 1990; 99, 139.

Stapp Henry P. The Hard Problem: A Quantum Approach. arXiv:quant-ph/9505023v2 (2008).

Upanishads Sri Sankara's Commentary Isa, Kena, and Mundaka. Translated by Sastry SitaRama S. Natebran & Co. Printers and Publishers Esplande 1898; 9.

Valarino Evelyn Elsaesser. The superluminal hypothesis in The Other Side of Life. Plenum Press New York, 1997; 193-228.

Wolf FA. The Timing of Conscious Experience. Journal of Scientific Exploration 1998; 12(4): 511-542.

Wolf FA. Is the Mind of God Found in Quantum Field Theory? Available from: http://www.fredalanwolf.com/myarticles/Quantum%20Field%20Theory.pdf June 2nd 2008; 1-19.

39

MY TEACHER - Prof. S. MEENAKSHI SUNDARAM

GOLLAPUDI MARUTHI RAO

Vishakapatnam

I was a bad student and the best actor of Andhra University during the academic years of

1956-59. I was a student of Mathematical physics faculty under the aegis of Prof.

S.Meenakshisundaram. It all happened in a peculiar way and for all the wrong reasons.When I was

checking my results of Intermediate class, I found my name missing, not surprisingly. But to my

shock, a friend of mine told me that I got first class! All due to the efforts of my uncle, who made

me interested in mathematics, ever since my IV form.

I had then decided that I belong to the Mathematics faculty and enrolled myself in to B.A.

(Mathematics) at the A.V.N.College. But I wasn’t comfortable there. Why? My instincts told me

that I don’t belong here. But where should I go? The popularity of Andhra University Open Air

Theatre and its activities under the guidance of Sri K.V.Gopalaswamy, who was the then registrar,

was my motivating force for the Activity. It was my attraction.

So, after three months of my stay at the college, I persuaded my father- who was a clerk

with bare minimum resources, to put me into some department in Andhra University. I was the

apple of his eye and he was only a matric failed student in his days .Therefore it must have tickled

his ego that his son could be a postgraduate from a University. He took me to the University. The

various faculties were full by then and I did not have many choices to make.

One afternoon, we went to Prof.Meenakshisundaram’s house. There was another professor

sitting with him over a cup of tea. He was Prof K.R.Srinivasa Iyengar, Head of the department of

English. They received us very kindly- and both of them offered seats in their respective faculties,

because I had secured good marks in Mathematics and English. I was a writer by then, doing some

amateurish scribbling, with little or no popularity. A fool I was to entertain the notion that a Telugu

writer had no place in an English faculty as it was foreign to my pursuit. (As the irony goes, I was

only studying English literature during the next three years- Priestly, Gal worthy, O’Neill,

Maugham, O.Henry- you name it- the second largest vocation otherthan theatre that was

40

responsible for my bad degree!) I was totally misguided by my misplacedapprehensions and my

poor father was in no position to guide me. Hence I opted for theMathematical Physics course.

It was a great subject and also the early days for the faculty. We were only 9 students- an

indication of the remoteness of the subject then- but an ever-developing area in the field of

education. I was inevitably the bad student in my class and right from the beginning everything

went wrong for me. I always ended up in the library, in the literature section of English and

Telugu- (in that order!) and all my teachers were unanimous about one truth- that I didn’t belong to

the faculty! Mr.Sambasivarao, stood out as a single teacher, who never minced words in driving

home this fact.

I was active during 1956-59 in the theatre activity- a favourite of Sri K.V.Gopalaswamy

presenting any number of plays. The theatre festival that year was held at the open place before

Coffee House as the Earskine Squire theatre was getting renovated. The play “Snanalagadi’’

(Bathroom) was directed by Gopalaswamygaru himself. I never looked back. I was selected for the

5thInter-university youth festival, and my Radio play “Anantham’’ was adjudged the Best Script in

the Inter-University Competition held by All India Radio. I received the award from Dr.B. V.

Keskar, Minister for Information and Broadcasting, while the Director General of All India Radio,

Mr J. C. Mathur presented me to the former at Akashvani Bhawan in New Delhi. I was a volunteer

at the Shakespearean Group festival of Jeffry Kendal who performed Shaw’s Pygmalion, Candida,

Arms and the Man, Shakespeare’s Henry V and Macbeth.There was a redeeming feature to all this

activity of mine.

Our Prof. Meenakshisundaram was a kind man with a malleable face and a deep,

understanding smile. He was a chain smoker and I never saw him without a fag inbetween his

fingers, except when he was in a class. I don’t remember many classes or the subjects he taught us.

He was always there in the front row of the audience whenever I performed and always enjoyed

my acting, as I could see a patronising smile on his face. Sri K.V.Gopalaswamy and

Prof.Meenakshisundaram stayed in the oppositesheds behind Sashtipoorthi Mahal and I am sure

they must have exchanged notes on me at sometime or the other. I was a star in the campus in

those days. I don’t remember- Prof.Meenakshisundaram chastising me even once. He was like an

understanding father of a prodigal.

41

As the time went on- my popularity grew in theatre and I was much more confident about

my inability to pursue my studies. I vividly remember a Zero in my mark sheets of my second year

examinations! And something fantastic happened in the final year. Prof.Meenakshisundaram called

me one day and asked me to move in to his house! And I did! I don’t remember whether I was

taking my meals there-I am sure I didn’t- but that was an honour normally extended to the brilliant

students of the faculty.This made me more guilty and equally helpless.

I knew, then, that I was going down the drain and there was no way I could get through the

examinations. Even today, I get this nightmare in my dreams sometimes and I get up with a shock

only to realise that I had outlived it long back. For three months-before I shifted to Prof,’s house, I

was in a trance- learning by rote- all that had to be taken- in a mechanical way. I remember

Schrodinger’s Wave Equation (?) which ran into some 25 pages. I used to write it, with all its

intricate details- all by heart!

During my stay at Prof.’s house, there was a Drama Competition at Vizianagaram(Bellary

Raghava Memorial Parishad) for which we were supposed to give a Pre-view. It had to be done

during my examination day of B.Sc.(Hons) final exams! I came out of Prof.’s house to the out

gate, got into a taxi, had my make up in the car and performed the play and came back to study for

the Mechanics-Paper I. This was unpardonable and scandalous. But can you drill any sense into the

mind of Bilvamangala, who scaled the walls of his paramour Chintamani on a rainy night holding

a snake, mistaking it for a rope?

I was literally living that role, the only difference being my paramour in those days was

“theatre’’.Only 8 marks were needed for my degree, after all this rigmarole. Who helped me?

K.V.Gopalaswamy, Prof.Meenakshisundaram or V.S.Krishna, the then Vice Chancellor.They were

added to my hard earned marks and I was given the degree of B.Sc.(Hons).Only two persons were

proud of this degree in my life. 1. My father, who had pinned many hopes on me and spent his

savings for my qualification. 2. My first film producer Dukkipati MadhusudanaRaogaru, who was

proud of presenting a post graduate as his writer, for my first film “Dr.Chakravarthi’’.

42

I met Prof. Meenakshisundaram at Guntur, during a function of anaffiliated university

course. I was working as the Transmission Executive in All India Radio, Vijayawada then. He

enquired about me very kindly. And I never met him afterwards. I remember

Prof.Meenakshisundaram as a profound scholar, a kind and understanding parent to his students

and more importantly a warm human being who couldaccommodate mediocrities not as a vice but

as a misplaced priority of an unfortunate student like me. It required a lot of objectivity to see

through my misgivings in those days, and one could ventilate one’s choices hoping for the best in

his chosen field.

I am a celebrity today, by my own right. I have 3 Doctoral degrees and 3 MPhil degrees on

my writings. I am a Sahitya Academy award winner twice- for my play “Kallu” and my Novel

“Sayankalamaindi’’ and this list is endless. But when I look back to those dark days, I was isolated

and alone in my combat in an area where my heart was not there.

And so, imagine my Professor standing by me, though not telling me in so many words.

They were great teachers with a sense of objectivity and commitment and this country is poorer by

the lack of such beacon lights. I am proud to be a student of Prof.Meenakshisundaram, though I am

not sure whether he would have said this of me. But as Adi Sankara said to Devi, there can be

anerring son but there can never be a parent who cannot pardon his offspring.

43

MY ACQUAINTANCE WITH REVERED TEACHER,

Prof. S. MINAKSHI SUNDARAM

Prof. T.K.V. IYENGAR

Department of Mathematics

National Institute of Technology

Warangal 506004 India

It was in the first week of August 1962 that I think, I entered the Department of Mathematics,

Andhra University, Waltair, now Visakhapatnam to pursue my Post Graduation in Mathematics. I

hail from a village and had some contact with atmosphere of a small town Eluru in W,G, Dt

where I completed my B.Sc. Degree by 15th year. I did have neither the knowledge of a great

University nor a great Department. It is needless to say that I knew nothing about the teachers.

My opinion (as is that of many students of those days) was that teachers were Gods, the place we

were studying was a temple and we are there only to hear the lessons and study and pass out of the

course possibly with honors.

Prof. S. Minakshi Sundaram was the Head of the Department then. By that time only few months

passed when he took over the Headship of the Department. There were several Teachers in the

Department whom we came to know gradually For people like me who entered the M.A. course

after getting a B.Sc Degree from an affiliated College of the University, studying Mathematics in

the University was not easy. There were some Students in B.A. Honors Course who were trained

for two years there itself and along with them we had to attend some common classes. The

honors students were more rigorous (!) in their approach and we did not have any great idea about

the so called rigor. Once one of our teachers asked, “ What is integral x dx?”. Many of us wrote

the answer ..x square /2. One of the honors students wrote , after 5 minutes of thinking, “the

integral exists”. Except few, many of the teachers liked the later type of answers rather than x

square by 2.

It actually took about three months for me to adjust to the new environment and to the teaching

procedures. Dr. N. V. Subrahmanyam, Dr. J. Gopala Krishna , Dr. U.V. Satyanarayana Sri A.

Siva Shankara Sasthry, Sri P.V. Krishnayya, Sri Rama kotaiah

44

Sri A.Radhakrishna , Sri K. Pattabhi Rama Sasthry and Sri I.H. Naga Raja Rao were our Teachers.

How great these people are , one can understand , if one has studied under these great gurus. Prof.

S.Minakshi Sundaram headed the Department consisting of the above stalwarts.

How great my teachers were , I understood only during the subsequent part of my life. I did not

even know the greatness of Prof. S. Minakshi Sundaram at that time. Just as I was having a

distance from my many other teachers, I was considerably away from Prof. SMS as well. Reasons

are many. He was our Head. He was Professor. I heard that he worked at Princeton where

Einstein worked. More than any thing, he was teaching Real Analysis in our First Year and “Real

Analysis is not a joke! It needs lot of RIGOR!” said one of my honors friend. Prof. SMS taught

Real Analysis for about three months. He taught us Fourier series, Riemann Integration and if

memory has not failed me, Improper integrals. Later Sri A. Radha Krishna was teaching us

convergence, uniform convergence and other more serious (!) things. ( Later he shifted to

Kolhapur and there from he came to Warangal to work at Kakatiya University and during our stay

at Warangal , he always showed his affection to me). Prof. SMS luxuriously used graphs and

figures and this aspect was nearer to the heart of people of my type who came from a less rigorous

background. Those were days when “Drawing a Figure is a mere luxury and not a necessity” as

was said by C.V. Durell in his Projective Geometry.

In our Second Year, Prof. SMS took the subject Measure Theory for us. This attracted the

attention of few staff members also. Sri K.L.N. Swamy, Sri K.P.R. Sastry and Sri. I. H. Naga Raja

Rao were also attending the lectures. Here again , Prof. SMS quickly completed the essentials of

the course and asked us the students to give seminars article wise from the prescribed text and Sri

K.P.R and I.H.N were asked to supervise the seminars. The first twelve articles from Functional

Analysis by Riesz and Nagy were covered by Sri K.P. R. Sastry.

By the middle of second year, we were in a position to wish him when he was in the corridors of

the Department. By the end of second year, I could pick up the necessary courage to enact the

opening scene from the famous play Kanyasulkam before him during the valedictory function of

the Mathematics Association.

Soon after my results were announced in the first week of August 1964, I was appointed as lecturer

in Mathematics at the Narsapur College, Narsapur in the same month. I had an opportunity to

45

attend the Summer School organized by Prof. SMS at the University during the summer of 1965. I

saw him then. The subsequent information about our revered Professor was only through my

friends in the field of Mathematics.

My classmate and friend Dr. G.V.N. Kameswara Rao had the privilege of working with Prof. SMS

and get his Ph.D under his supervision. He is said to be the last Ph.D. student of Prof. SMS. When

a meet of the admirers and former students of Prof. SMS was arranged by Smt Girija Sharma,

Daughter of Prof. SMS, somehow I was also spotted and invited to be in the meet. I attended the

meeting where the members decided to form the Prof. S. Minakshi Sundaram Memorial Society.

We recollected the old scenes and incidents of the Departments of Mathematical Physics / Applied

Mathematics and Mathematics and all of us went to our late teens and early twenties.

In view of the work I have been doing all along, I never tried to know the greatness of Prof. S.

Minakshi Sundaram. The Indian Journal for the Advancement of Mathematics Educationand

Research 2004, published by Andhra Pradesh Association for Mathematics Teachere (APAMT)

was dedicated to the fond memory of Prof. SMS. This issue contains excellent articles about the

life and personality of Prof. SMS, and about the impact of his research work

In this issue, Prof. M. S. Raghunathan, in his article “Artless Innocents Ivory Tower Sophisticates:

Some personalities on the Indian Mathematical Scne”states that Prof SMS was “arguably the most

gifted Indian Mathematician of his generation. His work on the eigen values of the Laplacian on

compact Riemannian manifolds was of the highest quality and has had a lasting impact”

Prof. Dani , in Hydeabad Intelligencer released during ICM 2010 at Hyderabad, has some

extremely nice words to say about Prof. SMS and the impact of his work on a new approach to the

celebrated index theorems for elliptic operators. One of his papers with Prof. Piejel , Prof. Dani

says “ continues to be cited regularly in contemporary literature –

Truly a feat for a paper over sixty years old.”.

Prof. M. Vanninathan, in his article on Partial Differential Equations, in Mathematics News Letter

: commemorating ICM 2010 in India, writes: “One of the most significant Indian contributions to

the theory of elliptic partial differential equations is the work of S. Minakshisundaram. His work

resulted in the genesis of a fertile research area, known today as geometric spectral

46

asymptotics….There was a flood of developments in this area in 1970’s. Together with A. Pleizel,

he introduced a function known as the Minakshisundaram – Pleijel Zeta function analogous to the

famous Riemann Zeta function.”

It is unfortunate that revered Prof. SMS did not live to see the explosive developments in the

spectral asymptotics in the early 1970’s.

References:

[1] Indian Journal for the Advancement of Mathematics Education and Research (2004)

Published by APAMT

[2} Hyderabad Intelligencer ; ICM 2010 , Springer (2010)

[3] Mathematics News Letter ; Special Issue Commemorating ICM 2010 in India

(Ramanujan Mathematical Society)

47

Prof. S.MINAKSHI SUNDARAM

A DAUGHTER’S TRIBUTE

K. GIRIJA

My father was born in Trichur, Kerala in 1913. He was the blessing and boon after several

years of penance by my grandparents. They had visited several holy places, temples and had taken

a vow in Guruvayur Temple of Krishna. My grandmother though married by the age of eight years

as a child she conceived at the age of 24. In those days it was considered very late and probably

she had to suffer the ill social talk also. Naturally the birth of the boy child brought great joy.

Being Saivites the child was named Minakshi Sundaram. He was called Jeja by the fond parents.

Jeja meaning God. The vow at Guruvayur was fulfilled. The infant was taken to Guruvayur place

on the large weighing scales. Equal weight of butter was offered to the deity of the temple.

Girl children are most loved and petted in the family. Till the age of eight he had long hair.

My grandmother would comb and braid his hair. In the traditional way the religious ritual of

upanayanam was performed at the age of 9. With the thread ceremony the long hair braid becomea

Namboodiri Kudumi. Living in the Kerala for several generations Malayalam was the language

spoken; yet Telugu was spoken at home in the adulterated fashion of Malayalam, Tamil and

Telugu.The life style, food habitsand religious rituals had the Malayalam and Tamil influences in

the family. My father had no sisters.

My father and his two younger brothers were educated in the Ramakrishna Matt

School,Mambalam,Chennai. Education in that school was free and in the next street from their

aunt’s home. After school my uncles did not opt for higher education due to monetary difficulties.

Both looked for small jobs. My father with his brilliance was able to get monetary assistance and

scholarships for further education. Naturally though the amount was paltry he lived and pursued in

higher education within the means happily. He cared for his father who was too ill to move. He

would help his mother in the household chores. If his mother was ill or followed traditional ways

he wouls cook and wash clothes of his parents.

Their life style was economically backward, traditional south Indian-Dakshinadi-Brahmin

Community. Since my father was born in Trichur and spent his childhood in Kerala, they spoke

Malayalam at home. Shifting to Chennapatnam – Madras – Chennai because of his father’s job in

48

the British Raj Tamil became the mother tongue of the family, so to say. But the original ancestors

of the family hail from Andhra and shifted to the deep south. Telugu is basically the mother tongue

and ‘arva-telugu’ was and is dominant in the family. Infact till recent times ancestral landed

property was in Peddapuram near Samalkot. Verdant , fertile, flourishing, prosperous fields which

the middle men looked after. Independent India and Land Ceiling Act helped them to grab the

lands. The family was not aware, even though my father and one uncle migrated back to Andhra. I

was born in Guntur and grew up in Vishakapatnam. During my childhood I heard my grandmother

and father converse at times is Malayalam. The teaching faculty of Andhra University had many

Tamilians in those days. So the contact and touch with Tamil persisted.

I recollect my parental grandmother first time narrating to me of an incident when I was

about nine years of age. In typical, traditional South Indian family ways my grandmother would

tell the tales of Ramayana and Mahabharath and Puranas. On one occasion I asked my

grandmother if the stories of all these gods were true. She smiled and narrated about my father. As

a child after his upanayanam religiously he would perform the Gayatri Japa-SandhyaVandanam

with his grandfather, morning and evening. It so happened one morning to the fields. Little Jeja

was told by his mother and grandmother to perform his Japa. The house was a traditional Kerala

house. A central open square court with a trellised roof with verandahs on all four sides with

rooms. On one side was the kichen, pantry and dining area. The large, lengthy verandah or savidi

was also main area of the activity of the family, what the Americans say-family room. Here on the

wall were two huge family room life size pictures of Lord Shiva and his consort Goddess Parvathi.

Little Jeja, as was the habit, sat down before these pictures and started his Gayatri japa. Within a

few minutes little jeja fled into the kitchen and behind his grandmother frightened. When

questioned what happened the little boy said:” The one in the picture was standing in front of me”.

His grandmother laughed, pacifiedhim and said nothing to worry and that he should go back to his

japa. After a while he went back to continue his japa. Hardly ten minutes had passed when he ran

into the kitchen again. This time he held his mother tight petrified. Again he repeated the God in

the photo frame came out and stood close in front of him. He was frightening with his matted hair

‘et al’. This time both mother and grandmother were speechless. They looked at the pictures and

the wide savidi but there was no one. They thought the child was frightened of the pictures or some

evil spell was on him. They performed a tiny ritual to remove the effect of some evil eye. Yet he

refused to go back to the japa.

49

As a child I believed the story. I would ask my grandmother to repeat the incident several

times. She would religiously re-tell without any alterations. I was amazed and in awe as I believed.

Today I know such spiritual experiences are true. The fortunate have such visions. Ever since I

have been blessed by Bhagwan Sri Bala Sai Baba’s grace my childish belief has been confirmed

.Since seven years I have been with Bhagwan and my experiences are unique.

My paternal grandmother was, in the modern sense, a woman of substance. Her

monumental patience, her ascetic forbearance, her unconditional love for any member of the

family was amazing. She served all with simplicity and humility. She loved and cared for all. She

bore three sons. All three were gems who loved and served their parents. She loved and cared for

her three daughters-in-law as her own daughters. All her three sons practised the art of family life

and respected and promoted the wife’s individuality. My mother was on the contrary out spoken

and has immense driving force. She studied till class 7. She is very fluent and proficient in Tamil

language. She was trained in Carnatic music to sing and play the violin. She promoted the same in

the daughters emphatically.

My father had two brothers and no sisters. My older sister’s birth was a great joy for the

family. My father was awarded D.Sc. after her birth. He was also appointed as Tutor in Madras

Loyola College. The two auspicious occasions were celebrated with great joy. I was born in 1945

and my father was invited to Princeton in 1946. So unlike in Indian families a girl child’s birth and

the girl children in the family are really loved and cared for. My father wanted that his first born

girl should be educated. Infact he encouraged my mother to study privately. Later he even arranged

for English learning through correspondence course. But my mother a true south Indian lady

preferred to bask in the glory of the husband. She was busy collecting silk clothes and jewels for

herself and the two daughters.Ambitiously she also acquired property for the family, a huge house.

She managed the home front show.

My father believed in freedom and equal right to women. He literally implemented in new

India the respect and promotion for a free, modern lady with equal infact more rights and

responsibility. My mother of course never could grasp the significance of my father’s foresight and

magnamity. The need to promote her individuality in the correct direction was his sincere aim. My

father was way ahead of his times. His outlook and attitude was a peculiar mixture of a yogi and

50

ultramodern concepts of the art of living. As always we never realised this value till late in life

when he was no more. My father would hand over his salary packet to my mother very obediently.

He never questioned her and left everything in her hands. I know not to this day of any man who

has such broad views and trust in a wife.

My father was a totality, an embodiment of true values. He implemented all he believed.

He was a man of few words and acted only at the required time and righteously. His presence at

home was felt and even today his presence permeates the house. We never heard or saw my father

except with his research work absorbing his very existence all the time.

Two instances stand out in my memory of my father’s response. Once my mother was

boasting to some housewives who visited her that we were Brahmins. My father who happened to

be at home passed by and overheard the conversation. Later that evening at the dining table he

politely, gently and in few words told my mother he wanted us all to forget that we were

“Brahmins and of high caste”. Again on another occasion my mother was scolding my brother as

he wanted money to buy cricket equipment. My father who was engrossed in his research work

suddenly heard mother’s sharp voice. She told my brother she had no money and sent him packing.

When my mother came into the room, he called her. He wanted to know how much money she

wanted. He wrote out a cheque and sent the office peon to the bank. He told my mother in a

simple, straight manner, “I don’t ever want to hear in my house that there is no money”.

My father had seen difficult times in his early life and had to struggle against poverty. My

paternal grandmother was forced to retire from the British Raj Government Job due to ill health

very early in his career. They lived in Mambalam, Chennai, in my father’s maternal aunt’s house,

free of rent. The very young genius Minakshi Sundaram would walk eleven miles to Pachappa’s

College in Saidapet everyday he would give tuition to students very early in the morning and late

in the evening before and after college hours. He would never ask for fees from the tuition boys.

My grandmother would goad him. He patiently explained that they will pay him when they have or

whenever they wanted. Most of them failed to pay as my father never asked. His two younger

brothers were schooling. Many a day would pass with nothing to eat. Infact I can recall my

grandmother telling that more often they would drink only watery buttermilk and a little rice mixed

51

with salt stored in a mud pot for two or three days. None of this diverted my father’s pursuit of

studies in mathematics. Very often the chula would be lit once in two or three days for cooking.

I remember my father once narrated that his first exam in class-I he failed. He obtained

zero in mathematics. Following academic year innocent child that he was; he went and sat in class-

II room. The teacher drove him away saying he failed and should go back to class-I. The shock and

realization such that from then on he was always the topper. His special attention and effort in

mathematics was outstanding and astounding. In the British Raj, the madras presidency of

educational standards was high. Especially the English of those days was really tough. My father

struggled in the intermediate level for English. He overcame and of course his English was

excellent and meticulous.

My father was religious not in the Hindu ritual religion but in his undaunted belief in

goodness, truth and humanity. To him all were good and treated everybody with great respect and

affection. He never harmed anyone not even in thought form. He had no time for pettiness of

human nature or life. Life was full of mathematics wonders for him. Like a child he was

enamoured of his world of mathematics and research.

My father had one weakness. Anyone approached him for monetary help for education he

gave generously without questioning or a thought. My father would observe everybody with calm

and soul searching eyes. My early memories of our home are very vivid. Our home had three large

rooms. At one end the western toilets, shower rooms and bath tubs spacious and clean. At the other

end the traditional Indian “outdoors” toilet and the night soil would be cleared by the scavenger

daily. The central and the 3rd room as we called were always occupied by four to six students. My

father accommodated students free of rent and even provided three meals a day. All those who

stayed at our house had won distinctions in education and distinguished careers too. Today many

are still in high posts or retired from international institutes or universities. Many of them I

happened to contact after 40 years. The nostalgia, sentiments and memories of their beloved

professor is most endearing and touching. These ‘Gems’ revere the genius with glittering

emotional expressions of gratitude.

52

My father would observe everybody and everything with calm and soul searching eyes. He

had the uncanny ability to assess and read a person’s nature. Most of the times he was too

engrossed in his research work. He never allotted or diverted his concentration from the study of

mathematics. My mother would remind us very often that we should be quite. My father was

always totally unaware of his surroundings. Any amount of noise we made it would not disturb

him. Any number of people in the house servants, friends, relations-none or nothing would disturb

him. Apart from the university and the home he had no interest in any other avocation.

Early years of his career in the Andhra University when Dr. C.R.Reddy’s and

Dr.V.S.Krishna’s tenure as Vice Chancellor he would visit the faculty club. Here my father would

pay the card game-especially bridge was his game and played very enthusiastically. He was the

faculty champion for several years. Later my father built his home and both the personalities who

influenced his life passed away he never visited the club. Till the last day of his career in A.U. he

would walk 4 to 5 Km. to the campus and back every day.

Infact the Vice Chancellor, in those days, was distinguished personality who inculcated and

inspired the faculty. Dr. C.R.Reddy an eminent Academician was unaware of the young

mathematician in his faculty. He received a letter from the Princeton institute of Advanced Studies

in Mathematics and Physics in 1945. The letter mentioned that Prof. Robert Oppenheinar, Director

of the institute, requested the V.C. of A.U. that this young genius ‘SMS’ should be spared and

given the opportunity to work in the research institute with several eminent mathematicians and

physicist such as Prof. Albert Einstein. SMS should be permitted to work for couple of years. Dr.

C.R.Reddy was amazed. He did not know who this young genius was. He called for the young

SMS. Thence began a beautiful relationship between them. Naturally with great pride Dr.

C.R.Reddy helped my father’s journey to U.S. under the British Raj. My father went to U.S. as

British Indian citizen. When he returned in 1947, India was a free Republic. Those days they

travelled by ship. My father was held up in Sri-Lanka-Ceylon-those days. To enter republic of

India his passport still showed him as British Indian. So my parental uncle and my mother

produced required government documents from Chennai-madras Presidency offices. My mother

had to identify and declare that SMS was her husband! The required extra amount was paid for

official clearance in Ceylon. I was a two year old child and they had to take me also by boat from

Dhanishkoti which was washed away in 1960’s by the heavy tidal waves, to Colombo.

53

While in U.S young Minakshi as they called him abroad to shorten the long tongue twisting

alien name-adopted the habit of smoking. The respect and regard the faculty had for Dr. C. R.

Reddy was such that whenever Dr. C. R. Appeared anywhere on the campus or visited

unexpectedly SMS in the Dept. the cigarette would disappear without any trace of smoke also. It

was an honour and the V.C would be conducted around with great reverence.

Likewise the successor of Dr. C.R. was Dr. V.S. Krishna another eminent professor, who

inspired great respect in all his faculty. My father enjoyed a wonderful relationship with him. SMS

was invited by Princeton Institute and also by the Maryland University for permanent research post

by 1950. Dr. V.S. advised that India needs such brilliant for progress. My father’s keen

participation with all the leading scholars in the conferences and research work endeared him. Dr.

Homi Bhabha who spearheaded in nuclear Research programmes in Trombay, and the Pioneer for

Nuclear Research in Free India has had great love and respect for SMS. Dr. Homi Bhabha also

influenced him with patriotism. More out of personal regard for Dr. V.S. My father conveyed to

the U.S. Institute and University very politely that he was needed here in India. Till Dr. V.S.

Krishna’s demise he never left the Andhra University.

I remember as a child every morning at 7.30 a.m. my father and his neighbour, Prof. S.T.

Krishnama Chari, French and German Department would visit Dr. V.S. Krishna in the V. C.

Lodge religiously. They would spend a half hour in “Satnang” about philosophy, spiritualism

relative subjects and Research. In fact every morning at 7:30 a.m. the pun was: whoever was ready

first would call for the other in tamil.”Yenna Sir, Koivlpolama?” “What Sir, shall we go to the

Temple?” The V.C’s Lodge was a Temple. Dr. V.S would wait for them. Such was the respect a

V.C. inculcated in the campus! They would return by 8’O Clock and hurry through morning

ablutions and proceed to their respective departments.

Dr. S. Radha Krishnan, the second president of Republic of India, was also the vice

chancellor of Andhra University years before Dr. C.R. Reddy. Dr. S. Radha Krishnan’s son Dr. S

Gopal the eminent Historian of India, started his teaching career in Andhra University SMS, STK

and SG were a famous trio in the A.U campus. They were good friends in those days India’s

population was less. The entire A.U. Campus was compact with all the departmental buildings,

54

administrative offices, faculty quarters, students’ hostels, sport grounds, open air theatre, India

Coffee House, faculty club, guest house, appointment houses of V. C., Principal and Registrar, also

ration shop and Kirana stores. Everybody knew everybody, staff, students and families were

connected socially too.

SMS AS AN ADMINISTRATOR

Librarian: Around 1960 the A. U. Librarian post was vacant. The V.C. Dr. V.S. Krishna

requested my father if he could officiate until such time a suitable person was appointed. My father

obliged and took the task as a challenge. This was his first exposure to Administrative work in

A.U. He divided his time daily to the department and library. In those days Dr. V.S.K visited the

library every day from 2.30 p.m. to 3.30p.m. It was his routine habit to work on his subject in the

library. My father made it a point to be on the premises of the library before his arrival. He would

conduct his department work to accommodate this time. Till the V. C. left he would be available in

the library for any necessity. Such was the regard for the V. C. in those days.

Dr.V.S. Krishna was appointed as U.G. C Chairman in 1961. The A.U. faculty members

were thrilled over a year he served. While addressing a conference in the U.G.C Offices he

collapsed with a massive heart attack. He dropped onto the conference table and passed away

instantaneously. This was an emotional blow to my father. His regard and association with Dr.

V.S.K. was intimate. Dr. V.S.K was the driving force otherwise he would have left A.U to U.S.

long before.

In 1962 again SMS was asked to take over the post of A.U Hostels Warden. There was a

lot of unrest among the students regarding the administrative lapses of the hostels. A district

change in the student community behavioural patterns cropped up. Sixties was the turbulent period

all over the world among student communities. All kinds of new attributes and living styles began.

The impact could be seen in the young India too. The hostel and mess maintenance, the inedible

food, malpractices in the lower level administrative staff, ill feelings and disputes between the

students and the management men boiled and exploded in to student strikes. Till then strikes and

student unrest was unknown and unheard of!

55

The warden post was considered a royal job. Yet when my father ascended, it was a thorns!

We shifted from the long barrack-houseaccommodation into the traditional bungalow of warden’s

house. It had gardens around the house. A car shed and four servant’s quarters. A gardener, an

office peon, a driver and the house maid and watchman lived in these. All these buildings were

built by the British military during the II World War. It housed British military personnel.

My father worked stupendously to straighten out all the problems for two years! he visited

every hostel block unannounced. Checked the rooms for cleanliness electricity and water, toilets

and shower rooms. Enquired of students various blocks and messes where food was cooked and

served. He checked with the stores and maintenance. He would lunch and dine in each mess with

the students as unexpected visitor. Soon he became familiar and popular figure.

Every week he would send for meals to be brought home. We all had to eat and express

our views. My mother and grandmother especially had the task to teach and guide the hostel

cooks-My father would call the cooks in turns from each mess to the house. He would talk to them

in friendly ways. Most of them were from Kerala or Tamil Nadu. As my parents and grandmother

were proficient in both languages and good styles it helped. Within a year of taking charge there

was a marked change in the hostels, messes. Teaching them responsibility and inculcating

enthusiasm to serve each other.

Towards the end of his tenure as warden a peculiar problem cropped up. The A.U. Doctor

was a good friend of my father’s. He resided in the campus quarters. One night after evening

duties in the A.U. Dispensary cum hospital the Doctor went to his father’s house into the town.

Late night a student fell ill and was taken to the tiny hospital. The night in charge tried to give

medicine. Even after an hour the student was running high fever. The In-charge telephoned to the

Doctor. He administered further injections and medicines under the guidance and instructions of

the Doctor. Unfortunately the student did not recover and expired. Within an hour the entire

student community in the hostels assembled before the doctor’s house. Shouting and pelting

stones. When they realized nobody was within they marched to the warden’s quarters.

By this time my father received a call from the hospital. He was waiting for the student

crowd. It was after midnight. The entire family that is my grandmother, mother, brother and

56

myself were worried. My brother was in B.Sc., and I was in High School. My father was waiting

in the front trellised verandah. Some chairs are arranged for visitors here. We turned on all the

lights inside and outside the house so that students need not be in the dark. The front door was

wide open. As we heard the shouting crowd we watched from the door of the drawing room

opening on to the verandah. My father arose as the students entered the gate. He signaled to us to

move inside. My brother was at the end of the verandah which right angled and was a cosy room

screened. He turned off the lights here and stood behind the wooden screen just thirty feet away

from the entrance door. My mother and I waited behind the curtain of the door. My father had

walked to the front door with his hands clasped behind his back. He waited very calmly for the

students. They rustled and surged forward. Tramping the garden and shoving each other. They

came right up to the front door. There were just three steps below the door was jam packed with

students shouting slogans for justice and dismissal of the doctor. For 15 minutes the crowds

jostled, shouted and yelled. My father waited patiently watching them from all sides. Slowly the

shouting lessened and in 20 minutes there was silence.

My father smiled sympathetically and spoke in a clear voice slowly, kindly and gently. He

calmed the violent emotions of the students with soothing words but firm voice. Having pacified

their emotions he explained the situation and the tragedy of the student’s death. Then his voice

picked up momentum and force driving home to the students the irrationality of their attitude and

behaviour. He told them all necessary precautions will be Made to ensure the medical needs of

students. He told them to go back and rest. He waited. There was silence but no movement from

the students. The situation was tense. The silence and waiting seemed eternal. Suddenly from

somewhere at the back, in the darkness, a single voice shouted “Dismiss the doctor”. A stone

came with great force and landed on the roof over my father’s head.

From the slit in the curtain I observed my brother about to move out. I was about to move

also. But my father’s stance and voice froze us. Not only us even the students froze. He raised

his voice very challengingly. He invited the student who flung the stone to come up. He goaded

them to be bold, to come to him and attack. He chided them not tobe cowards. He said justice will

prevail in anything and everything. He told them he was not afraid. There was a pregnant silence.

Then the students ashamed, apologized. The sensible ones convinced turned wishing my father

57

goodnight. As majority were convinced the rest followed like sheep. It was a half hour by the time

all cleared, gates closed, doors bolted and lights turned off. We were relieved and retired soon.

Next morning as promised my father organized enquiry and settlement. The doctor retired

from services. This was another emotional blow for my father. The doctor was a good friend of

SMS. My father’s tenure ended. He was offered and invited to continue. He refused politely and

firmly.

Twice after 1945, SMS was invited by the U.S. and U.K. universities for guest lectures and

as visiting professor. Many exchange programs of visiting professors from Europe and U.S. A

were organized. My father actively conducted the seminars and lectures. On both the occasions

when he returned from abroad he brought box loads of books by surface mail for A. U Library and

department.

Student research scholars, students from other departments, young demonstrators of

various subjects used to visit our home. My father was a willing guide and encouraged everyone in

whatever endeavor they approached. He whole heartedly supported and assisted in every and

whatever manner they required. Many a youngster found his avocation and goal. He was also

responsible for encouraging and establishing new departments of various subjects. A positive

approach and the Vice-Chancellor, would appreciate my father’s valuable suggestions. The

department of psychology was opened with my father’s guidance by Dr. K. Ramakrishna Rao.

Even in his student days K.R.R. was a regular visitor to our home. He is the pioneer of para

psychology and established the N. Carolina Institute of para psychology.

From 1946 to 1948 when SMS worked in Princeton he lived as a paying guest in an

independent house owned by an elderly lady. Princeton is very cold in winter with severe snow

fall. The land lady was a typical American with warm nature. She was kind and affectionate

towards, this young foreign-alien-genius from far off India. Unfortunately the young man was an

absent minded professor! He would leave the front door open even in winter. The house would

become dreadfully cold inside. She spoke to the genius several times. Sincerely SMS would

apolgise with a promise to rectify the slip. Unfortunately he would more often forget. Then she

would leave a note on the door. This helped some times. Then the note became a large hanging

58

with block letter CLOSE THE DOOR – instructions. Young SMS was too engrossed and hurry-

burry that the problem persisted. Ultimately the land lady with much regret requested the young

mathematician to vacate as she suffered with arthritis.

During his first tenure in US he started smoking. Gradually he became a chain smoker. By

mid 50’s he suffered a mild heart attack. He was advised to give up smoking. He was advised six

weeks rest with medication. Those days medical sciences had limitations. SMS returned to work

after a few weeks rest. The smoking commenced again.

As a child I would ask my father to give up smoking. As advised by the doctor we kept

sweets and chocolates within reach. They were never touched. Once on questioning why he never

gave up smoking which is injurious for health he promptly replied, “Smoking is my inspiration”.

Sometimes to forget and ignore difficulties and pain, emotional, mental or otherwise we seek a

diversion. May be my father, found, after addiction to smoking, an easy way to overcome this.

In 1966 SMS was invited to the Indian institute of Advanced studies in Simla. My father

was very happy. He never felt happy just teaching and the academic value of the subject was not

his forte. He had introduced General Education as a subject in the graduate level. Sciences,

fundamentals of sciences were taught to Arts students, and to the science graduates the Fine Arts

and social subjects. My father had a wide range knowledge. His interest in philosophy and the

quest for the unknown force, the source of energy was fascinating as to all scientists and

mathematicians. My father had a wonderful collection, library at home, of books on all the varied

subjects. Some real rare and expensive books. Today most of them have been gifted to various

libraries and people who needed them. So when the offer from IIAS came he was very happy. Now

there were no ties that kept him in A.U. He gladly accepted and we proceeded to Simla.

In the wonderful surroundings, atmosphere of the foot hills of the Himalayan range he

could work peacefully and with verve. The last work of his life began. I was a degree student. I

saw the joy of his soul as he mused and worked. He cherished this as one of great value to the

future of mathematics and to mankind. He knew this contribution of his was a major break

through. Distinguished scholars from all over India and a few from abroad also were a part of the

faculty. The RastrapathiNivas in Simla housed the IIAS. This used to be the summer capital of

59

British Raj as the English man could not bear the heat of Delhi! Naturally the regar grandeur of the

seminars held here is something to be seen in those days. Dr. Niharanjan Ray, Historian, head of

history was the first Director of IIAS.

A Wonderful personality and distinguished Historian from Calcutta University. As a

daughter all through life I enjoyed the attention and pampering of all these distinguished people

who came in contact with my father. His stay was exactly one year and two months.

In 1967 the then Vice-Chancellor of A.U. Dr.K.R. Srinivasa Iyengar invited my father to

start the Nagarjuna University, Nallapadu, Guntur, Dr. KRS Iyengar another doyen of A.U. was a

man of literature. My father accepted the offer. His manuscript was almost complete. The last

chapter had to be finalised. Naturally with the new administrative task he could not allot all his

time. SMS came to Vizag by March 1967 we were guests in the V.C’s Lodge for 15 days before

proceeding to Guntur. As destiny would have it Maryland University Director sent an invitation to

SMS to be the head of the Research Programmes of mathematics in US. The offer of $20,000 per

month as salary with all the perks. As I was a degree student, I was given a seat in the graduation

course III year there. My father accepted and I was to join from Fall of 1967. Meanwhile SMS

became special Officer of the Guntur P.G. centre in 1967-68 which in a couple of years was to

become a University. The heat and hectic teething problems of this Institute took a toll on my

father’s health. I was married in 1967 at Guntur. By August my parents passports, visas and tickets

were organised to Maryland. Again destiny played a tragic game. My father had a massive heart

attack.

The damage to the heart was critical. The valve of the left ventricle was damaged. Even the

left side muscles and ventricle was damaged. A second attack had caused the damage. He was

taken to Vellore Christian Hospital. In those days that hospital had reputed heart specialists. He

was there for a couple of months. He was brought to Chennai. He stayed with his mother and

brother for a few days. He spent a month in my sister’s house with the grandchildren. He had

another mild attack while at Vellore. The doctors said his condition was very delicate. Another

attack and he will not survive. Of course though he was not informed my father’s intuition was

always sharp and accurate. He sensed his delicate situation. He kept telling my mother that they

should go back to Vizag. My uncle, sister discouraged as they would be far and alone. For several

60

days the discussion dilly-dallied. My father eventually decided to come back to Vizag and forced

everyone to make arrangements.

He told my mother that he wanted to be in his own home. If anything happened it should be

in his own home. The sentiment and attachment made my mother and brother to bring him back to

Vizag. He was 53 years of age. He told the V.C. he wanted to take Voluntary Retirement.

Naturally this created uproar in the University and family. Dr.K.R.S.,V.C. was baffled. V.C. spoke

several times but he refused. All his near and dear, friends, colleagues, family told him not to be

hasty.

My father felt morally it was wrong to draw salary when he could not attend the

department daily and follow the rules and regulations. The UGC Chairman Dr.Kothari was

informed. He wrote official and personal letters to the V.C. and my father. It was no avail.

Dr.Kothari visited the Vizag Dr.K.R.S. the V.C. brought Dr.Kothari home. For over an hour he

stayed with my father. Dr.Kothari requested and gave the authority to the V.C. that his car should

sent for SMS twice in the week. SMS would go to the dept. for a couple of hours and serve the

A.U. thereby he need not take VRS. My father was moved but he knew he was incapable of any

work and therefore his conscience did not permit him to accept.

Such purity of nature, simplicity in living the values, undaunted sincerely to truth, a strong

moral binding character only a genuine genius can possess. The decision did not surface any

unhappiness, regret, a sense of loss or failure. On the contrary he felt happy, relieved, and free.

These are divine qualities. So he retired and on August 13th, 1968 at 10.p.m. in the night he had an

attack. I was by his side. My father was looking at me as life passed out of him. He could not

speak because of the pain. The expression in his eyes was powerful and he seemed to will

something through me.

Unfortunately both my grandmothers outlived my father. My parental grandmother’s stoic

nature found a crack at the age of 84 then. A year later a son was born to me. At the time living in

Ernakulam, Cochin, just one hour journey to Trichur, my father’s birth place. We had visited the

Guru Vayur Krishna Temple. My parental grandmother when she heard she desired strongly to

come to Ernakulam. Of course she was too old and my uncle did not, permit. My parental

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grandmother died in June1976 exactly 8 years after my father’s death. Exactly 6 months later my 6

year old son returning from school was knocked down by a Matador van and killed in Ernakulam.

Many a time I wondered if my father’s last look was strong wish to be reborn to me. See

his mother die and then left me to bear the pain.

The Humour of SMS: An old student of my father, a retired naval officer, narrated this

anecdote. SMS teaching of Quantum Analysis was something marvellous. Both the teacher and the

taught were lost in the magical world of topic oblivious to time and place. Such was his sensational

flair for the subject. Every batch raved about his teaching. The ash tray would precede to the

classroom. At times while lecturing he would hold a cigarette in his left hand and chalk piece in

the right. All the while he wrote and explained his left hand would steadily hold the cigarette not

allowing even a tiniest speck of ash to drop. On one such an occasion while teaching, one student

distracting raised a doubt, halting and cutting the magical trend. For a few seconds SMS was silent

observing the youngster. The pregnant silence of tension eased with SMS voice reciting.

Meerucheppinadimaakutheliyaka,

Memucheppinadimeekutheliyaka,

Manamucheppinadimanaketheliyaka,

GanithaSastramethikamakamakathika.

This was a popular song from a popular movie then. The class was enjoyed this because

such a diversion from SMS was rare. Besides the man’s greatness was that nobody attributed any

filmy distractions from him! My father never went to movies or indulged in any light meaningless

entertainment banter. The last line was my father’s addition.

Once FNI meet in Aurangabad of mathematical association 1958-59 my father attended.

All the members, professors and teaching faculties of several universities were accommodated in

several hostels. My father was arrived but his name was not listed in any of the buildings. The

organisers were alarmed and frantic. Meanwhile in the accommodation provided for the women

faculty one room was unoccupied. They discovered that room was reserved for the faculty member

from A.U. Prof. S. Minakshi Sundaram.

62

“So you have made me a lady?” My father asked smiling. Imagine the horrible

embarrassment of the convenors. My father’s name is misleading. People thought he was

Tamilian. Actually we are Telugu people but ancestors migrated to deep south Kerala. Hence my

father’s birth in Trichur, Kerala.Then settled in Tamil Nadu last two generations, so educated in

Chennai. My father came back to Andhra for his career. So the return of the Prodigal son ! People

often misconstrued the name to be a lady.

On another occasion as the Special Officer P.G. Centre Guntur he had to shoulder the

teething problems of such establishment, which are well known. The staff were a little irritated

with each other. One Sunday morning Telugu Professor visited my father at home. He was pouring

his woes of how some of the staff teased him with popular saying:

Vana pamu oka pamena, menatha koduku oka mogudena, telugu professor oka professorena?

My father had great difficulty to console him because my father too is menatha koduku to

my mother.

I have recorded what little I could of my father. The memoir can be lengthy but there is

much I have omitted. Of his subject I know nothing. Honestly mathematics is beyond my

comprehensive imagination, whereas within my imaginative comprehension! In fact on one

occasion after discussing about literature he gave a speech inter-connecting literature and

mathematics. The commonality of relationship was unique which he delineated. I pray that

posterity cherishes a daughter’s small tribute.

63

List of Donors and Life Members of

Prof. S. Minakshisundaram Memorial Society

List of Donors 1. Dr. G V N Kameswara Rao. Rs.10,000 2. Dr. Chelluri Sastri Rs.10,000 3. Prof. D. Rama Kotaiah Rs.10.000 4. Dr. Krishna Kumari $ 500 5. Sri. V. Vani Prasad Rao Rs.5000

List of Life Members

1. Dr.PV.Arunachalam, Former V.C.Dravida Univ. 526, Balaji Colony, Tirupathi-517502.

2. Dr.C.R.Rao,Sc.D.Frs Padma Vibhushan, National Medal of Sci. Laureate, USA

Professor Emeritus&Advisor, C.R.Rao AIMSCS, Aryabhata,

Univ.of Hyd Campus, Prof.C.R.Rao Road, Hyderabad-500046.

3. Mr.V.Vani Prasad Rao, ISS.Rtd. Director, Ministry of Surface Transport, Govt.of India, 316, Kanthi Shikara Apts. Somajiguda, Hyd.--5ooo82.

4. Dr.G.Gurunadham, Rtd.Prof. I.I.T. Mumbai, Cincinnati, USA.

5. Dr.B.Subramanian. Youngston, Ohio, USA.

6. Dr.V.Vardarajulu,

Rtd.Senoir Scientist,DRDL, 24 RB Colony, Malakpet, Hyd.-500036.

7. Dr.PVSSSR.Somayajulu, 2-2-1106/E, Flat:305,Sai Mithra Res. Tilak Nagar, Nallakunta, Hyd--500044.

8. Mr.RSN.Murti Rtd.Director, Indian Postal Dept. No:51, Postal Colony, Kharkhana, Secunderabad.

9. Mr.VCV.Rao, 73, Lumbini Springs, Gachibowli, Hyd.--50082.

10. Dr.T.Krishna Kumar, Rtd Prof.IIM. Bengeluru, 110 Sobha Opal, 39th.cross st.18th main, 4th Block, Jayanagar, Bengelu560041.

11. Dr.TKV.Iyengar, Prof.Maths.Dept.

64

NITW Warangal--506004.

12. Dr.GVN.Kameswara Rao. Vijayawada.

13. Dr.Mrs.K.Leela Lakshmi, Head Maths.Railway Degree College, 2-87/7Pearl,Navratna, Road : 2, Kakatiya Nagar, Hapsiguda, Hyd.--500007.

14. Dr.J.Venkatapaiah, 12-13-825/5 Gokul Nagar, Taranaka, Hyd.--500017.

15. Dr.Chelluri. Sastri, Canada.

16. Dr.YRK.Sarma, Rtd.prof.ISI Kolkata, Plot-7. Sitaram Nagar, Sikh Village, Secunderabad-500009.

17. Dr.Krishna Dayanidhi, New-Jersey, USA

18. Dr.Ramkotiah, Rtd.V.C.AN'Juna Univ. B 63 SVN Colony, Guntur-522006.

19. Mrs.K.Girija. 202, Excel Tulips, Domalguda, Hyderabad--500029.

20. Mr.G.Maruthi Rao, Dramatist, Cine Actor, 8/6 Saradambal st. Gokulam colony, Chennai--17.

21. Dr.PV.Subba Rao, Scientist, Consultant,

ISRO Plot:8 H:13-1-105/2, Mothy Nagar,Erragada, Hyderabad--500018.

22. Dr.B.Sadasivudu, Plot:109, Nav Nirman Nagar, Jubliee Hills, Hyd---500033.

23. Wg.Cdr.B.Neelakantam, 91, P&T Colony, Vikrampuri, Secunderabad--500009.

24. Dr.S.Bhaskara Rao, Director, CR.Rao AIMCS, Central Univ. Campus, Hyd--500046.

25. Dr.KLN.Swamy, Rtd.Prof.AU. 52, Pandurangapuram, Visakhapatnam--530003.

26. Dr.Koti Reddy, 107, Everest Block, Aditya Enclave, Maitri vanam, Ameerpet, Hyd--500038.

27. Ms. M. Suneetha C/o T K V Iyengar Hyderabad.

28. Ms. G. Shantha Department of Mathematics M G I T, Hyderabad.

29. Prof. I. H. Nagaraja Rao Gayathri Vidya Parishad Visakhapatnam.

30. Dr. A. A. L. S. Charyulu G I T A M, Visakhapatnam

65

31. Prof. A. Chandra Sekhar

Professor & Head Department of Engineering Mathematics GITAM University

32. Department of Engineering Mathematics GITAM University

33. Dr. V. Yogeswara

Associate Professor Department of Engineering Mathematics GITAM University

34. Dr.N.Ravi Shankar

Associate Professor Department of Engineering Mathematics GITAM University

35. Dr.S.K. Vali

Associate Professor Department of Engineering Mathematics GITAM University

36. Dr. V. Lakshmi Narasamma

Associate Professor Department of Engineering Mathematics GITAM University

37. Dr.P.S.R.Murthy

Associate Professor Department of Engineering Mathematics GITAM University

38. Dr.Ch.Pragathi

Associate Professor Department of Engineering Mathematics GITAM University

39. Smt.I. Lakshmi Gayatri Assistant Professor Department of Engineering Mathematics GITAM University

40. Smt. Ch. Suneeta

Assistant Professor Department of Engineering Mathematics GITAM University

41. Dr. T. Vinutha

Assistant Professor Department of Engineering Mathematics GITAM University

42. Sri.P.Phani Bushan Rao

Assistant Professor Department of Engineering Mathematics GITAM University

43. Mr. B. Ravi Kumar

Assistant Professor Department of Engineering Mathematics GITAM University

44. Mr. T. Surendra

Assistant Professor Department of Engineering Mathematics GITAM University

45. Dr.M.M.Sandeep Kumar

Assistant Professor Department of Engineering Mathematics GITAM University

46. Smt. G. Naga Lakshmi

Assistant Professor Department of Engineering Mathematics GITAM University

.

66

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Vishnupur, BHIMAVARAM, W.G. Dt. – 534 202, Ph. 08816-250864, 251460, Fax: 08816-250099

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� Civil Engineering (CE) 60

� M.C.A. 60

� M.B.A. 60

� M.Tech. (Power Electronics) 36

� M.Tech. (VLSI) 18

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Vishnu Institute of Technology (Approved by AICTE & Affiliated to JNTUK, KAKINADA (Code: PA)

Vishnupur, BHIMAVARAM, W.G. Dt. – 534 202,

Ph. 08816-210044, 251333, Fax: 08816-250099

Website: www.vishnuit.in Mail Id: info@vishnuit.in

Vishnu Institute of Technology (VIT) has been established in a serene atmosphere with a perfect ambience at

Vishnupur, Bhimavaram, West Godavari District on a sprawling campus of 100 acres. It is one of the many

educational Institutes of Sri Vishnu Educational Society.

Courses Offered

� Electrical & Electronic Engg. (EEE) 60

� Electronics & Comm. Engg. (ECE) 120

� M.B.A. 60

� Computer Science & Engg. (CSE) 120

� Information Technology (IT) 60

� Mechanical Engineering (ME) 60

Sri Vishnu Educational Society Vishnupur, BHIMAVARAM, W.G. Dt. – 534 202,

Ph. 08816-250885, 250385, Fax: 08816-250869

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