Bibliography

A. Aaboe, Episodes from the Early History of Mathematics (Random House, New York, 1964)A.D. Aczel, Fermat’s Last Theorem: Unlocking the Secret of an Ancient Mathematical Problem

(Four Walls Eight Windows, New York, 1996)D. Adamson, Blaise Pascal: Mathematician, Physicist, and Thinker About God (St. Martin’s Press,

New York, 1995)R.P. Agarwal, H. Agarwal, S.K. Sen, Birth, Growth and Computation of Pi to ten trillion digits.

Adv. Differ. Equat. 2013, 100 (2013)A.A. Al-Daffa’, The Muslim Contribution to Mathematics (Humanities Press, Atlantic Highlands,

1977)A.A. Al-Daffa’, J.J. Stroyls, Studies in the Exact Sciences in Medieval Islam (Wiley, New York,

1984)E.J. Aiton, Leibniz: A Biography (A. Hilger, Bristol, Boston, 1984)R.E. Allen, Greek Philosophy: Thales to Aristotle (The Free Press, New York, 1966)G.J. Allman, Greek Geometry from Thales to Euclid (Arno Press, New York, 1976)E.N. da C. Andrade, Sir Issac Newton, His Life and Work (Doubleday & Co., New York, 1954)W.S. Anglin, Mathematics: A Concise History and Philosophy (Springer, New York, 1994)W.S. Anglin, The Queen of Mathematics (Kluwer, Dordrecht, 1995)H.D. Anthony, Sir Isaac Newton (Abelard-Schuman, New York, 1960)H.G. Apostle, Aristotle’s Philosophy of Mathematics (The University of Chicago Press, Chicago,

1952)R.C. Archibald, Outline of the history of mathematics.Am. Math. Monthly 56 (1949)B. Artmann, Euclid: The Creation of Mathematics (Springer, New York, 1999)C.N. Srinivasa Ayyangar, The History of Ancient Indian Mathematics (World Press Private Ltd.,

Calcutta, 1967)A.K. Bag, Mathematics in Ancient and Medieval India (Chaukhambha Orientalia, Varanasi, 1979)W.W.R. Ball, A Short Account of the History of Mathematics (Dover, New York, 1960)S.F. Barker, Philosophy of Mathematics (Prentice-Hall, Englewood Cliffs, 1964)M.E. Baron, The Origin of Infinitesimal Calculus (Dover, New York, 1993)J.D. Barrow, Pi in the Sky: Counting, Thinking, and Being (The Clarendon Press, New York, 1992)C. Baumgardt, Johannes Kepler: Life and Letters (Victor Gollancz, London, 1952)P. Beckman, A History of � (St. Martin’s Griffin, New York, 1976)A. Beiler, Recreations in the Theory of Numbers (Dover, New York, 1964)B. Belhoste, Augustin–Louis Cauchy: A Biography, Translated by F. Ragland (Springer, New York,

1990)E.T. Bell, Men of Mathematics (Touchstone Books, New York, 1986)

© Springer International Publishing Switzerland 2014R.P. Agarwal, S.K. Sen, Creators of Mathematical and Computational Sciences,DOI 10.1007/978-3-319-10870-4

453

454 Bibliography

E.T. Bell, The Development of Mathematics, 2nd edn. (Dover, New York, 1992)D.C. Benson, The Moment of Proof: Mathematical Epiphanies (Oxford University Press,

New York, 1999)J.L. Berggren, Episodes in the Mathematics of Medieval Islam (Springer, New York, 1986)D. Berlinski, A Tour of Calculus (Vintage, New York, 1995)B.E. Berndt, Notebooks of S. Ramanujan (Springer, New York, 1985)B.C. Berndt, R.A. Rankin, Ramanujan Letters and Commentary (Affiliated East West Press,

New Delhi, 1997)E.W. Beth, The Foundations of Mathematics (North-Holland, Amsterdam, 1959)E.W. Beth, Mathematical Thought: An Introduction to the Philosophy of Mathematics (D. Reidel,

Dordrecht, 1965)T.G. Bhaskar, D. Kovach, V. Lakshmikantham, The hybrid set theory. Nonlinear Anal. Hybrid Syst.

1, 414–416 (2007)M.G. Bishop, Pascal, the Life of Genius (Reynal & Hitchcock, New York, 1936)M. Black, The Nature of Mathematics: A Critical Survey (Routledge & Kegan Paul, London, 1965)D. Blatner, The Joy of Pi (Walker Publishing Co., New York, 1997)D.M. Bose, S.N. Sen, B.V. Subbarayappa, A Concise History of Science in India (Indian National

Science Academy, New Delhi, 1971)C. Boyer, The History of the Calculus and Its Conceptual Development (Dover, New York, 1959)C. Boyer, A History of Mathematics, 2nd edn. (Wiley, New York, 1991)J.W. Brewer, M. Smith, Emmy Noether, a Tribute to Her Life and Work (Marcel Dekker Inc.,

New York, 1981)D.E. Brody, A.R. Brody, The Science Class You Wish You Had: The Seven Greatest Scientific Dis-

coveries in History and the People Who Made Them (Berkeley Publishing Group, New York,1997)

R.S. Brumbaugh, Plato’s Mathematical Imagination (Indiana University Press, Bloomington,1954)

L.N.H. Bunt, P.S. Jones, J.D. Bedient, The Historical Roots of Elementary Mathematics (Prentice-Hall, Englewood Cliffs, 1976)

D.M. Burton, The History of Mathematics: An Introduction, 4th edn. (McGraw-Hill, New York,1999)

F. Cajori, The history of the notations of calculus. Ann. Math. 25, 1–46 (1923)F. Cajori, Leibniz, the master builder of notations. Isis 7, 412–429 (1925)F. Cajori, A History of Mathematics, 4th edn. (Chelsea Publishing, New York, 1985)R. Calinger, Gottfried Wilhelm Leibniz (Rensselaer Polytechnic Institute, Troy, 1976)R. Calinger (ed.), Classics of Mathematics (Prentice-Hall, Englewood Cliffs, 1995)R. Calinger, A Contextual History of Mathematics: To Euler (Prentice Hall, Upper Saddle River,

1999)G. Cantor, Contributions to the Founding of the Theory of Transfinite Numbers, Translated by

P.E.B. Jourdain (Dover, New York, 1952)M. Cantor, Vorlesungen über Geschichte der Mathematik (Teubner, Leipzig, 1907)G. Cardano, The Book of My Life, Translated by J. Stoner (Dover, New York, 1962)G. Cardano, The Great Art, Translated by T.R. Witmer (MIT Press, Cambridge, 1968)S. Chandrasekhar, Newton’s Principia for the Common Reader (Oxford University Press, Oxford,

1995)M. Ranga Charya (ed.), Mahavira (author), Ganita Sara Sangraha (Madras Government Publica-

tions, Madras, 1912)D. Chattopadhyaya, History of Science and Technology in Ancient India: The Beginnings (Firma

KLM PVT, Calcutta, 1986)M. Clagett, Greek Science in Antiquity (Collier, New York, 1963)W.E. Clark (ed.), The Aryabhatia of Aryabhata (The University of Chicago Press, Chicago, 1930)C.C. Clawson, Mathematical Mysteries: The Beauty and Magic of Numbers (Plenum Press,

New York, 2000)M.P. Closs (ed.), Native American Mathematics (University of Texas Press, Austin, 1986)

Bibliography 455

I.B. Cohen, Sir Issac Newton’s Papers and Letters on Natural Philosophy (Harvard UniversityPress, Cambridge, 1958)

J.R. Cole, Pascal: The Man and His Two Loves (New York University Press, New York, 1995)L. Conant, The Number Concept. Its Origin and Development (Macmillan, New York, 1923)R. Cooke, The Mathematics of Sonya Kovalevskaya (Springer, New York, 1984)J.L. Coolidge, The Mathematics of Great Amateurs (Dover, New York, 1963)N. Copernicus, On the Revolutions of Heavenly Spheres. Great Mind Series (Prometheus Books,

New York, 1995)R. Courant, H. Robbin, I. Stewart, What Is Mathematics? (Oxford University Press, New York,

1996)J.G. Crowther, Six Great Scientists (Barnes & Noble, USA, 1995)C. Cullen, Astronomy and Mathematics in Ancient China: The Zhou Bi Suanjing (Cambridge

University Press, Cambridge, 1996)P. Damerow, Mathematics in Ancient Iraq: A Social History (Princeton University Press, Princeton,

2008)B. Datta, The Bakhshali manuscript. Bull. Calcutta Math. Soc. 21, 1–60 (1929)B. Datta, The Science of the Sulbas: A Study in Early Hindu Geometry (Calcutta University Press,

Calcutta, 1932)B. Datta, A.N. Singh, History of Hindu Mathematics, vol. 2 (Asia Publishing House, Bombay,

1962)B. Datta, Ancient Hindu Geometry: The Science of the Sulba (South Asia Books, Bombay, 1993)J.W. Dauben, Georg Cantor: His Mathematics and Philosophy of the Infinite (Harvard University

Press, Cambridge, 1979)J.W. Dauben (ed.), The History of Mathematics from Antiquity to the Present. A Selective

Bibliography (Garland, New York, London, 1985)M. Davis, The Universal Computer: The Road from Leibniz to Turing (W.W. Norton & Co.,

New York, 2000)P.J. Davis, R. Hersh, The Mathematical Experience (Birkhäuser, Boston, 1981)P. Dedron, J. Itard, Mathematics and Mathematicians, vol. 2 (The Open University Press, Milton

Keynes, England, 1973)R. Descartes, The Geometry, Translated by D.E. Smith and M.L. Latham (Dover, New York, 1954)R. Descartes, Discourse on Method and the Meditations on First Philosophy, 4th edn. (Hackett

Publishing Company, Indianapolis, 1998)A. Dick, Emmy Noether 1882–1935 (Birkhäuser, Basel, 1970)L.E. Dickson, History of the Theory of Numbers (Chelsea, New York, 1971)E.T. Drake, Restless Genius: Robert Hooke and His Earthly Thoughts (Oxford University Press,

Oxford, 1996)J.L.E. Dreyer, A History of Astronomy from Thales to Kepler (Dover, New York, 1953)J.M. Dubbey, The Mathematical Work of Charles Babbage (Cambridge University Press,

Cambridge, 1978)W. Dunham, Journey Through Genius: The Great Theorems of Mathematics (Penguin, New York,

1991)W. Dunham, The Mathematical Universe: An Alphabetical Journey Through the Great Proofs,

Problems, and Personalities (Wiley, New York, 1994)W. Dunham, Euler: The Master of Us All (MAA, Washington, DC, 1999)G.W. Dunnington, Carl Friedrich Gauss, Titan of Science: A Study of His Life and Work (Hafner,

New York, 1955)M. Dzielska, Hypatia of Alexandria, Revealing Antiquity (Harvard University Press, Cambridge,

1996)S. Edeen, J. Edeen, Women Mathematicians (Dale Seymour Publications, Parsippany, 1990)C.H. Edwards Jr., The Historical Development of the Calculus (Springer, New York, 1979)H.M. Edwards, Fermat’s Last Theorem. A Genetic Introduction to Algebraic Number Theory

(Springer, New York, 1977)A. Einstein, Ideas and Opinions (Bonanza Books, New York, 1986)

456 Bibliography

A. Einstein, World As I See It (Citadel Press, New York, 1993)H.W. Eves, An Introduction to the History of Mathematics (Holt, Rinehart and Winston, New York,

1969)H.W. Eves, In Mathematical Circles: A Selection of Mathematical Stories and Anecdotes (Weber

& Schmidt, Boston, 1969)H.W. Eves, In Mathematical Circles: A Second Collection of Mathematical Stories and Anecdotes

(Weber & Schmidt, Boston, 1971)H.W. Eves, Great Moments in Mathematics: Before 1650 (The Mathematical Association of

America, Washington, DC, 1981)H.H. Eves, Great Moments in Mathematics: After 1650 (The Mathematical Association of

America, Washington, DC, 1982)H.W. Eves, Return to Mathematical Circles: A Fifth Collection of Mathematical Stories and

Anecdotes (PWS-Kent Publishing, Boston, 1988)J.J. Fahie, Galileo, His Life and Work (John Murray, London, 1903)J. Fauvel, J.J. Gray, The History of Mathematics: A Reader (The Open University, London, 1987)L.P. Fibonacci, The Book of Squares, annotated and Translated by L.E. Sigler (Academic, Boston,

1987)J.V. Field, J.J. Gray, The Geometrical Work of Girard Desargues (Springer, New York, 1987)M. Fierz, Girolamo Cardano, 1501–1576 (Birkhäuser, Boston, 1983)D.H. Fowler, The Mathematics of Plato’s Academy: A New Reconstruction (Clarendon Press,

Oxford, 1987)H.A. Freebury, A History of Mathematics (Macmillan, New York, 1961)W. Frucht, Imaginary Numbers (Wiley, New York, 2000)G. Galilei, Dialogue on the Great World Systems (The University of Chicago Press, Chicago, 1953)G. Galilei, Dialogues Concerning Two New Sciences. Great Mind Series (Prometheus Books,

New York, 1995)M.J. Gazale, Number: From Ahmes to Cantor (Princeton University Press, Princeton, 2000)C. Gillespie, Pierre–Simon Laplace 1749–1827: A Life in Exact Science (Princeton University

Press, Princeton, 1997)R.J. Gillings, Mathematics in the Time of the Pharaohs (Dover, New York, 1982)H.H. Goldstine, A History of Numerical Analysis from the 16th Through the 19th Century

(Springer, New York, 1977)H.H. Goldstine, A History of the Calculus of Variations from the 17th Through the 19th Century

(Springer, New York, 1977)J. Gow, A Short History of Greek Mathematics (Hafner, New York, 1923)R.P. Graves, Life of Sir William Rowan Hamilton, vol. 3 (Hodges, Figgis, Dublin, 1882)J.V. Grabiner, The Origins of Cauchy’s Rigorous Calculus (MIT Press, Cambridge, 1981)I. Grattan-Guinness, The Development of the Foundations of Mathematical Analysis from Euler to

Riemann (MIT Press, Cambridge, 1971)I. Grattan-Guinness (ed.), From the Calculus to Set Theory, 1630–1910. An Introductory History

(Duckworth, London, 1980)I. Grattan-Guinness, The Fontana History of the Mathematical Sciences (Fontana Press, Glasgow,

1997)R. Grimsley, Jean d’Alembert [1717–1783] (The Clarendon Press, Oxford, 1963)L.S. Gristien, P.J. Campbell, Women of Mathematics: A Biobibliographic Sourcebook (Greenwood

Press, New York, 1987)M. Guillen, Five Equations that Changed the World (MJF Books, New York, 2000)J. Gullberg, P. Hilton, Mathematics: From the Birth of Numbers (W.W. Norton & Co., New York,

1997)R.C. Gupta, Madhava’s and other medieval Indian value of pi. Math. Educ. 9, B45–B48 (1975)J. Hadamard, An Essay on the Psychology of Invention in the Mathematical Field (Princeton

University Press, Princeton, 1945)E. Hairer, G. Wanner, Analysis by Its History (Springer, New York, 1996)A.R. Hall, From Galileo to Newton 1630–1720 (Harper & Row, New York, 1963)

Bibliography 457

A.R. Hall, Philosophers at War: The Quarrel Between Newton and Leibniz (Cambridge UniversityPress, Cambridge, 1980)

T. Hall, Gauss, a Biography (MIT Press, Cambridge, 1970)T.L. Hankins, Sir William Rowan Hamilton (Johns Hopkins University Press, Baltimore, 1980)G.H. Hardy, Mathematical proof. Mind 38, 1–25 (1928)G.H. Hardy, Ramanujan (Chelsea, New York, 1959)G.H. Hardy, A Mathematician’s Apology (Cambridge University Press, Cambridge, 1967)R. Harre (ed.), Early Seventeenth Century Scientists (Pergamon, Oxford, 1965)T.L. Heath, The Thirteen Books of Euclid’s Elements, vol. 3 (Dover, New York, 1956)T.L. Heath, The Works of Archimedes (Dover, New York, 1953)T.L. Heath, A Manual of Greek Mathematics (Dover, New York, 1963)T.L. Heath, A History of Greek Mathematics, vol. 2 (Dover, New York, 1981)J.L. Heilbron, Geometry Civilized: History, Culture and Technique (Clarendon Press, Oxford,

1998)R. Hersh, What Is Mathematics, Really? (Oxford University Press, New York, 1997)D. Hilbert, Foundations of Geometry, Translated by E.J. Townsend (Open Court, Chicago, 1902)P. Hoffman, Archimedes’ Revenge: The Joys and Perils of Mathematics (W.W. Norton, New York,

London, 1988)A. Hooper, Makers of Mathematics (Random House, New York, 1948)D. Hutchings (ed.), Late Seventeenth Century Scientists (Pergamon, Oxford, 1969)G. Ifrah, From One to Zero: A Universal History of Numbers (Viking, New York, 1985)G. Ifrah, The Universal History of Numbers: From Prehistory to the Invention of the Computer

(Wiley, New York, 1999)P. Jha, Aryabhata I and His Contributions to Mathematics (Bihar Research Society, Patna, 1988)G.G. Joseph, The Crest of the Peacock (Princeton University Press, Princeton, 2000)V. Kagan, N. Lobachevski and His Contributions to Science (Foreign Languages Publishing House,

Moscow, 1957)R. Kaplan, The Nothing that Is: A Natural History of Zero (Oxford Press, New York, 1999)L.C. Karpinski, The History of Arithmetic (Rand McNally, Chicago, 1925)D.S. Kasir (ed.), The Algebra of Omar Khayyam (AMS Press, New York, 1972)V.J. Katz, A History of Mathematics: An Introduction (Harper Collins, New York, 1993)V.J. Katz, Ideas of calculus in Islam and India. Math. Mag. 68, 163–174 (1995)G.R. Kaye, Indian Mathematics (Amd Simla, Calcutta, 1915)A. Keller, Expounding the Mathematical Seed. Vol. 2 (The Translation & the Supplements): A

Translation of Bhaskara 1 on the Mathematical Chapter of the Aryabhatiya (Birkhäuser, Basel,2006)

B. Kemp, Ancient Egypt: Anatomy of a Civilization (Routledge, London, 1991)H. Kennedy, Peano: Life and Work of Giuseppe Peano (D. Reidel, Dordrecht, Holland, 1980)J. Kepler, Epitome of Copernican Astronomy & Harmonies of the World. Great Mind Series

(Prometheus Books, New York, 1995)F. Klein, Development of Mathematics in the Nineteenth Century, Translated by M. Ackerman

(Math Science Press, Brookline, 1979)M. Kline, Mathematics in Western Culture (Oxford University Press, New York, 1953)M. Kline, Mathematics: A Cultural Approach (Addison-Wesley, Reading, 1962)M. Kline, Mathematics, the Loss of Certainty (Oxford University Press, New York, 1980)M. Kline, Mathematics and the Physical World (Dover, New York, 1981)M. Kline, Mathematical Thought from Ancient to Modern Times, 2nd edn. (The Clarendon Press,

New York, 1990)I.L. Kushyar, Principles of Hindu Reckoning (University of Wisconsin Press, Madison, 1966)D.F. Lach, Asia in the Making of Europe, vol. 2 (Chicago University Press, Chicago, 1965)V. Lakshmikantham, The Origin of Human Past (Children of Immortal Bliss) (Bharateeya Vidya

Bhavan, Bombay, 1999)V. Lakshmikantham, S. Leela, J. Vasundhara Devi, The Origin and History of Mathematics

(Cambridge Scientific Publishers, Cambridge, 2005)

458 Bibliography

V. Lakshmikantham, J. Vasundhara Devi, What India Should Know (Bharateeya Vidya Bhavan,Bombay, 2006)

L.Y. Lam, A Critical Study of the Yang Hui Suan Fa, a 13th Century Mathematical Treatise(Singapore University Press, Singapore, 1977)

L.Y. Lam, T.S. Ang, Fleeting Footsteps: Tracing the Conception of Arithmetic and Algebra inAncient China (World Scientific, Singapore, 1992)

J.P. LaSalle, L. Solomon (eds.), Recent Soviet Contributions to Mathematics (Macmillan,New York, 1962)

Y. Li, S.R. Du, Chinese Mathematics: A Concise History, Translated from the Chinese and with apreface by J.N. Crossley and A.W.C. Lun (The Clarendon Press, New York, 1987)

U. Libbrecht, Chinese Mathematics in the Thirteenth Century (MIT Press, Cambridge, 1973)A. Macfarlane, Lectures on Ten British Mathematicians of the Nineteenth Century (Wiley,

New York, 1916)D. MacHale, George Boole. His Life and Work (Boole Press, Dublin, 1985)M.S. Mahoney, The Mathematical Career of Pierre de Fermat, 1601–1665 (Princeton University

Press, Princeton, 1973)E. Maor, E: The Story of a Number (Princeton University Press, Princeton, 1998)J.C. Martzloff, The History of Chinese Mathematics, Translated by S. Wilson (Springer, New York,

1994)K.O. May, Bibliography and Research Manual of the History of Mathematics (University of

Toronto Press, Toronto, 1973)E.A. Maziarz, T. Greenwood, Greek Mathematical Philosophy (Frederick Ungar, New York, 1968)J. McLeish, Number: The History of Numbers and How They Shape Our Lives (Fawcett

Columbine, New York, 1991)K. Menninger, Number Words and Number Symbols: A Cultural History of Numbers (Dover,

New York, 1992)J. Merz, Leibniz (Hacker Press, New York, 1948)H. Meschkowski, Ways of Thought of Great Mathematicians (Holden-Day, San Francisco, 1964)H.O. Midonick, The Treasury of Mathematics (Philosophical Library, New York, 1965)Y. Mikami, The Development of Mathematics in China and Japan (Chelsea, New York, 1913/1974)R.E. Moritz, On Mathematics and Mathematicians (Dover, New York, 1958)J. Muir, Of Men and Numbers: The Story of Great Mathematics (Dover, New York, 1996)T.S.B. Murthy, A Modern Introduction to Ancient Indian Mathematics (Wiley Eastern, New Delhi,

1992)P.J. Nahin, An Imaginary Tale (Princeton University Press, Princeton, 1998)S.H. Nasr, Science and Civilization in Islam (Harvard University Press, Cambridge, 1968)J. Needham, Science and Civilization in China (Cambridge University Press, Cambridge, 1959)R. Netz, The Shaping of Deduction in Greek Mathematics: A Study in Cognitive History. Ideas in

Context, vol. 51 (Cambridge University Press, Cambridge, 1999)O. Neugebauer, The Exact Sciences in Antiquity, 2nd edn. (Dover, New York, 1969)O. Neugebauer, A History of Ancient Mathematical Astronomy, vol. 3 (Springer, New York, 1975)J.R. Newman (ed.), The World of Mathematics (Simon and Schuster, New York, 1956)O. Ore, Niels Henrik Abel (University of Minnesota Press, Minneapolis, 1957)O. Ore, Number Theory and Its History (Dover, New York, 1988)L.M. Osen, Women in Mathematics (MIT Press, Boston, 1974)M.D. Pandit, Mathematics as Known to the Vedic Samhitas (Sri Satguru Publications, New Delhi,

1993)T. Pappas, The Joy of Mathematics (Wide World Publishing/Tetra, San Carlos, 1989)T. Pappas, Mathematical Scandals (Wide World Publishing/Tetra, San Carlos, 1997)S. Paramesvaran, The Golden Age of Indian Mathematics (Swadeshi Science Movement, Kerala,

1998)D. Pedoe, Geometry and the Visual Arts (Dover, New York, 1976)T. Perl, Women and Numbers (Wide World Publishing/Tetra, San Carlos, 1993)J.-P. Pier, Developments in Mathematics 1900–1950 (Birkhäuser, Boston, 1994)

Bibliography 459

D. Pingree, Census of the Exact Sciences in Sanskrit, vol. 4 (American Philosophical Society,Philadelphia, 1970–1981)

K. Plofker, Mathematics in India (Princeton University Press, Princeton, 2008)G. Polya, How to Solve It: A New Aspect of Mathematical Method (Princeton University Press,

Princeton, 1945)G. Polya, Mathematical Discovery, vol. 2 (Wiley, New York, 1962/1965)G. Prasad, Mathematical Research in the Last Twenty Years (Walter de Gruyter, Berlin, 1923)G. Prasad, Some Great Mathematicians of the Nineteenth Century, Their Lives and Their Works,

vol. 2 (Benares Mathematical Society, Benares, 1933–1934)C.T. Rajagopal, M.S. Rangachari, On medieval keralese mathematics. Arch. Hist. Exact Sci. 35,

91–99 (1986)S. Ranganathan, Ramanujan: The Man and the Mathematician (Asia Publishing House, Bombay,

1967)S.B. Rao, Indian Mathematics and Astronomy: Some Landmarks (Jnana Deep Publications,

Bangalore, 1994)C. Reid, Hilbert (Springer, New York, 1970)C. Reid, Courant in Göttingen and New York: The Story of an Improbable Mathematician

(Springer, New York, 1976)E. Rosen, Three Imperial Mathematicians (Abanis, New York, 1986)R. Rucker, Infinity and the Mind (Bantam Books, New York, 1983)B. Russell, The Autobiography of Bertrand Russell, vol. 2 (Little, Brown & Co., Boston, 1951)S. Saliba, A History of Arabic Astronomy (New York University Press, New York, 1994)T.A. Sarasvati, Geometry in Ancient and Medieval India (Motilal Banarsidass, Delhi, 1979)K.V. Sarma, A History of the Kerala School of Hindu Astronomy (Viveshvarand Institute Publica-

tions, Hoshiarpur, 1972)G. Sarton, The Study of the History of Mathematics and the Study of the History of Science (Dover,

New York, 1957)W.L. Schaaf, A Bibliography of Recreational Mathematics. A Guide to the Literature, 3rd edn.

(National Council of Teachers of Mathematics, Washington, DC, 1970)J.F. Scott, The Scientific Work of René Descartes (Taylor & Francis, London, 1952)J.F. Scott, A History of Mathematics from Antiquity to the Beginning of the Nineteenth Century

(Taylor & Francis, London, New York, 1969)J.F. Scott, The Mathematical Works of John Wallis, D.D., F.R.S. (1616–1703) (Chelsea, New York,

1981)A. Seidenberg, The origin of mathematics. Arch. Hist. Exact Sci. 18, 301–342 (1978)C. Seife, Zero: The Biography of a Dangerous Idea (Viking, New York, 2000)G.E. Sen, The Pageant of Indian History (David McKay Co., New York, 1948)S.K. Sen, R.P. Agarwal, �; e; � with MATLAB: Random and Rational Sequences with Scope in

Supercomputing Era (Cambridge Scientific Publishers, Cambridge, 2011)S.N. Sen, A.K. Bag, The Sulbasutras (Indian National Science Academy, New Delhi, 1983)K. Shen, J.N. Crossley, A.W.C. Lun, The Nine Chapters on the Mathematical Art (Oxford

University Press and Science Press, Beijing, 1999)K.S. Shukla, Aryabhatiya of Aryabhata with the Commentary of Bhaskara I and Somesvara (Indian

National Science Academy, New Delhi, 1976)G.F. Simmons, Calculus Gems: Brief Lives and Memorable Mathematics (McGraw-Hill,

New York, 1992)J. Singh, Great Ideas of Modern Mathematics: Their Nature and Use (Dover, New York, 1959)S. Singh, J. Lynch, Fermat’s Enigma: The Epic Quest to Solve the World’s Greatest Mathematical

Problem (Bantam Books, New York, 1998)D.E. Smith, L.C. Karpinski, The Hindu–Arabic Numerals (Ginn, Boston, 1911)D.E. Smith, Y. Mikami, A History of Japanese Mathematics (Open Court, Chicago, 1914)D.E. Smith, History of Mathematics, vol. 2 (Dover, New York, 1958)D.E. Smith, A Source Book in Mathematics (Dover, New York, 1959)

460 Bibliography

D.E. Smith, J. Ginsburg, A History of Mathematics in America Before 1900 (Arno, New York,1980)

D. Solow, How to Read and Do Proofs (Wiley, New York, 1990)D.A. Somayaji, A Critical Study of the Ancient Hindu Astronomy (Karnataka University, Dharwar,

1971)N. Spielberg, B. Anderson, Seven Ideas that Shook the Universe (Wiley, New York, 1987)L.A. Steen, On the Shoulders of Giants: New Approaches to Numerary (National Academy Press,

Washington, DC, 1990)L.A. Steen (ed.), Mathematics Today (Springer, New York, 1978)S. Stein, Archimedes: What Did He Do Besides Cry Eureka? (MAA, Washington, DC, 1999)S. Stein, Mathematics: The Man Made Universe (Dover, New York, 2000)J. Stillwell, Mathematics and Its History (Springer, New York, 1989)D.J. Struik, A Sourcebook in Mathematics, 1200–1800 (Princeton University Press, Princeton,

1986)D.J. Struik, A Concise History of Mathematics, 4th edn. (Dover, New York, 1987)B.V. Subbarayappa, K.V. Sarma (eds.), Indian Astronomy, a Source Book (Nehru Center, Bombay,

1985)J.W.N. Sullivan, The History of Mathematics in Europe, from the Fall of Greek Science to the Rise

of the Conception of Mathematical Rigour (Oxford University Press, New York, 1925)J. Suzuki, A History of Mathematics (Prentice Hall, Upper Saddle River, 2002)F.J. Swetz, T.S. Ang, A brief chronological guide to the history of Chinese mathematics. Hist.

Math. 11, 39–56 (1984)F.J. Swetz (ed.), From Five Fingers to Infinity (Open Court, Chicago, 1994)I. Todhunter, A History of the Mathematical Theory of Probability from the Time of Pascal to that

of Laplace (Chelsea, New York, 1949)H.W. Turnbull, The Great Mathematicians (New York University Press, New York, 1969)B.L. van der Waerden, Science Awakening, Translated by A. Dresden (Kluwer, Dordrecht, 1975)B.L. van der Waerden, Geometry and Algebra in Ancient Civilizations (Springer, Berlin, 1983)B.L. van der Waerden, A History of Algebra (Springer, Berlin, 1985)B. van Nooten, Binary numbers in Indian antiquity. J. Indian Philos. 21, 31–50 (1993)V.S. Varadarajan, Algebra in Ancient and Modern Times (American Mathematical Society,

Providence, 1998)K. Venkatachalam, Bharateeya Sakamula (Arya Vijnanadeepa Publications, Vijayawada, 1950)K. Venkatachalam, The Plot in Indian Chronology (Arya Vijnanadeepa Publications, Vijayawada,

1950)F. Viéte, The Analytic Art, Translated by T.R. Witmer (Kent State University Press, Kent„ 1983)A. Weil, Number Theory: An Approach Through History: From Hammurabi to Legendre

(Birkhäuser, Boston, 1983)D.G. Wells, You Are a Mathematician: A Wise and Witty Introduction to the Joy of Numbers (Wiley,

New York, 1997)R.S. Westfall, Never at Rest: A Biography of Isaac Newton (Cambridge University Press,

Cambridge, 1980)H. Weyl, Philosophy of Mathematics and Natural Science (Princeton University Press, Princeton,

1949)E. Whittaker, From Euclid to Eddington (Dover, New York, 1958)N. Wiener, I Am a Mathematician: The Later Life of a Prodigy (Doubleday, New York, 1956)R.L. Wilder, The Foundations of Mathematics (Wiley, New York, 1965)R.L. Wilder, The Evolution of Mathematical Concepts: A Historical Approach (Wiley, New York,

1968)M. Williams, A History of Computing Technology (Prentice-Hall, Englewood Cliffs, 1995)E. Zebrowski, A History of the Circle: Mathematical Reasoning and the Physical Universe

(Rutgers University Press, Piscataway, 1999)M.C. Zeller Sr., The Development of Trigonometry from Regiomontanus to Pitiscus (Edwards

Brothers, Ann Arbor, 1946)

Name Index

Aal-Mamun (786–833), 105, 106, 108al-Mansur/Messala/Messahalla, Caliph

(714–775), 105al-Mutasim (around 794–842), 108al-Mutawakkil (822–861), 108al-Rashid, H. (766–809), 105al-Shatir, A. (1304–1375), 125al-Tusi, N. (1201–1274), 121al-Wafa, A. (940–998), 10al-Wathiq (816–847), 108Ammal, J., 369Ammal, P., 376Ammannati, G. (1538–1620), 151Ampére, A.-M. (1775–1836), 251, 280Amyclas, 70Anaxagoras of Clazomanae (500–428 BC), 61Anaximander of Miletus (around 610–547

BC), 52–53Anaximenes of Miletus (around 585–525 BC),

54Anderson, B., 18Anderson, C.A. (1940–), 401Andrews, G. (1938–), 370Andrews, P.B. (1937–), 401Andronicus II (1259–1332), 124Andronov, A.A. (1901–1952), 413Anne, F., 270Anne, O., 357Anne, Q. (1665–1714), 184Anthemius of Tralles (around 474–558), 99Anthony, H.D., 368Antiphon of Rhamnos (around 480–411 BC),

64Apastamba, 40, 41

Apollo, 71, 156Apollonius of Perga (around 262–200 BC),

83–84Appel, K. (1932–2013), 35, 36Appell, P.É. (1855–1930), 327Aquinas, S. (1225–1274), 163Arago, D.-F.-J. (1786–1853), 233, 262Aratus (around 315–240 BC), 85, 94Archimedes of Syracuse (287–212 BC), 78–80Archytas of Tarentum (around 428–347 BC),

68Argand, J.-R. (1768–1822), 221Ariosto (1474–1533), 151Aristaeus of Croton (about 400 BC), 71Aristaeus the Elder (around 370–300 BC), 74Aristarchus of Samos (310–250 BC), 77–78Ariston of Chios (flourished about 250 BC),

81Aristotle (around 384–322 BC), 72–73Arsinoe (around 305–248 BC), 81Artin, E. (1898–1962), 320Aryabhatta (born 2765 BC), 7, 12, 21, 41–43,

86, 109Askey, R. (1933–), 370Asmussen, O., 326Asoka, 87Atanasoff, J.V. (1903–1995), 28Athari, M. (740–815), 105Athenaeus (flourished about 200), 81Atiyah, E. (1903–1964), 436, 437Atiyah, M.F. (1929–), 436–437Aubrey, J. (1626–1697), 176Auguste, de Thou (1553–1617), 146Augustine, S. (354–430), 52Autolycus of Pitane (360–290 BC), 96

© Springer International Publishing Switzerland 2014R.P. Agarwal, S.K. Sen, Creators of Mathematical and Computational Sciences,DOI 10.1007/978-3-319-10870-4

461

462 Name Index

Ayyangar, C.N.S., 368Ayyar, C.S. (1885–1960), 415

BBabbage, C. (1791–1871), 240–241Babuška, I.M. (1926–), 434Bach, J.S. (1685–1750), 427Bachmann, P.G.H. (1837–1920), 289Backus, J.W. (1924–2007), 432Bacon, F. (1909–1992), 17Bacon, R. (1214–1294), 15–17Bailly, J.-S. (1736–1793), 211Baire, R. (1874–1932), 317, 332Bairstaw, U. (1880–1963), 352Bairstow, L. (1880–1963), 352Baker, H.F. (1866–1956), 369Baker, W.R.G. (1892–1960), 448Bakhshali Manuscript (about 200 BC), 84Balakrishnan, S. (1891–1931), 415Ball, W.W.R. (1850–1925), 21Balzan, E. (1874–1953), 435, 444Banach, S. (1892–1945), 382–383, 389Banarsidass, M., 365Banneker, B. (1731–1806), 210Barrow, I. (1630–1677), 175, 176, 181, 182Barry, G. (1894–1986), 336Bartels, J.C.M. (1769–1836), 223–224, 241Bashforth, F. (1819–1912), 269Bass, H. (1932–), 421Bateman, H. (1882–1946), 357Battaglini, G. (1826–1894), 314Baudhayana (born 3200 BC), 40, 41Bauer, G., 329Becker, R. (1887–1955), 392Bedé, V. (673–735), 104Beg, U. (1393–1449), 128, 129Bell, E.T. (1883–1960), 4, 17, 29, 168Bellarmino, C.R. (1542–1621), 153Bellavitis, G. (1803–1880), 188, 251Beltrami, E. (1835–1900), 77Bénard, H.C. (1874–1939), 413Bendixson, I.O. (1861–1935), 14, 316–317Benedetti, G. (1530–1590), 153Benedict XIV, Pope (1675–1758), 155, 206,

209Berenice, 75Berkeley, B.G. (1685–1753), 183Bernays, P.I. (1888–1977), 353Berndt, B.C. (1939–), 370Berners-Lee, T.J. (1955–), 32Bernoulli, D. (1700–1782), 200, 201, 203, 208,

222

Bernoulli, Jacob (1654–1705), 12, 125, 158,189, 197

Bernoulli, Johann (1667–1748), 12, 193,201–203

Bernoulli, N. (1695–1726), 199Bernstein, F. (1878–1956), 294Bernstein, J. (1945–), 422Bernstein, S.N. (1880–1968), 272Berthollet, C.C.L. (1748–1822), 237Besant, A. (1847–1933), 364Bessarion, C. (1403–1472), 130Bessel, F.W. (1784–1846), 234Betti, E. (1823–1892), 288, 316Bézout, É. (1730–1783), 232Bhabha, H.J. (1909–1966), 16, 395, 430Bhagavantam, S. (1909–1989), 378Bhaskara I (before 123 BC), 9, 11, 86, 88, 91,

108, 128Bhaskara II/Bhaskaracharya (working 486), 7,

10, 13, 89, 100–102, 128, 137, 168Bhatnagar, P.L. (1912–1976), 417–418Bhatnagar, S.S. (1894–1955), 428, 450Bhattathiri, M.N. (1559–1632), 127, 150Bianchi, L. (1856–1928), 303Bianconi, M.-L. (1880–1950), 331Bias of Priene (about 600 BC), 50Bidder, G.P. (1806–1878), 280Bieberbach, L.G.E.M. (1886–1982), 374Bienaymé, J. (1796–1878), 271Biham, E., 448Bille, B. (1526–1605), 147Binet, J.P.M. (1786–1856), 235Bingham, C., 381Biot, J.B. (1774–1862), 235Birkhoff, G. (1911–1996), 352, 363, 397Birkhoff, G.D. (1884–1944), 351, 362–363Blackwell, D.H. (1919–2010), 429Bliss, G.A. (1876–1951), 341–342, 358Blumenthal, L.O. (1876–1944), 321Bôcher, M. (1867–1918), 8, 329Bode, J.E. (1747–1826), 227Boethius, A.M.S. (around 475–526), 99–100,

120Bohr, A. (1922–2009), 368Bohr, C. (1855–1911), 367Bohr, E.A. (1860–1930), 367Bohr, H.A. (1887–1951), 367Bohr, N.H.D. (1885–1962), 367–368Bolibruch, B., 321Boltzmann, L.E. (1844–1906), 311Bolyai, F.W. (1775–1852), 229, 250Bolyai, J. (1802–1860), 229, 250, 404, 446Bolza, O. (1857–1942), 342

Name Index 463

Bolzano, B.P.J.N. (1781–1848), 233–234Bombelli, R. (1526–1573), 143–144Bombieri, E. (1940–), 444Bonaparte, N. (1769–1821), 212Boncompagni, B. (1821–1894), 106Boole, G. (1815–1864), 265Boole, J. (1777–1848), 265Boole, M.E. (1832–1916), 241Borel, A. (1923–2003), 431Borel, F.É.J.É. (1871–1956), 232–233Born, M. (1882–1970), 391Borromeo, C.F. (1564–1631), 164Borsuk, K. (1905–1982), 376Bortolotti, E. (1866–1947), 143Bose, A., 385Bose, Satyendra N. (1894–1974), 385–387Bose, Surendra N., 385Boškoviæ, R.J./Roger J.B. (1711–1787), 206Bosse, A. (1602–1676), 160Bossut, C. (1730–1814), 214Bothwell, A. (around 1527–1593), 148Bott, R. (1923–2005), 438Bouquet, J.-C. (1819–1885), 314Bourbaki, N. (1939–), 443–444Boussinesq, J.V. (1842–1929), 297Bouvelles, C. (around 1470–1553), 152Bowditch, N. (1779–1838), 217Boyle, R. (1627–1691), 176Braga, G.M., 449Brahe, O. (1518–1571), 147Brahe, T. (1546–1601), 147Brahmagupta (born 30 BC), 7, 8, 10, 11,

88–89, 91, 104, 107, 109Brauer, R.D. (1901–1977), 355Breit, G. (1899–1981), 395Brianchon, C.J. (1785–1864), 234–235Briggs, H. (1561–1630), 148Brioschi, F. (1824–1897), 288Briot, S., 314Brömmel, L., 281Brougham, L. (1778–1868), 231Brouncker, W.V. (1620–1684), 12, 101, 171,

190Brouwer, L.E.J. (1881–1966), 353–354Brown, L., 437Brown, R. (1773–1858), 347Bruce, C.W. (1816–1900), 416Bruce, E., 269Bruhat, F.G.R. (1929–2007), 424Bruno, G. (1548–1600), 129Brusentsov N. (1925–), 30Bryson of Heraclea (about 450 BC), 68Buddha, Gautama (1887–1807 BC), 17, 45, 59Buniakovski, V.J. (1804–1899), 254

Bunsen, R.W.E. (1811–1899), 246, 280Burali–Forti, C. (1861–1931), 300Bürgi, J. (1552–1632), 150Buridan, J. (around 1300–1358), 154Busby, R. (1606–1695), 176Bush, G.W., 428Bush, V. (1890–1974), 31Buxton, J. (1707–1772), 280Byron, L. (1788–1824), 264

CCaccini, F.T. (1574–1648), 153Caddenhead, 178Cahn, A. (1922–1999), 434Calabi, E. (1923–), 447Callimachus (around 310–240 BC), 81Callippus of Cyzicus (around 370–300 BC), 74Campanus of Novara (around 1220–1296), 122Campbell, J.F. (1821–1885), 270Cannon, J. (1943–), 445Cantelli, F.P. (1875–1966), 332Cantor, G. (1845–1918), 298–301Carathéodory, C. (1873–1950), 253, 336, 342,

354, 372, 373Cardano, F. (1444–1524), 137Cardano, G. (1501–1576), 7, 137–140Carmichael, R.D. (1879–1967), 350–351Carnap, R. (1891–1970), 302Carnot, L. (1753–1823), 220Carr, G.S. (1837–1914)), 368Cartan, É.J. (1869–1951), 258, 296, 402Cartan, H. (1904–2008), 402–403, 421, 434,

443Carter, J. (1924–), 442Casorati, F. (1835–1890), 288–289Cassini, G.D. (1625–1712), 191, 196Cassini, J. (1677–1756), 196Castelli, B. (1578–1643), 164Castillon, J. (1704–1791), 202Cataldi, P.A. (1552–1626), 149Catherine, Queen, 147, 171, 205, 416Cauchy, A.-L. (1789–1857), 237–239Cavalieri, B.F. (1598–1647), 164–165Cayley, A. (1821–1895), 273–274Celsius, A. (1701–1744), 201Celsius, M. (1621–1679), 201Celsius, N. (1658–1724), 201Cesáro, E. (1859–1906), 314–315Cesi, M.F., 153Challis, J., 268Chanakya, 18Chandra, H. (1923–1983), 395, 430–431Chandrasekhar, S. (1910–1995), 415–416

464 Name Index

Chapman, S. (1888–1970), 400Charak, A. (before 600 BC), 53Charles I, 164Charles II, King of Britain (1630–1685), 164,

169, 171, 190Charles V, Holy Roman Emperor, 141Charles V, King of France (1338–1380), 125Chasles, C.-H., 243Chasles, M.F. (1793–1880), 243, 296Chastellet, F.C., 202Chatterjee, S.K., 378, 379Chauvenet, W. (1870–1920), 342Chebyshev, P.L. (1821–1894), 271–272Chennus, P., 84Cheops (flourished about 2680 BC), 43Chern, S–S. (1911–2004), 410, 447Chevalley, C. (1909–1984), 291Chih, Tsu Chih/Chongzhi (429–500), 98–99Chilon of Sparta (about 600 BC), 51Chitrabhanu (about 1530), 144Chiu-Shao, Ch’in (around 1202–1261),

121–122Cholesky, A.-L. (1875–1918), 337Christina, Queen (1626–1689), 162Christoffel, E.B. (1829–1900), 227, 283–284Chrystal, G. (1851–1911), 358Chudnovsky, G.V. (1952–), 320Chuquet, N. (around 1445–1488), 131–132Church, A. (1903–1995), 401Cimabue (1240–1302), 163Ciompa, P., 18Clairaut, A.C. (1713–1765), 207, 233Clasen, B.I., 296Clavius, C. (1537–1612), 145Clebsch, R.F.A. (1833–1872), 287Clement VIII, Pope (1536–1605), 103Cleobulus of Lindos (about 600 BC), 50–51Cleomedes (about 20), 80Clifford, W.K. (1845–1879), 298Cock, C., 176Cohen, A., 440Cohen, M., 440Cohen, P.J. (1934–2007), 14, 319, 440Colburn, Z. (1804–1840), 280Cole, A.L., 414Cole, F.N. (1861–1926), 337Colladon, J.-D. (1802–1893), 251Collins, J. (1625–1683), 175Colson, J. (1680–1760), 209Conant, L.L. (1857–1916), 450Conon of Samos (about 245 BC), 83Converse, W., 292Conway, J. (1937–), 443Cooley, J.W. (1926–), 32

Copernicus, N. (1473–1543), 133–134Copley, G. (1653–1709), 233Cotes, R. (1682–1716), 197Coulomb, J. (1904–1999), 443Countess of Lovelace (1815–1852), 256, 264Courant, R. (1888–1972), 379–380Coxeter, H.S.M. (1907–2003), 315Crafoord, H. (1908–1982), 426Craig, J. (1663–1731), 193Cramer, A.M., 201Cramer, G. (1704–1752), 201–202Cramér, H. (1893–1985), 429Cramer, J., 201Crelle, A.L. (1780–1855), 248Cremona, L. (1830–1903), 314Croesus, 51Cromwell, O. (1599–1658), 164Crookes, 311Crosio, C., 313Cross, W.L. (1862–1948), 468Ctesibius of Alexandria (working 285–222

BC), 81Cuneiform Tablets (about 2000 BC), 4, 6, 7,

43–45Curie, Madame (1867–1934), 386Cyzicenus, 70

Dda Coi, Z.T. (about 1530), 144da Vinci, L. (1452–1519), 137, 160d’Alembert, J.R. (1717–1783), 208, 213, 216,

226, 239Damo, 60Damodara (around 1410–1510), 131, 136Dán, K., 399Dandelin, G.P. (1794–1847), 242Dante, 123, 163, 338Dantzig, G.B. (1914–2006), 363Dantzig, T. (1884–1956), 363Darboux, J.G. (1842–1917), 296Darley, R., 169Darwin, C.R. (1809–1882), 15, 177Darwin, F. (1848–1925), 1Dase, J.M.Z. (1824–1861), 279–280Davenport, H. (1907–1969), 390Davidov, A. (1823–1885), 301Davis, M.D. (1928-), 401de Bardi, N., 232de Bessy, B.F. (around 1605–1675), 166de Buffon, C. (1707–1783), 201de Bure, A., 238de Condorcet, M. (1743–1794), 213de Coulomb, C.-A. (1736–1806), 395

Name Index 465

de Fermat, P. (1601–1665), 165–168de Giorgi, E. (1928–1996), 321de Grouchy, S. (1764–1822), 213de La Hire, L. (1606–1656), 179–180De la Hire, P. (1640–1719), 179–180de la Ramée, P. (1515–1572), 142de la Roche, E. (about 1480), 131de la Vallée–Poussin, C. (1866–1962), 219,

226, 343de Lacaille, A.N.L. (1713–62), 211de Lespinasse, J. (1732–1776), 208de Maupertuis, P.L.M. (1698–1759), 201de Méziriac, C.G.B. (1581–1638), 158–159De Moivre, A. (1667–1754), 194, 195, 201De Morgan, A. (1806–1871), 24, 205,

256–257, 262, 264, 265, 273, 274, 294,303, 323

de Possel, R. (1905–1974), 443de Prony, M.R. (1755–1839), 220de Rham, G. (1903–1990), 410de Richelieu, D., 202de Roberval, G.P. (1602–1675), 12, 169de Saint-Lambert, M., 203de Saint-Venant, A. (1797–1886), 287, 297de Saint-Vincent, G. (1584–1667), 287, 297de Tencin, Madame (1682–1749), 208de Thou, J.A. (1553–1617), 146de Torquemada, T., 143de Véretz, C.O. (died 1905), 297de Villa Dei, A., 106De Witt, J. (1625–1672), 175Debreu, G. (1921–2004), 439Debye, P. (1884–1966), 392Dedekind, J.L.U., 284Dedekind, J.W.R. (1831–1916), 14, 15, 71,

167, 255, 278, 282, 284–285Dehn, M. (1878–1952), 319, 321del Ferro, S. (1465–1526), 132–133, 135, 136Delambre, J.B. (1749–1822), 235Democritus of Abdera (around 460–362 BC),

66–67Demylus, 62Denjoy, A. (1884–1974), 339, 388Desargues, G. (1591–1661), 160, 179Descartes, R. (1596–1650), 8, 12, 15, 83, 98,

117, 125, 150, 158–165, 169, 170, 172,173, 181, 182, 189, 221

Desestre, M.-M., 237Deslartes, J. (1903–1968), 443Destouches, C.L.-C. (1668–1726), 208Devi, S. (1929–2013), 280Dewey, J. (1859–1952), 334di Agnesi, P., 208Diamond, F. (1964–), 168

Dicaearchus of Messana (around 350–285BC), 74–75

Dickson, L.E. (1874–1954), 336–337Diderot, D. (1713–1784), 205, 208Dieck, A., 365Dieudonné, J. (1905–1992), 443Dijkstra, E.W. (1930–2002), 437Dini, U. (1845–1918), 314, 338Dinostratus (around 390–320), 71Diocles (around 240–180 BC), 84Diocletian (284–305), 96Diodorus (florished about 60 BC), 79Dionysodorus of Caunus (around 250–190

BC), 7Diophantus of Alexandria (about 250), 95–96Dirac, F., 394Dirac, P.A.M. (1902–1984), 395Dirichlet, P.G.L. (1805–1859), 4, 236,

254–255, 259, 270, 274, 277, 278, 283,285, 286, 324

Dodgson, C.L./Lewis Carroll (1832–1898), 8,285–286

Doll, W.R.S. (1912–2004), 381Donaldson, S.K. (1957–), 437Donnan, F.G. (1870–1956), 292Donsker, M.D. (1925–1991), 444, 445Dora, 334Doraiswamy, L., 415Dorodnow, A.W., 66D’Ovidio, E. (1842–1933), 313Draper, C.S. (1901–1987), 432Dreyfus, A., 327Droppers, J.G., 362du Bois–Reymond, E. (1818–1896), 311Dubost, A. (1842–1921), 330Duhem, P.-M.-M. (1861–1916), 292Duke Wilhelm of Cleve (1516–1592), 141Dvoretzky, A. (1916–2008), 396Dwaipayana, Krishna/Veda Vyasa (born 3374

BC), 38–40

EEarl of Bothwell (1534–1578), 148Eckertm, J.A.P. Jr. (1919–1995), 29, 30Eddington, A.S. (1882–1944), 348Edward VI, King (1537–1553), 140Egorov, A.D., 400Egorov, D.F. (1869–1931), 360Ehresmann, C. (1905–1979), 443Eickemeyer, R., 326Eileen, R., 381Eilenberg, S. (1913–1998), 420–421Einstein, A. (1879–1955), 346–350

466 Name Index

Einstein, H. (1847–1902), 346Einstein, P. (1858–1920), 346Eisenhart, L.P. (1876–1965), 342, 358Eisenhower, D.D. (1890–1969), 30, 397Eisenlohr, 49Eisenstein, F.G. (1823–1852), 167, 235, 254,

283, 410Elizabeth, B., 269Elizabeth II Queen, 381Elizabeth, Margaret, 363Elizabeth, Marnie, 357Elizabeth Protestant Queen, 141, 194Émilie, M.C.-L. (1706–1749), 202–203Encke, J.F. (1791–1865), 274Epicureans (founded around 307 BC), 77Eratosthenes of Rhodes (around 276–194 BC),

81–82Erdös, P. (1913–1996), 351, 419–420Etienne, 172, 232, 327Eubulides (about 400 BC), 308Euclid of Alexandria (around 325–265 BC),

75–77Euclid of Megara (around 435–365 BC), 75Eudemus of Rhodes (around 350–290 BC), 83Eudoxus of Cnidus (around 400–347 BC),

70–71Euler, L. (1707–1783), 4, 10, 13, 66, 101, 162,

166, 167, 196, 197, 199, 201, 203–205,208, 209, 211, 213, 217, 222, 226, 235,246, 248, 258, 272, 281, 342, 420

Euphorbus, 59Eurytas of Metapontum (around 400 BC), 69Eutocius of Ascalon (around 480–540), 68Euwe, M. (1901–1981), 354Everest, G. (1790–1866), 241, 265Exner, F. (1849–1926), 371

FFahrenheit, G.D. (1686–1736), 198Fairfax, M.C., 231–232Fairfax, W.G. (1739–1813), 231Fatou, L.P.J. (1878–1929), 345Faulhaber, J. (1580–1635), 158Fechner, G. (1801–1887), 18Feige, U., 448Feigenbaum, M.J. (1944–), 446Fejér, L. (1880–1959), 336, 351–352Fekete, M. (1886–1957), 396Ferguson of Raith (1723–1816), 215Fermi, E. (1901–1954), 398Ferrari, L. (1522–1565), 7, 136, 138, 142–143Feynman, R. (1918–1988), 292, 399, 412Fiat, A. (1957–), 448

Fibonacci/Leonardo of Pisa (around1170–1250), 118–119

Fields, J.C. (1863–1932), 424Filippa, 132Finch, E. (1900–1978), 335Finé, O. (1494–1555), 134Fiore, A.M. (about 1506), 133, 135, 136Fischer, E.K.B. (1824–1907), 311Fisher, G., 380Fisher, K., 380Fisher, R.A. (1890–1962), 380–381, 428Flaccus, Q.H., 151Flamsteed, J. (1646–1719), 187, 190, 192Florensky, P.A. (1882–1937), 360Fontana, N./Tartaglia (1500–1557), 7, 135–136Fontenelle, 201Föppl, A.O. (1854–1924), 340Forsyth, A.R. (1858–1942), 16, 274Fourier, J.B.J. (1768–1830), 221–223, 245,

251, 252Fowler, R.H. (1889–1944), 415Fowler, W.A. (1911–1995), 415Francis, Grand Duke of Tuscany, 206Franck, J. (1882–1964), 391Frankel, A.H. (1891–1965), 14Franklin, B. (1706–1790), 213Fréchet, M.R. (1878–1973), 346Frederick II, Emperor (1194–1250), 118Fredholm, E.I. (1866–1927), 8, 258, 316, 328Frege, F.L.G. (1848–1925), 300–302, 333Frend, S., 257Frend, W., 264Frenet, J.F. (1816–1900), 223Fresnel, A.J. (1788–1827), 174Frey, G. (1944–), 167Fricke, R. (1861–1930), 303Friedrichs, K.O. (1901–1982), 380Frisius, G. (1506–1555), 141Frobenius, F.G. (1849–1917), 8, 266, 336, 342Fuchs, I.L. (1833–1902), 287–288Fuchs, W.H.J. (1915–1997), 443Fuks, D.B., 422Fulkerson, D.R. (1924–1976), 450Fuller, T. (1710–1790), 280Furtwängler, P. (1869–1940), 390, 408

GGabriel-Philippe (1677–1719), 180Gadbled, C. (1734–1782), 216Galenus, C. (129–217), 115Galilei, G. (1564–1642), 151–155Galilei, V. (1521–1591), 151Gallai, T. (1912–1992), 264

Name Index 467

Galöis, E. (1811–1832), 260–261Galton, F. (1822–1911), 276–277Gamba, M., 154Gamow, G., 322Gandhi, M.K. (1869–1948), 6Ganea, T. (1922–1971), 421Garfield, J.A. (1831–1881), 22Garga, 87Gause, G.F., 252Gauss, K.F. (1777–1855), 225–231Gay-Lussac, 218Geiser, K.F. (1843–1934), 373Geissler, J.H.W. (1814–1879), 246Gelfand, I.M. (1913–2009), 421–422Gelfand, S., 422Gelfond, A.O. (1906–1968), 404Gelfond, O.I., 404Gelon, King (around 230 BC), 78Geminus of Rhodes (around 10 BC-60 AD), 89Genocchi, A. (1817–1889), 313Gentzen, G. (1909–1945), 319George VI, King (1895–1952), 335Gerbert d’Aurillac (945–1003), 114Gergonne, J. (1771–1859), 237Germain, M.-S. (1776–1831), 224–225Gershgorin, S.A. (1901–1933), 408Gerson, L. (1288–1344), 172Gherardo of Cremona (around 1114–1187), 42Ghosh, A. (1872–1950), 364Ghosh, J.C. (1894–1959), 385Ghosh, U., 385Gibbs, J.W. (1839–1903), 291–292Gilbert, W.S. (1836–1911), 304Ginsburg, J., 111Ginzburg, V.L. (1916–2009), 412Girard, A. (1595–1632), 160Glauert, 341Gleason, A. (1921–2008), 319Glyde, S. (1619–1695), 169Gödel, K.F. (1906–1978), 404–407Gödel, R., 404Gokhale, G.K. (1866–1915), 364Goldbach, C. (1690–1764), 199Goleniscev, V. (1856–1–947), 49Gonzalo, C.F., 143Goode, H.H. (1909–1960), 441Gopala, 103Gordan, P.A. (1837–1912), 287Gosselin, G. (1536–1600), 144Goursat, É.J.-B. (1858–1936), 296Govindasvami/Govindasvamin/Govindaswami

(around 800–860), 108Gräffe, K.H. (1799–1873), 242Grafius, M.E., 363

Gram, J.P. (1850–1916), 304–305Grandi, L.G. (1671–1742), 195–196Grassmann, H.E., 258Grassmann, H.G. (1809–1877), 257–258Graunt, J. (1620–1674), 170–171Great Pyramid at Gizeh (erected around 2600

BC), 43Green, B.J. (1977), 451Green, G. (1793–1841), 242–243Gregory, D.F. (1813–1844), 273Gregory, J. (1638–1675), 177–179Greig, C.S., 231Grimaldi, Jesuit, 186Grimm, P., 203Gromov, M.L. (1943–), 445–446Gross, E.P. (1926–1991), 418Gudermann, C. (1798–1852), 266Guggenheim, 431Guldin, P. (1577–1643), 96Gunter, E. (1581–1626), 158Gutenberg, J. (around 1400–1468), 132Guy, W.A. (1810–1885), 428

HHaar, A. (1885–1933), 339Hadamard, A., 326Hadamard, J.S. (1865–1963), 326–328Hadley, J. (1682–1744), 182Hahn, H. (1879–1934), 375Haken, W. (1928–), 36Hakim, Caliph (985–1021), 115Halayudha (about 975), 61Haldane, J.B.S. (1892–1964), 18Hales, T.C. (1958–), 320Halley, E. (1656–1742), 190–192Halsted, G.B. (1853–1922), 336Hamel, G.K.W. (1877–1954), 319Hamilton, J. (1512–1571), 139Hamilton, W. (1788–1856), 17Hamilton, W.D. (1936–2000), 381Hamilton, W.R. (1805–1865), 255–256Hamming, R.W. (1915–1998), 422–423Hammurabi, King (1792–1750 BC), 43ha-Nasi, A.B.H. (1070–1136), 117Hankel, H. (1839–1873), 258Hardy, G.H. (1877–1947), 343–345Hardy, I., 343Hardy, S.H., 343Harnack, C.G.A. (1851–1888), 305Harnack, T. (1817–1889), 305Harriot, T. (1560–1621), 150Harvey, W. (1578–1657), 163Hasse, H. (1898–1979), 389–390

468 Name Index

Hausdorff, F. (1868–1942), 330Hawking, S. (1942–), 395Heath, R., 205Heaviside, O. (1850–1925), 291Hecataeus of Miletus (around 550–476 BC),

52Hecke, E. (1887–1947), 321Hegel, G.W.F. (1770–1831), 225Heine, H.E. (1821–1881), 270–271Heisenberg, K.E.A., 390Heisenberg, W.K. (1901–1976), 390–393Hempel, C.G. (1905–1997), 321Heng, Z. (78–139 AD), 91–92Henkin, L.A. (1921–2006), 401Henrion, D. (1580–1632), 58Henry III, King (1551–1589), 145Henry IV, King (1553–1610), 145Henry VIII (1491–1547), 124Hensel, K. (1861–1941), 278Hera in Tarentum, 59Herglotz, G. (1881–1953), 380Hermann, J. (1678–1733), 197Hermeas, King, 72Hermite, C. (1822–1901), 275–276Hermotimus, 70Hero of Byzantium, 81Herodotus (around 484–425 BC), 43Heron of Alexandria (about 75 AD), 90–91Herrejoni, 110Herschel, C. (1750–1848), 231Herschel, F.W. (1738–1822), 241Hertz, H. (1857–1892), 8Hesse, L.O. (1811–1874), 261Hevelius, J. (1611–1687), 190Heydrich, R.T.E. (1904–1942), 392Hiero II (around 307–216 BC), 78Hilbert, D. (1862–1943), 318–323Hilbert, F. (1893–1969), 318Hildebrandt, T.H. (1888–1980), 438Hill, A.B. (1897–1991), 381Hill, G.W. (1838–1914), 290Himmler, H. (1900–1945), 392Hipparchus (around 190–120 BC), 84–85Hippasus of Metapontum (about 500 BC), 61Hippias of Elis (about 460 BC), 66Hippocrates of Chios (about 470 BC), 65–66Hitler, A. (1889–1945), 332Hittorf, J.W. (1824–1914), 246Hoare, C.A.R. (1934–), 441Hobbes, T. (1588–1679), 170Hobson, E.W. (1856–1933), 369Hodge, W.V.D. (1903–1975), 434Hoecke, V., 140Hölder, O.L. (1859–1937), 315

Holmboe, B.M. (1795–1850), 249Homer (around 800–700 BC), 80Hooke, R. (1635–1703), 176–177Hopf, H. (1894–1971), 412Hopper, G.M. (1906–1992), 407–408Horace (65–8 BC), 25Horner, W.G. (1786–1837), 121Horowitz, 245Householder, A.S. (1904–1993), 402Hui, Liu (around 220–280), 93–94Hui, Yang (1238–1298), 123–124Hull, M.D., 415Hurewicz, W. (1904–1956), 401–402Hurwitz, A. (1859–1919), 266Hutton, J. (1726–1797), 216Huxley, A. (1894–1963), 185Huygens, C. (1629–1695), 173–174Hypatia of Alexandria (370–415), 97–98Hypsicles (around 190–120 BC), 83

IIamblichus (around 245–325), 94–95ibn Ezra, A.M. (around 1090–1167), 118ibn Luqam, Q. (died 912), 123ibn Tariq, Y. (died about 796 AD), 106ibn Tibbon, J.M. (around 1236–1304), 123Ignacy, 372Inaudi, J. (1867–1950), 280Innocent XIII, Pope (1655–1724), 103Isidore of Seville (560–636), 103Isidorus of Miletus (about 540), 102Iyer, R.C. (born 1866), 376

JJacobi, C.G.J. (1804–1851), 252–253Jaimani, 38James VI, King (1566–1625), 148James, W. (1842–1910), 294Jamesome, M., 178Janiszewski, Z. (1888–1920), 374–375Jarden, D., 23Jeanne, 297Jefferson, T. (1743–1826), 210Jelinek, F. (1932–2010), 443Jerosch, K., 318Jing-Run, C. (1933–1996), 439Johannes Widman of Eger (1460–1500), 221John of Seville (about 1125), 106John Paul II, Pope (1920–2005), 155John, St., 149, 394Jones, P.S., (Not cited in the text)Jones, W.W., 41

Name Index 469

Jordan, M.E.C. (1838–1922), 290–291Jordan, W. (1842–1899), 295–296Joseph, G.G., 127Joseph, H., 365Jourdain, P.E.B. (1879–1919), 308Julia, G.M. (1893–1978), 383Julia, P.G., 435Justinian, Emperor (483–565), 69Jyesthadevan (around 1500–1600), 136–137

KKaczmarz, S. (1895–1939), 372Kagan, V.F. (1869–1953), 319Kaiser Rudolph II, Emperor (1552–1612), 155Kakutani, S. (1911–2004), 397Kale, L., 431Kalmár, L. (1905–1976), 403Kamil, A. (850–930), 112Kanaka, 107Kanellakis, P.C. (1953–1995), 448Kanigel, R. (1946–), 370Kant, I. (1724–1804), 225Kapitsa, P. (1894–1984), 411Karmarkar, N. (1957–), 449Karnaugh, M. (1924–), 433Kasiski, F. (1805–1881), 240Kästner, A.G. (1719–1800), 223Katyayana, 6, 40, 41Kayal, N., 33Keatinge, R., 263Keller, A., 457Kemeny, J.G. (1926–1992), 401Kemp, C., 249Kempe, A.B. (1849–1922), 302Keng, Tsu /Zu Gengzhi (450–520), 99Kepler, J. (1571–1630), 155–156Key, M.M., 360Khan, Khublai (1216–1294), 120Khayyám, Omar (1048–1131), 116–117Khinchin, A.Y. (1894–1959), 272Khufu (2589–2566 BC), 43Khwajah Nizami of Samarkand, 117Kielhau, M., 249Kirchhoff, G.R. (1824–1887), 280–281Kirillov, A.A. (1936–), 422Klammer, 340Kleene, G.A., 414Kleene, S.C. (1909–1994), 414–415Klein, F.C. (1849–1925), 303Kleiner, A. (1849–1916), 347Kline, M. (1908–1992), 413Knaster, B. (1893–1980), 376Kneschke, A. (1902–1979), 341

Kneser, A. (1862–1930), 266Kneser, H. (1898–1973), 321Knuth, D.E. (1938–), 441–442Kolmogorov, A.N. (1903–1987), 399–400Komalatammal, 368König, J. (1849–1914), 300König, R. (1885–1979), 321Koppelman, L., 243Kornfield, K., 434Korteweg, D.J. (1848–1941), 353Kossuth, L. (1802–1894), 404Kotarbinski, T. (1886–1981), 393Kothari, D.S. (1905–1993), 418Kovalevskaya, S.V. (1850–1891), 304Kövesi, M., 399Kowa, S. (1642–1708), 180Kowalewski, W.H.G. (1876–1950), 341Krai, C., 147Kramers, H.A. (1894–1952), 368Krishnamurthy, E.V. (1934–2012), 440–441Krishnan, K.S. (1898–1961), 378Kronecker, I., 277Kronecker, L. (1823–1891), 277–279Krook, M. (died 1985), 418Kummer, E.E. (1810–1893), 259–260Kummer, M., 297Kuratowski, K. (1896–1980), 388–389Kurdyka, K., 419Kursunoglu, B. (1922–2003), 395Kutta, M.W. (1867–1944), 329–300

LLacroix, S.F. (1765–1843), 220–221Ladyzhenskaya, O.A. (1922–2004), 429Lagadha, Sage (before 1350 BC), 50Lagrange, J.L. (1736–1813), 211–213Laguerre, E.N. (1834–1886), 288Lalla (around 720–790), 104Lalouvére, A. (1600–1664), 165Lambert, J.H. (1728–1777), 209–210Lamé, G. (1795–1870), 244, 246Lanchester, F.W. (1868–1946), 340Landau, E. (1877–1938), 285, 342–343, 373,

390Landau, H. (1877–1938), 342–343Landau, L.D. (1908–1968), 411–412Lane, L., 298Langlands, R.P. (1936–), 431Laplace, P.S. (1749–1827), 216–218Larmor, J. (1857–1942), 270Lasker, E. (1868–1941), 321Latadeva, 86Laurent, P.-A. (1813–1854), 228

470 Name Index

Lax, H., 434Lax, P.D. (1926–), 434Le Bouteiller, J., 297le Canu, P., 216Le Monnier, R., 212Le Verrier, U.J.J. (1811–1877), 262, 268Lebesgue, H.L. (1875–1941), 338–339Lebovitz, N.R., 416Leelavati, 100, 126, 137, 440Lefévre, J. (1455–1536), 132Lefschetz, S. (1884–1972), 310Legendre, A.-M. (1752–1833), 218–220Leibniz, G.W. (1646–1716), 185–187Lenin, V.I. (1870–1924), 379Lenobu, S.T. (1662–1712), 180Leo X, Pope (1475–1521), 134Leodamas (about 380 BC), 70Leon (about 375 BC), 70Lerch, M. (1860–1922), 278Lesniewski, S. (1886–1939), 393Leucippus (about 440 BC), 66Levens, J., 436Lévi, P., 432Levi-Civita, T. (1873–1941), 227Levitan, B. (1914–2004), 422Lévy, M.-H., 424Lévy, P.P. (1886–1971), 424Lewis, D.K. (1941–2001), 396Lewy, H. (1904–1988), 380L’Hôpital, G.F.A. (1661–1704), 13, 192L’Huilier, S.A.J. (1750–1840), 128Li, Chih (1192–1279), 120Li, Y., 120Lian, Bong, 447Liapunov, A.M. (1857–1918), 310–311Libri, G. (1803–1869), 238Lichtenberg, G.C. (1742–1799), 223Lie, S. (1842–1899), 295Liénard, A.M. (1869–1958), 331Lifshitz, E.M. (1915–1985), 412Lily, 324, 431, 437Lincoln, A. (1809–1865), 325Lindelöf, E.L. (1870–1946), 310Liouville, J. (1809–1882), 258–259Lipschitz, R.O.S. (1832–1903), 286Listing, J.B. (1808–1882), 240Littlewood, J.E. (1885–1977), 21Liu, Kefeng (1965–), 447Livia (born 1601), 154Lobachevsky, N.I. (1792–1856), 241–242Lokasundari, 376Lomnicki, A.M. (1881–1941), 382London, F.W. (1900–1954), 412Lorentz, H.A. (1853–1928), 324

Lorenz, E.N. (1917–2008), 425–426Lotka, A.J. (1880–1949), 351Lotze, R.H. (1817–1881), 301Louis IX, King (1214–1270), 120Louis XVI, King (1754–1793), 212Louis-Francois (1760–1848), 237–239Louis-Philippe (1773–1850), 235Louvois, 188Lowndes, T. (1692–1748), 268Lubin, J.D. (1936–), 434Lucas, F.É.A. (1842–1891), 294Lucas, H. (1610–1663), 175Lucius, 90, 151Lukasiewicz, J. (1878–1956), 345–346Lun, Tshai (around 50–121), 132Luther, M., 311Luzin, N.N. (1883–1950), 360Lysanias of Cyrene, 81

MMacColl, H. (1837–1909), 294MacLane, S. (1909–2005), 421Maclaurin, C. (1698–1746), 199–200Macropedius, 141MacWilliams, J. (1917–1990), 443Madhava of Sangamagramma (1340–1425),

126–127Magnus, A. (around 1193–1280), 120Mahalanobis, P.C. (1893–1972), 385Maharaja, B.K.T. (1884–1960), 364–365Maharaja, T.T., 364Mahavira (817–875), 109–111Mahavira, V. (around 1894–1814 BC), 45–48Mainardi, G. (1800–1979), 288Maitrayana, 40Malthus, T.R. (1766–1834), 221Manava, 40Mandelbrojt, S. (1899–1983), 443Mandelbrot, B. (1924–2010), 432–433Manzur, S. (1905–1981), 383Mar, G., 401Marangoni, C.G.M. (1840–1925), 292Marcellus (266–208 BC), 78Marconi, G. (1874–1937), 449Maria, H. (1609–1669), 164Maric, M. (1875–1948), 347Marina, 399Markov, Andrei A. (1856–1922), 308–309Markov, Andrey A. (1903–1979), 308–309Markov, Vladimir A. (1871–1897), 308Marolois, S. (1572–1627), 160Maro,P.V. (70–19 BC), 151Marre, A., 131

Name Index 471

Martha, 232Mary, Queen (1516–1558), 140, 148Mascheroni, L. (1750–1800), 218Mathieu, 291, 327Mathieu, É.L. (1835–1900), 291Matiyasevich, Y.V. (1947–), 320Matteucci, C. (1811–1868), 379Mauchly, J.W. (1907–1980), 29Maupetuis, 202Maurice of Nassau (1567–1625), 147Maurolico, F. (1494–1575), 135Maurya, King (1472–1436 BC), 87Maximilian I, Emperor (1459–1519), 130Maxwell, J.C. (1831–1879), 228Mazurkiewicz, S. (1888–1945), 375–376McCarthy, J. (1927–2011), 435–436McClintock, B. (1902–1992), 292McCluskey, E.J. (1929–), 414McDowell, W.W., 432Meeks, W.H., 447Melissus, 64Menaechmus of Proconnesus/Alopeconnesus

(around 375–325 BC), 73–74Mendel, G.J. (1822–1884), 275Menelaus of Alexandria (around 70–140 AD),

90Menger, K. (1902–1985), 274Mengoli, P. (1625–1686), 125Menzel, D.H. (1901–1976), 418Mercator, G. (1512–1594), 141–142Mercator, Nicolaus/Kauffmann (1620–1687),

171Mersenne, P.M. (1588–1648), 159Mertens, F. (1840–1927), 278Metrodorus (about 500), 92Meyer, T. (1882–1972), 340Michael VIII, P. (1223–1282), 124Michelangelo, 151Micheria, C., 137Midas, Phrygian King, 59Milgram, A.N. (1912–1961), 434Mill, J.S. (1806–1873), 161Millbanke, A. (1792–1860), 264Milman, V.D. (1939–), 396Minkowski, H. (1864–1909), 324Minos, King, 71Mitra, S.K., 428Mittag-Leffler, S.G. (1846–1927), 266Mnesarchus, 54, 60Möbius, A.F. (1790–1868), 239–240Mohr, D.G. (1640–1697), 218Moisieva, 241Monge, G. (1746–1818), 214–215Montel, P. (1876–1975), 388

Montgomery, D. (1909–1992), 421Moore, E.H. (1862–1932), 337Moore, G.E. (1873–1958), 333Moore, J. (1646–1714), 190Moore, J.C. (1923–), 421Moore, R.L. (1882–1974), 359–360Moray, R. (1608–1673), 178Mordell, L.J. (1888–1972), 410Morgenstern, O. (1902–1977), 397Morley, F. (1860–1937), 357Morse, C.P., 325Morse, H.C.M. (1892–1977), 325Moschopulus, M. (around 1350–1450), 179Moscow, P. (about 1850 BC), 48–50Moser, J. (1928–1999), 434Moses, 141Mostowski, A. (1913–1975), 418–419Mostowski, T., 419Moulton, F.R. (1872–1952), 33Mukherjee, A. (1864–1924), 377Müller, W., 392Murarka, N.P., 440Murray, F.J. (1911–1996), 398Musa, B. (around 800–860), 106Mussolini, 344Myllias, 59Myrica, G., 141Myson of Chene, 51

NNagata, M. (1927–2008), 320Naimark, M.A. (1909–1978), 422Namboodri, P. (around 1370–1460), 128Napier, A. (1534–1608), 148Napier, J. (1550–1617), 148–149Nash, J.F. (1928–), 321Naucrates, 75Naur, P. (1928–), 436Navakshethra, 128Nave, H., 132Navier, C.-L. (1785–1836), 222Nearchus, 63Nemorarius, J. (1225–1260), 123Neocleides, 70Neugebauer, O. (1899–1990), 23Neumann, F.E. (1798–1895), 280Neumann, K.G. (1832–1925), 287Neumann, N., 379Nevanlinna, R.H. (1895–1980), 409Newton, H.A. (1623–1679), 180Newton, I. (1642–1727), 181–185Neyman, J. (1894–1981), 429Nicholas IV, Pope (1227–1292), 122

472 Name Index

Nicholas of Cusa (1401–1464), 129–130Nick, P., 443Nicolas, J. (1685–1727), 180Nicolette, 410Nicomachus of Gerasa (around 60–120 AD),

89–90Nicoteles of Cyrene (about 250 BC), 83Nightingale, F. (1820–1910), 263Nikodym, O.M. (1887–1974), 382Nilakanthan, S. (around 1444–1544), 382Nisanku, 86Nissen, R. (1896–1981), 349Noether, A.E. (1882–1935), 354–356Nonni, G., 338Nørlund, M., 367Nrpatunga, Rastrakuta King Amoghavarsa

(814–877), 109

OObama, B. (1961–), 445Odlyzko, A. (1949–), 443Ogilvie, A., 357Ohm, G.S. (1789–1854), 235–236Omar I, Caliph (579–644), 97Onsager, L. (1903–1976), 292Oppenheimer, J.R. (1904–1967), 395Oresme, N. (1320–1382), 125–126Osgood, W.F. (1864–1943), 325Ostrogradsky, M.V. (1801–1862), 245–246Ostrowski, A.M. (1893–1986), 328Oughtred, W. (1575–1660), 157Ourisson, A., 363

PPacioli, L. (1446–1517), 133Paganini, B.N.I., 112Paila, 38Painlevé, P. (1863–1933), 287, 308Pais, A. (1918–2000), 386Palit, T.N., 377Panaetius of Rhodes (around 185–109 BC), 85Pandit, N. (1340–1400), 126Panini (about 500 BC), 60Pappus of Alexandria (around 290–350),

96–97Parmenides (about 480 BC), 62Parry, W.E. (1790–1855), 232Parseval, M.-A. (1755–1836), 220Parusinski, A., 419Pascal, B. (1623–1662), 171–173Pascal, É. (1588–1651), 172Pasteur, L. (1822–1895), 73

Paul II, Pope (1417–1471), 130Paul III, Pope (1468–1549), 138Pauli, W.E. (1900–1958), 430Peacock, G. (1791–1858), 2221Peano, G. (1858–1932), 313–314Pearl, R. (1879–1940), 252Pearson, K. (1857–1936), 311Peirce, B. (1809–1880), 15Peirce, C.S. (1839–1914), 293–294Pell, J. (1610–1685), 86Pelletier/Peletier, J. (1517–1582), 142Pericles, 63Perrin, J. (1870–1942), 348Perron, O. (1880–1975), 352Pestalozzi, J.H. (1746–1827), 244Péter, R. (1905–1977), 403Petersen, J.P.C. (1839–1910), 292–293Petrarch, F. (1304–1374), 151Pettis, B.J. (1913–1979), 422Peyrard, F., 75Pfaff, J.F. (1765–1825), 223Phaedrus (around 444–393 BC), 49Pherecydes of Syros (about 600 BC), 54Phidias, 78Philip of Macedonia, King (382–336 BC), 72Philipp II (1527–1598), 146Philippus, 70Phillippe XIV, Louis (1638–1715), 165Philo of Byzantium (about 250 BC), 81Philo of Gadara, 94Philolaus of Croton (around 480–405 BC),

64–65Philoponus (about 490), 71Piazzi, G. (1746–1826), 227Picard, C.E. (1856–1941), 309–310Picard, C.M.J.Picard, J. (1620–1682), 135Pick, G.A. (1859–1942), 297Pierre, 327Pingala (about 500 BC), 60–61Pisharati, T.A. (1550–1621), 149Pittacos of Mytilene (around 640–568 BC), 50Plancherel, M. (1885–1967), 431Planck, M. (1858–1947), 268Planudes, M. (1260–1330), 124Plato of Athens (around 427–347 BC), 68–70Plato of Tivoli (around 1132–1146), 117Playfair, J. (1748–1819), 215–216Playfair, J.G., 216Pliny the Elder (23–79), 104Plouffe, S. (1956), 443Plücker, J. (1801–1868), 246–247Plume, T. (1630–1704), 197Plutarch (around 46–120), 51

Name Index 473

Pococke, E., 59Poincaré, J.H. (1854–1912), 306–309Poisson, S.D. (1781–1840), 232–233Poitou, G. (1926–1989), 434Polkinghorne, J.C. (1930), 395Polya, G. (1887–1985), 372–374Poncelet, J.-V. (1788–1867), 236–237Pond, J., 247Pontryagin, L.S. (1908–1988), 412–413Porkert, A., 406Posidonius of Apamea (135–51 BC), 85Post, E. (1897–1954), 405Prandtl, L. (1875–1953), 340–341Prausnitzer, F., 277Prausnitzer, J., 277Prithuyasas, 87Proclus, D. (410–485), 16Protagoras of Abdera (around 484–414 BC),

63–64Ptolemaeus, A.C. (around 90–168 AD), 92Ptolemy I, 75Ptolemy II Philadelphus, King (around

283–246 BC), 81Ptolemy III Euergetes, 81Ptolemy, King, 77Puranic, 88Pürbach, G. (1423–1461), 130Purser, M., 274Pushkin, A.S. (1799–1837), 308Pythagoras (around 582–481 BC), 54–60Pythais, 54Pythonax of Crete, 60

QQuincke, G.H. (1834–1924), 311Quine, W.V.O. (1908–2000), 414Qurra, T. (826–901), 111–112

RRabin, M.O. (1931), 401Rajagopal, C.T. (1903–1978)Raleigh, W. (1552–1618), 150Ramachandran, G.N.I. (1922–2001), 440Raman, C.V. (1888–1970), 376–379Ramanujan, S. (1887–1920), 368–370Ramsey, F.P. (1903–1930), 396Rao, B., 429Rao, C.R. (1920), 428Rao, N.R., 449Raphson, J. (1648–1715), 187Rapoport, A., 18Rashevsky, N., 18

Rayleigh, J.W.S. (1842–1919), 242Recorde, R. (around 1510–1558), 140–142Regiomontanus/Johann Müller (1436–1476),

130–131Reid, C.B. (1918–2010), 426Reinhardt, K.A. (1895–1941), 320Rhind, A.H. (1833–1863), 49Rhind Papyruses (about 1650 BC), 48–50Ribet, K. (1948–), 167Riccati, F. (1676–1754), 196Riccati, V. (1707–1775), 196Ricci, M. (1552–1610), 127Ricci, O. (1540–1603), 151Ricci-Curbastro, G. (1853–1925), 227Richard, L.-P.-É. (1795–1849), 260Richard of Wallingford (1292–1336), 124Richardson, L.F. (1881–1953), 433Richelot, C., 280Richelot, F.J. (1808–1875), 280Riemann, G.F.B. (1826–1866), 281–282Riesz, F. (1880–1956), 346Rivest, R.L. (1947–), 447Robert of Chester (about 1150), 106Robespierre, 222Robinson, J.H.B. (1919–1985), 426–427Robinson, R.M. (1911–1995), 426Robison, J. (1739–1805), 216Roch, G. (1839–1866), 285Rockefeller, J. (1839–1937), 373Rodrigues, O. (1794–1851), 243Rogers, H. (1926), 401Rohn, K. (1855–1920), 303Rolle, M. (1652–1719), 188–189Roosevelt, F.D. (1882–1945), 349Rosen, F., 106Rossby, C.G. (1898–1957), 426Rosser, J.B. (1907–1989), 401Rowe, D. (1950), 410Rudolff, C. (1499–1545), 168Ruffini, P. (1765–1822), 120Rumford, C. (1753–1814), 269Runge, C.D.T. (1856–1927), 309Runge, N., 379Runkle, J.D. (1822–1902), 290Russell, B.A.W. (1872–1970), 333–335Ruth, 324, 381Rutherford, E. (1871–1937), 367

SSaccheri, G. (1667–1733), 77Sachs, A. (1915–1983), 23Sacrobosco, J. (around 1195–1256), 132Sadleir, M. (died 1706), 273

474 Name Index

Safford, T.H. (1836–1901), 280Sagan, C.E. (1934–1996), 416Saha, M. (1893–1956), 385Sahl, I. (940–1000), 157Saks, S. (1897–1942), 338Salam, A. (1926–1996), 395Salem, R. (1898–1963), 450Salmon, G. (1819–1904), 270–271Salvatorus, S., 142Salviati, 153Samuel, 357, 420Samuelson, P.A. (1915–2009), 292Sarte, J.-P. (1905–1980), 163Satkhandagama, 48Saunderson, N. (1682–1739), 194Savile, H. (1549–1622), 148Savio, M. (1942–1996), 439Sawyer, W.W. (1911–2008), 16Saxena, N. (1981), 33Scarlatti, G.D. (1685–1757), 427Schauder, J.P. (1899–1943), 383Scheffers, G. (1866–1945), 295Schering, E.C.J. (1824–1897), 301Scheutz, E., 28Scheutz, P.G. (1785–1873), 28Schlömlich, O.X. (1823–1901), 279Schmidt, E. (1876–1959), 304Schneider, T. (1911–1988), 320Schnirelmann, L.G. (1905–1938), 403Schoen, R. (1950), 447Schöenflies, A.M. (1853–1928), 291Scholasticus, S. (380–450), 97Schoute, P. (1846–1923), 315Schröder, E. (1841–1902), 294Schrödinger, E. (1887–1961), 371Schubert, H. (1848–1911), 427Schumacher, E., 393Schur, I. (1875–1941), 339–340Schwartz, J.T. (1930–2009), 437–438Schwartz, L.-M. (1915–2002), 424Schwarz, K.H.A. (1843–1921), 297–298Sciama, D.W.S. (1926–1999), 395Scott, C.A. (1858–1931), 312–313Scott, D.S. (1932), 401Segal, I.E. (1918–1998), 422Seifert, H. (1907–1996), 341Selberg, A. (1917–2007), 421Senator, F.M.A.C. (490–585), 102Seneca (4 BC-65 AD), 151Senff, K.E. (1810–1849), 223Serre, J.-P. (1926), 434–435Serret, J.A. (1819–1885), 223Shafarevich, I.R. (1923), 434Shah, S.M. (1055–1092), 116

Shakespeare, W. (1564–1616), 151Shamir, A. (1952), 448Shannon, C.E. (1916–2001), 425Shastri, V.V., 364Sheffer, H.M. (1883–1964), 362Shelley, P.B. (1792–1822), 333Shi Huang, Emperor (213 BC), 93Shih-Chieh, Chu (about 1300), 124–125Shilov, G.E. (1917–1975), 422Shimura, G. (1930), 167Shirakatsi, A. (610–685), 103Shrautasutras, 40Siegel, C.L. (1891–1981), 410Sierpinski, K., 341Sierpinski, W.F. (1882–1969), 358–359Simonis, E. (1810–1893), 148Simplicio, 153Simplicius (about 520), 89Simpson, T. (1710–1761), 205–206Singh, H.K., 418Siu, Yum-Tong (1943), 447Sixtus IV, Pope (1414–1484), 130Skolem, A.T. (1887–1963), 332Slater, J.C. (1900–1976), 368Sloan, A.P. (1875–1966), 431Sloane, N.J.A. (1939), 442–443Smale, S. (1930), 438–439Smith, B., 180Smith, D.E. (1860–1944), 111Smith, H.J.S. (1826–1883), 111Smith, J., 242Smith, P.A. (1900–1980), 447Smith, R. (1689–1768), 197Smith, W., 242Smullyan, R.M. (1919), 427–428Snell, W. (1580–1626), 157Sobolev, S.L. (1908–1989), 30Socrates (around 469–399), 64Sohncke, L. (1842–1897), 243Solomon, L., 310Solon (around 638–559 BC), 50Somayaji, N. (around 1444–1544), 131Somayaji, P. (around 1600–1740), 165Somerville, M.F. (1780–1872), 231–232Somerville, W. (1771–1860), 231Sommerfeld, A. (1868–1951), 306Speiser, A. (1885–1970)Spence, P., 334Spole, A. (1630–1699), 201Sponius, 140Sporus of Nicaea (around 240–300), 94Sridhara (before 486), 100Sripati (around 1019–1066), 116Stabius, J., 141

Name Index 475

Steenrod, N.E. (1910–1971), 421Stein, E.M. (1931), 45Steiner, J. (1796–1863), 244Steinhaus, H.D. (1887–1972), 372Steinmetz, C.P. (1865–1923), 325–326Stevin, S. (1548–1620), 147–148Stieltjes, T.J. (1856–1895), 339Stifel, M. (1486–1567), 134Stirling, J. (1692–1770), 199Stobaeus (about 500), 73Stokes, G.G. (1819–1903), 269–270Stolz, O. (1842–1905), 315Stone, M.H. (1903–1989), 383Stott, A.B. (1860–1940), 315–316Stott, W., 315Straus, E.G. (1922–1983), 407Stroock, D.W. (1940), 445Strutt, J.W., 242Sturm, J.C.F. (1803–1855), 250–251Sudhrut, A. (before 600 BC), 53Sulbasutras (about 3200 BC), 40–41Sullivan, A. (1842–1900), 304Sumanthu, 38Sushruta (before 800 BC), 53Swami, P., 86Sylvester II, Pope (945–1003), 114Sylvester, J.J. (1814–1897), 262–264Szabó, Á. (1913–2001), 21Szegö, G. (1895–1985), 373Szemerédi, E. (1940), 422Szilard, L. (1898–1964), 349

TTakagi, T. (1875–1960), 321Talmud, M., 347Tamagawa, T. (1925), 410Taniyama, Y. (1927–1958), 167Tao, Terence Chi-Shen (1975), 450–451Tarski, A. (1902–1983), 393–394Tasso, 152, 202Tate Jr., J.T. (1925), 453–454Tauber, A. (1866–1942), 384Tayler, R.J. (1929–1997), 416Taylor, B. (1685–1731), 198Taylor, R. (1962), 167Telauges (about 500 BC), 60Teller, E. (1908–2003), 349Teresa, 325Thales of Miletus (around 625–545 BC),

50–51Thasus, 70

Theaetetus (around 417–369 BC), 70Theano of Crotona (about 546 BC), 60Theodoric (King) (454–526), 99, 102Theodorus of Cyrene (about 431 BC), 68Theodosius of Bithynia (around 160–100 BC),

96Theon of Alexandria (about 390), 75Theophrastus (around 371–287 BC), 75Theudius (about 350 BC), 70Theuth, 49Thibaut, G. (1848–1914), 40Thiele, R., 321Thiele, T.N. (1838–1910), 289Thom, R. (1923–2002), 419Thomson, J.J. (1856–1940), 367Thomson, W./Lord Kelvin (1824–1907), 15Thrasyllus of Mendes (around 50 BC-36 AD),

87–88Threlfall, W. (1888–1949), 341Thucydides, 64Thymaridas of Paros (around 400–350 BC), 8Tiberius, Emperor (42 BC-37 AD), 88Timaeus of Locri (around 420–380 BC), 69Tippett, L.H.C. (1902–1985), 381Todd, J. (1911–2007), 408Todd, O.T. (1906–1995), 408–409Toeplitz, O. (1881–1940), 373Tokugawa, L.S. (1662–1712), 180Tomlinson, R.S. (1941), 32Tooke, M., 191Toomer, G.J. (1934), 105Torricelli, E. (1608–1647), 168Trénel, L.-A., 326Trilokaprajnapti, 48Tschebatorew, N.G., 66Tsetlin, 422Tsu, Sun (about 400), 98Tukey, J.W. (1915–2000), 423Turán, P. (1910–1976), 351Turing, A.M. (1912–1954), 416–417Turing, J.M. (1873–1947), 416Turing, S. (1881–1976), 417Turnbull, H.W. (1885–1961), 366–367Tzitzéica, G. (1873–1939), 296Tzu, Mo (around 470–391 BC), 154

UUlam, S.M. (1909–1984), 389Unguru, S. (1931), 410Urban IV, Pope (1195–1264), 122Urysohn, P.S. (1898–1924), 360

476 Name Index

VVaisampayana, 38Valmes, P., 143van Beethoven, L. (1770–1827), 225van Ceulen, L. (1539–1610), 145van der Pol, B. (1889–1959), 380van der Waals, J. (1837–1923), 292van der Waerden, B.L. (1903–1996), 355van Roomen, A. (1561–1615), 146van Schooten, F. (1615–1660), 168–169van Waveren Hudde, J. (1629–1704), 174–175Vandermonde, A.-T. (1735–1796), 210–211Varadhan, S.R.I.S. (1940), 444–445Varaha, 38, 40Varahamihira, D. (working 123 BC), 86–87Variar, S. (around 1500–1600), 137Varignon, P. (1654–1722), 189Varman, S. (1800–1838), 245Veblen, O. (1880–1960), 342Venn, J. (1834–1923), 288Verdet, É. (1824–1866), 297Verhulst, P.F. (1804–1849), 252Vidhula, 40Viéte, F. (1540–1603), 145–146Vijayanandi (around 940–1010), 113–114Vikramaditya (102 BC-18 AD), 86–87Vincent of Beauvais (around 1190–1264),

120Vincenzio (born 1606), 154Vinogradov, I.M. (1891–1983), 381–382Virahanka (about 600 AD), 103Virasenachary, 47Virgil (70–19 BC), 151, 202, 204, 238Virginia (1600–1634), 154Vitali, G. (1875–1932), 338Vitruvius (around 75–15 BC), 81Voltaire, F. (1694–1778), 80Volterra, V. (1860–1940), 316von Dyck, W.F.A. (1856–1934), 329von Eötvös, L.B. (1848–1919), 373von Goethe, J.W. (1749–1832), 16von Harnack, A. (1851–1930), 305von Helmholtz, H. (1821–1894), 278von Humboldt, A. (1769–1859), 218von Kármán, T. (1881–1963), 340von Lindemann, C.L.F. (1852–1939),

305–306von Mises, H.G. (1893–1973), 361von Mises, R.E. (1883–1953), 361von Neumann, J.L. (1903–1957), 396–399von Peuerbach, G. (1423–1461), 130von Seidel, P.L. (1821–1896), 274–275von Staudt, K.G.C. (1798–1867), 251von Strasznicky, L.R.S. (1803–1852), 279

von Tschirnhaus, E.W. (1651–1708), 188von Walterhausen, S. (1809–1876), 230

WWabewski, T. (1896–1972), 388Wallace, A.R. (1823–1913), 381Wallace, W. (1768–1843), 231Wallis, J. (1616–1703), 169–170Wallman, H. (1915–1992), 401Wallmarks, V.A., 328Wantzel, P. (1814–1848), 262Ward, S. (1617–1689), 176Waring, E. (1736–1798), 212Warner, W. (1563–1643), 150Waterman, A.T. (1892–1967), 450Watson, G.N. (1886–1965), 369Weaver, W. (1894–1978), 387–388Weber, E. (1795–1878), 18Weber, H. (1842–1913), 390Weber, S.V., 373Weber, W. (1804–1891), 228Wecklein, A., 390Wedderburn, J.H.M. (1882–1948), 357–358Wéfá, A. (940–997), 113Weierstrass, K.T.W. (1815–1897), 265–268Weil, A. (1906–1998), 409–410Weil, S. (1909–1943), 409Weinberg, W. (1862–1937), 343Weldon, W. (1860–1906), 312Wendroff, B. (1930), 434Wendt, H., 341Wessel, C. (1745–1818), 221Weyl, H. (1885–1955), 365–366Weyl, L., 365Whately, R. (1787–1863), 280Whewell, W. (1794–1866), 232Whiston, W. (1667–1752), 194White, L.A. (1900–1975), 15Whitehead, A.N. (1861–1947), 317–318Wiberg, M. (1826–1905), 28Widmann, J. (1462–1500), 140Wien, W.J. (1864–1928), 391Wiener, N. (1894–1964), 384–385Wigler, M. (1947), 438Wigner, E. (1902–1995), 349Wigner, M. (1904–2002), 394Wilder, R.L. (1896–1982), 412Wiles, A. (1953), 167Wilkes, M.V. (1913–2010), 30Wilkie, 215Wilkins, J. (1614–1672), 176Wilkosz, W. (1891–1941), 382Wilks, S.S. (1906–1964), 423

Name Index 477

William of Moerbeke (1215–1286), 122William, W. (1667–1752), 194Wilowski, M.J., 394Wilson, E. (1879–1964), 292Wingate, E. (1596–1656), 164Wittegenstein, L.J. (1889–1951), 302Woepcke, F., 117Wolf, J.R. (1816–1893), 403Wolff, C. (1675–1715), 202Wolfskehl, P.F. (1856–1906)Woodhouse, R. (1773–1827), 224Wren, C. (1632–1723), 157Wright, E. (1561–1615), 151Wright, E.M. (1906–2005), 410–411Wright, S.G. (1889–1988), 18Wronski, J.M.H. (1776–1853), 255

XXenocrates of Chalcedon (around 396–314

BC), 72Xenophon, 18Xylander, G. (1575), 144

YYahweh, Lord, 44Yamabe, H. (1923–1960), 319Yau, Shing-Tung (1949), 447–448Young, G.C. (1868–1944), 303Young, W.H. (1863–1942), 323Yu (Yii), Great Emperor (around 2200–2100

BC), 94

ZZaremba, S. (1863–1942), 323–324Zariski, O. (1899–1986), 409Zenarchus, 75Zeno of Citium (around 334–262 BC), 81Zeno of Elea (around 495–435 BC), 62–63Zenon, 99Zermelo, E. (1871–1953), 331–332Zhukovski, N.Y. (1847–1921), 301Zippin, L. (1905–1995), 319Zoccolanti, F., 136Zuse, K. (1910–1995), 415–416Zygmund, A. (1900–1992), 376

Subject Index

AAbaci, construction of, 26, 114, 236Abacus

Chinese, 25Russian, 236wax, 25

Abdominal aortic aneurysm, 349Aberration, spherical, 115Abodes of different devatas, 39Abraham–Lorentz–Dirac force, 395Abstract, shortest possible, 37Accident, carriage, 173Accounting, 89Acoustical diaphragms, 224Acoustics, 10, 159, 208, 222, 278, 328, 377Actuarial science, 13, 18, 191Adda in Bengali, 387Adjoint, 218, 337, 395Aerodynamics, 301, 329, 340, 341, 361Aerostatics, 216Aesthetics, 18, 92, 363, 442Agarwal–Kayal–Saxena (AKS) primality test,

33, 34, 36Ages, seven, 56Agnesi, witch of, 209Agni (15,400 verses), 38Airfoil design, 363Alchemical writings, Newton’s, 184Alchemy, 140, 149, 185Algebra, computer, 8Algorithm

non-numerical, 27oldest known, 23semi-numerical, 27

ALGOrithmic Language (ALGOL) 68, 31

Algoritmi de numero Indorum, 106Altars, precisely measured, 5Amphetamines, 420Analysis, quantitative, 26, 284Anatomy, 53, 200, 286Anchor Ring, 342Androgyny, 56Anecdote, 51, 146, 200, 230, 322, 344, 349,

352, 374, 380, 384Anemia, pernicious, 295Anemometer, 177Anesthesia, 53Angina pectoris, 184Angula, 48, 110Anthropology, 372Antichrist, 149Anti-electron, 395Antikythera, 26, 89Antilogies, 64Antinomies, 14Antinomy, Russell’s, 333Antiquity, 2–4, 9–11, 21, 50, 78, 82, 84, 85,

96, 146, 218Anti-typhoid vaccines, 383Apameia, 85Apeiron, 52Aphorism, Einstein’s often-quoted, 334Aplanatic surface, 115Apocryphal story, 154, 205Apoplexy, 188Appendix, ruptured, 324Approximation, 9, 12, 13, 23, 41, 42, 44, 78,

83, 86, 92–94, 99, 115, 127, 128, 154,171, 195, 207, 242, 271, 272, 279, 297,310, 340, 341, 348, 370

© Springer International Publishing Switzerland 2014R.P. Agarwal, S.K. Sen, Creators of Mathematical and Computational Sciences,DOI 10.1007/978-3-319-10870-4

479

480 Subject Index

Aqen, the ferryman, 3Arabic numerals, 365Aranyakas (theologies), 38Aratus’ Phaenomena, 94Archaeology, 66Archimedes’ axiom, 20, 79Archimedes’ death, 80Archimedes’ number, 79Archimedes’ paradox, 79Architecture, von Neumann, 28, 398Ardhacheda, 47, 48Ardha-jya, 42Arithmetic(s)

of algebras, 337binary, 28, 186computational, 118infinite, 314multiple-modulus residue, 98, 450operations (Ganit), 38p-adic, 450

ARPANET, 32Arthashastra, 18Artificial intelligence, 25, 294, 398, 425, 435,

436Art of Computer Programming, 442Aryabhatteeyabhashya, 86Aryabhattiyam, 21, 42Asanna, 42ASCC. See Automatic sequence controlled

calculator (ASCC)Assassination, 199Asteroid, 156, 187, 227, 291, 380, 416, 433,

436Asthadhyayi, 60Astigmatism, 247Astrology

Hindu, 87horoscopic, 105predictive, 87

AstronomerBible of planetary, 227Yavana (not Greek), 87

AstronomyAristotle’s view of, 152descriptive, 224Greek, 87Indian, 87

Atharvaveda, 38, 39, 365Atlas Coelestis, 187Atlas, Farnese, 85Atmosphere, 115, 190, 191, 206, 222, 376,

385, 415, 422Atomic collisions, 412Atomic model, Bohr’s, 367, 393

Atom, motion of the, 67Automatic Computing Engine (ACE), 28Automatic sequence controlled calculator

(ASCC), 29, 407Automotive engineering, 340Axiom, 14, 18, 20, 21, 75, 79, 241, 250, 285,

301, 302, 313, 318–320, 322, 332, 359,374, 405, 406, 421, 440

Axiom of Archimedes, 20

BBaboon’s fibula, 2Backus–Naur form (BNF), 31, 432, 436Ballistics, 29, 245, 333, 390, 397Bamboo sticks, 25Bark fibers thread, 53Barometer, 168, 177, 187, 198Baudhayana, 6, 40, 41Beads, mounted, 26Belief(s)

Aristotelian, 103in Gods, 67religious, 37in spirits, 54

Bell curve, 277Bhagavad Gita, 38, 409Bhagavata (18,000 verses), 38Bhagavata Purana, 38, 150Bhagvati Sutra, 45, 47Bhatnagar–Gross–Krook (BGK) model, 418Bhavishya, 38Bijaganitam, 100BINAC, 30Binary system, 28, 186Bindu, 39Bioinformatics, 361, 438Biologist, evolutionary, 312, 380, 381Biometrics, 18Birch barks, 84Black body radiation, 280Black holes, 416, 447Blood transfusion, 407Blueness of the sea, 377BNF. See Backus–Naur form (BNF)BNF notation (Backus–Naur form), 31Body, seven parts of the, 56Bohr–Einstein debate, 367Bone

dead, 163Ishango, 2Lebombo, 2tumor, 432

Bosons, 386

Subject Index 481

Boyle’s law, 176Brahma (24,000 verses), 38Brahmanas (rituals), 38Brahmanda (12,000 verses), 38Brahmavaivarta (18,000 verses), 38Bridges, arches of, 152Bronchial trouble, 239Brotherhood, secret, 55Bugs, 73Bull-choking sandwich, 78Bushel, 104Butterfly effect, 425–426

CCalculator, pocket, 26Calculus

absolute differential, 338of finite differences, 186, 198fluxional, 181–183lambda, 401

Calendar, Gregorian, 180, 201Canal, building of, 93Cancer, 150, 381, 383, 393, 399, 426, 427, 438Cannonball, 136, 154, 294Canon, Buddhist, 94Canons, five astronomical, 87Capillarity, 347Captured (married), 420Cardinality for infinite quantities, 299Cards

IBM, 29punched, 28

Cartography, 10, 75, 210Cataracts, 53, 154Caterpillar vehicle, 225CAT scans, 11Causality, 67, 396CDC 6600, 434Chakravala method, cyclic, 7, 101Chakra-yantra, 43Chalk and slate, 25Chandas (meter), 39Chandrasekhar limit, 416Chaos, 16, 18, 40, 52, 91, 217, 307, 426, 446Charcoal ink, 25Chariot, mechanical South Pointing, 99Cheapest science, 374Cheating methods, 140Chemical castration, 417Chhandah-shastra, 60, 61Chhatra-yantra, 43Chhaya-yantra, 43Chou (literally, “calculating sticks”), 25

Christ, horoscope of, 139Chromatic aberration, 228Chudamani Maheshvar, 100Cipher, undecipherable, 240Circle squaring, 41, 88, 94, 96, 259, 305Clay tablet, 2, 6, 23Clerk, accounts, 369COBOL, validation software for, 408Cock-fight, 110Collar, leather, 180Colleague, vindictive, 177Colon, double, 157Color mixing, 413Colors of flower, 378, 379Combination, candle and mirror, 155Combinatorics, 61, 72, 264, 373, 420, 449, 450Comets, 4, 147, 153, 156, 181, 192, 197, 206,

207, 211, 219, 268, 269, 292, 436Comets, artificial, 181Communion, 238Compass, Geometric and Military, 152Complexity

computational, 442, 446theory, 400, 449

Composite numbers, 20, 82Compressible flow, 340Computability, 28, 401, 406, 414Computation

error-free, 98, 450mental, 225

Computeranalog, 26, 31, 89Leelavati, 440mechanical, 27, 240program-controlled, 28proofs, 35, 36security, 446–448, 450simulation, 26stored-program, 28, 30virus, 446

Computing platform, distributed, 27Computing, time-sharing and parallel, 435, 438Concentration

camp, 330, 388, 419intense, 37, 78

Congruence, 33, 175, 283, 319, 410Conics, 76, 83, 97, 135, 200, 243, 312, 365Conjecture, 20, 32, 35, 96, 129, 133, 167, 168,

170, 177, 199, 219, 249, 254, 258, 272,289, 320, 322, 344, 360, 366, 373, 381,398, 401, 410, 419, 421, 431, 434–436,438, 439, 444, 447

Conjecturing, Art of, 158, 189, 208Consciousness, 163, 411, 427

482 Subject Index

Consistency, 15, 319, 405, 406, 413, 440Constellations, 57, 85, 91, 250Constructive proof, 23Continued fractions, 78, 127, 143, 149, 159,

170, 171, 180, 204, 210, 324, 352, 369Continuity, 156, 206, 234, 239, 267, 271, 277,

284, 286, 292Continuum-hypothesis, 330, 332, 359, 406,

440Contradiction, proof by, 23–24Convolutions, 189Coordinates

of latitudes, 107polar, 189, 197rectangular, 162, 246

Coprime, 33, 219Corollary, 20, 34Correctness of computer programs, 435Correlation, 53, 276, 277, 381Cosmography, 48, 101, 103Cosmology, 45, 46, 48, 317Cosmos, 39, 55, 80Counterexample, 20, 32, 35, 36, 320Counter-reformation, 155Counting boards, 26, 122Counting, zig-zag glyph for, 3Cow-catcher, 241Craft, underwater, 149Cray XE6 Hopper supercomputer, 408Creation, process of, 56Cricket match, 344Criminology, 277Crowing roosters, 140Cryptanalysis, 109, 417, 448Cryptography

public-key, 448visual, 448

Cryptology, 109Crystal diodes, 29Crystallography, 10, 257, 291Cube(s), 7, 23, 38, 42, 44, 47, 56, 58, 70, 71,

88, 94, 96, 102, 133, 146, 148, 155,156, 166, 183, 262, 315, 322, 370

doubling, 68, 84, 262of sums, 110

Cubits, 44, 101Cuneiform tablets, 4, 6, 7, 11, 43–45Curve

bell-shaped, 209catenary, 193fitting, 226

Cybernetics, 384Cycloid, 152, 165, 169, 171, 173, 174, 179,

192

Cyclone, anti, 276Cylinder, volume of the smallest, 11, 79Cylindrical helix, 83

DDancing, 235, 269Danda, 48Dark Things, 49DARPA/ISTO, 438Darwinism, 311Dasha, 110Data

census, 252statistical, 263structures, 442

Deacon, 164, 187Dead, Book of the, 3Deadlock avoidance, 437Death

with clubs, 100freezing to, 236threats, 37

Debugging, 408Decad, 56Decidability, 414Decimal fractions, 93, 147Deductive science, 21Delta, Kronecker’s, 278Despicable teachers, 373Determinant, 8, 180, 186, 210, 211, 225–227,

239, 253, 263, 264, 273, 274, 286, 326,328, 341, 366

Deterministic chaos, 426Devil

pact with the, 114soul to the, 114wife of the, 209

Devouring, 161Dhanur-yantra, 43Dharmic life, 39Dhavala commentary, 47Dhikotidakarana, 116Dhruvamanasa, 116Diabetes, 53, 253Diagram, polar-area, 263Dialogue on Ancient and Modern Music, 151Dials, 190Dice, 49, 137, 348Dictionary, New Hacker’s, 414Dictionary of Scientific Biography, 243Differences, finite, 186, 198, 214, 232, 265Differentiability, 319Differentiable curve in space, 253

Subject Index 483

Differentiationfractional, 258logarithmic, 189

Diffusion processes, 445Digital signatures, 446Diophantus identity, 182Dioptra, 91Diphtheria, 306Discourse on Method, 161Discrete Fourier transform, 32Discriminant, 263Disease

bladder, 216liver, 171

Dislocations, 53Dispensator, 26Disposition, affectionate, 156Dispute, Newton-Leibniz, 194Distribution of primes, 272, 315, 344, 444Divergence, 125, 193, 228, 245Divinity, 124, 158, 200, 270, 291Divisible, infinitely, 73Division by two, 2DNA as a computational system, 446–447Doctrine of Chances, 195Dodecahedron, 56, 58, 70, 83, 155Dogs, howling, 140Door and key to the sciences, 15Double siphon, 81Dove, wooden, 68Dragon heads, 91Draughts (checkers), 15Dreamer, 163Drink only water, 55Drone, 156Duality, 56, 97, 174, 237, 246, 413, 434, 435Duel, forced into a, 261Duplication of a cube, 71, 73, 96, 146Dwarfism, 325Dynamic energy, 39Dysplasia, hip, 325

EEarth

axis, tilt of the, 82circumference, 42, 82, 85diameter, 46, 78, 234hollow, 191to the Moon, distance from the., 78period of the, 156radii, 92shadows of, 157to the Sun, distance from the, 78

Earthquakes, discourse of, 177Easter, date of, 202, 226Eccentric orbits, 83Eclipse

lunar, 86, 88, 91, 104, 113, 116projection of, 113solar, 5, 85, 101, 104, 113, 149

Ecology, 400Econometrics, 18, 428Ecuador, 26Edo period, 180EDSAC 1. See Electronic delay storage

automatic calculator (EDSAC 1)Education, desultory, 231EDVAC. See Electronic Discrete Variable

Automatic Computer (EDVAC)Egg, yolk of the, 91Egypt, 5, 18, 21, 43, 49, 50, 54, 58, 59, 66, 67,

69, 70, 73, 75, 79, 81, 82, 88, 92, 96,97, 112, 115, 214, 222, 327, 336, 436

Egypt, jewel of, 67Eigenvalues, locations of the, 408Eka, 110Elasticity of air, 81Elastic vibrations, 233Electric discharge, 246Electricity and magnetism, 216, 228, 233, 242,

278Electric sparks, 214Electromagnetic radiation, 368Electromagnetic waves, 8, 270Electronic delay storage automatic calculator

(EDSAC 1), 30Electronic discrete variable automatic

computer (EDVAC), 29, 30Electronic numerical integrator and computer

(ENIAC), 29Electronic valves (vacuum tubes), 29Electron pulses, 28Elements, Latin translations of the, 75Elephant, order of the, 367Elimination, method of, 232Ellipse, super, 246Ellipsoid, 207, 218, 219, 227, 233, 310, 416Email communication, 32Embrace, parents, 171Embryology, 53, 311Empirical rules, 108Empty locations, gaps, or discontinuities,

284Encyclopedia, compiler of an, 103Enemy of Torricelli’s, personal, 169Energy, conservation of, 228Engine, difference, 28, 240

484 Subject Index

ENIAC. See Electronic numerical integratorand computer (ENIAC)

Entertainment media, 25Enumeration and comparison of relations, 15Environmental hostility, 37Epernon, 243Epicycloids, 179Epidemiologist, 381Epigrams, 92, 335Epilepsy, 279Episode, blind man, 17Epistemology, 353Epsilon, 84, 420Equation(s)

determinate, 222Diophantine, 42, 88, 98, 101, 144, 309, 320for the electron, relativistic, 395integer solution to, 42logistic, 252natural, 341solvability of, 277using radicals, 252, 262, 317

Equilibria, stable and unstable, 148Equinox, spring, 74Equivalence of matter and energy, 347Errors

conceptual, 152in reasoning, 76

Essential singularity, 310Ether in magnetic fields, 347Etymology, 39Eudoxus, 12, 67, 69–71, 73, 74, 76, 85, 284Eudoxus, Phaenomena of, 85Eugenics, 277, 312Eunuchs, 47Eureka, 79Europe, medieval, 106Evolutionary approaches, 34Excavation, 202Exhaustions, method of, 71, 76Exile, dreary, 157Exodus of the Israelites, 88Expiatory rites, 59Explosion, primus stove, 412Exponents, prime, 260Extraordinarily subtle insight, 19Extraterrestrial life, 174Eye of the mind, 69

FFable of the Bees, 203Fallacies, 20, 76, 249Famine, 156, 271

Fanatics, savage and merciless, 97Fascism, 316Fast Fourier transform (FFT), 32, 423Father of Algebra, 95Fatigue, 237Feminine Divine, 39Feminine, union of the first, 56Fencing, 145, 266Fertile human-land, 38Feud, Abusive public, 193Fever, violent, 197FFT. See Fast Fourier transform (FFT)Fig tree, 282Fingerprints, 277Finger’s breadth, 48Fire of London, great, 190Firmware, 25Fixed points of recursive programs, 448Flatulence, 55Fluid mass, rotating, 200Fluorescence, 269, 378Fluxions, Doctrine and Application, 197Flywheel Masses in Crank Drives, 361Foci, 99, 156Focused minds, 37, 38Force

centrifugal, 174, 207centripetal, 174supernatural, 54

Forest management, 304Formalism, Ostrogradsky, 245Formal language, 18, 31, 394Formulas, mnemonic for, 148FORmula TRANslator (FORTRAN), 31, 432Fortification, 145, 147, 202, 214Fortune teller, 205Fossil record, 177Fractal, 314, 359, 383, 424, 433, 446Fraction

continued, 78, 127, 143, 147, 149, 159,171, 180, 204, 324, 352, 369

of a point, 62Fractures, 53France, Newton of, 216Frauds, 159Free speech movement, 439Freezing point, 201Frequency components, spectrum of its, 222Frustum, 11, 45, 49, 91, 93Functional programming, 31, 401Functions

calculus of, 240characteristic, 310elementary, 258, 272

Subject Index 485

logarithmic, 48, 178notion of a, 234primitive recursive, 403

Fundamental concepts of deduction, 21

GGambling, 137, 138, 161, 202, 361Game, lottery, 252Game of Logic, 286Games of chance, 173, 208Gang of four, 439Ganitasara (Essence of Mathematics), 100Ganitatilaka, 116Ganymede, 152Garuda (19,000 verses), 38Gear mechanism, oldest known complex, 26Gears, ratchet, 81Generalizations, empirical, 339Generalized inverse of a matrix, 428Generation, spontaneous, 73Genesis 11:4, 45Genetics, 18, 308, 312, 361, 381Genius, universal, 185Genomics, 361Geodesy, 11, 227, 269, 284, 289, 295, 337Geography, universal, 96Geologic timescale, 82Geology, 140, 185, 223, 306, 329, 400Geometrical paradoxes, 96Geometry

computational, 6higher dimensional, 263projective, 6, 160, 172, 215, 240, 244, 251,

258, 287, 449German cipher machine, 417Giddiness, 177Glassblowing, 198Glaucoma, 154Global communication, 32Globe of the stars, 141Glycerin, 378God

existence of, 73, 205Invariable, 101mind of, 89, 157

Goddess Athena, virgin, 56Goladhyaya, 100Golden mean, 60Gold pieces, 110Gout, 186, 256Govardhan Matha Monastery in Puri, 364Grahaganitam, 100Grantham, 181

Graphical computer program, 433Graphical Statics, 340Gravitation, universal law of, 212Gravity, universality of, 262Greatest creations of mankind, 18Grhasthas, 39Grid, 162Grooves, carved, 26Guitar, 59Gun, rapid-fire, 149Guruvayur, 150Gynecologist, 342Gyroscope, 140, 325

HHabits, methodical, 156Hall of Fame for Great Americans, 292Hall of Fame, National Inventor’s, 326Hall of Fame of India’s National Institution,

429Hands, using the, 104Harappan period, 42Hard disk space, 33Hardware, 25, 27, 29, 33, 414Harivamsa (16,000 verses), 38Harmony of the Worlds, 156Harvard Mark I computer, 28, 407Harvest, sheaves of a good, 93Hawk, 86Head, large, 16Health, state of, 56Heart attacks, 230, 255, 309, 314, 343, 358,

368, 387, 418, 419, 431Heavenly bodies, position of, 88Heaven, map of the, 91HEC 2M. See Hollerith Electronic Computer

2M (HEC 2M)Helium II, a liquid, 412Hell, location of, 152Hemoglobin, 384Heptad, 56Herbs, 67Heredity, 275–277, 312, 361Hero of the revolution, 439Hiker and climber, 415Hindu–Arabic numeral, 106, 118, 119, 131Hindu Art of Reckoning, 106Hindustani classical music, 377History, chronology of ancient, 82Hoax, 115Hollerith Electronic Computer 2M (HEC 2M),

387Homosexual relationship, 417

486 Subject Index

Honeybee, 275, 420Hora Saara, 87Hormone therapy, 417Horoscopes of prominent persons, 107Horse’s hair, 53Human-land, fertile, 38Hunchback, 325Hydraulic organ, 79Hydrogen bomb, 398Hygrometer, 177Hymn, 38, 39Hypercomplex numbers, 255, 358Hyper-computing facilities in India, 418Hypertext transfer protocol (http), 32Hypotenuse, 6, 41, 58, 96Hypothesis, generalized continuum, 330, 406

IIBM 704 computer, 432Icosahedron, 56, 58, 70, 83, 155, 303Identity, 119, 163, 182, 235, 253, 271, 296Immunology, 446Imposter, 344Imprisonment, life, 153, 327Incommensurable magnitudes, 70Indestructible part of a line, 62Indestructible part of time, 62Indian numeral, 118India’s first second generation computer,

ISIJU, 30, 440Induction, mathematical, 24, 114, 135, 256Inequalities, 9, 55, 150, 191, 206, 239, 247,

254, 271, 292, 297, 305, 308, 315, 322,323, 326, 328, 366, 373, 381, 382, 445,446

Infallibility of the Church, 270Infinite amount of sex, 66Infinite dimensional case, 254Infinite, paradox of the, 109Infinitesimals, 12, 71, 101, 125, 129, 156, 165,

174, 185, 190, 209, 251, 288, 295, 296,313, 314, 338

Infinity of infinities, 14Influenza, 253, 260, 304, 335, 375Insane, 115, 225Instability, 35Integers

complex, 227smallest, 56sums of powers of, 158

Integrals, volume, 258Integration, numerical, 12, 29, 269, 333, 398Intercourse, 60

Internet, 32, 103, 159, 294Interpolation, 9, 10, 87, 88, 99, 128, 131, 178,

183, 199, 289, 339, 341, 384Intervention, divine, 67, 217, 369Intuition, spirit of, 173Invasion, Aryan, 21Irrationals, 3, 23, 34, 41–43, 58, 61, 67, 68, 71,

77, 83, 101, 112, 117, 131, 134, 144,210, 258, 267, 277, 278, 284, 289, 320,404

Itihasa-Purana, 39

JJacobites, 199Jain monk, 109Jambudvipa, 48Jaundice, 171, 396Java, 31Jaws of animals, 53Jesuit priest, 206Jewels, nine, 86Jupiter, satellites of, 211Jyotisha, 39, 50

KKalpa (ritual), 39Karana Padhhathi, 165Karmic, finite, 14Katyayana, 6, 40, 41Keyboard, octave, 174Khandakhadyaka (Edible Bite), 88, 104Kidney failure, 147Kithara, 59Knife, stealing a, 262Knots, 25, 26, 170, 437Knowledge-based systems, 433Knowledge, erroneous, 104Knucklebones, 2Kosmos, 59Kronecker’s opposition to Cantor’s work, 267Kuttaka, 7, 42, 137

LLadies’ Diary, 205Laghubhaskariya, 86Lalla’s teachings, 116Lamp, shaded, 230Lancets, 53Lands, measuring of, 106Land surveying, 11, 114, 117, 241Languages, four thousand, 3

Subject Index 487

Lawof continuity, 156, 206of large numbers, 189, 233, 271natural, 197Planck’s, 386Snell’s, 157Stokes’, 269

Laws of nature, ten, 162Laws of Thought, 265Learning, Perverse, 69Learning, Revival of, 16Least action, principle of, 91Lenses, focal length of, 164Letters, enciphered, 170Leukemia, 427Life, aristocratic, 196Lightning, 52Light Quantum Hypothesis, 386Light, speed of, 126, 154Light-years, 234Lilavathi Bhasya, 13, 128Limits

narrower, 262variable, 228

Linear combination, 144, 290Linga (11,000 verses), 38Lobsters, 424Loci, surface, 76Logarithm

common, 158device called the, 148Napierian, 204natural, 171, 298

Logiccomputational, 438intuitionistic, 400programming, 31symbolic, 256, 288, 394, 401, 419

Longitude at sea, 191Lotus flower, 39, 101, 102, 421Loudspeakers, 224Love knot, 170Lunar year, 65Lune, 11, 65Lungs, action of the, 200

MMachine

general-purpose, 29–31learning, 447theoretical/hypothetical turing, 28

Machine-independent programming languages,408

Madhyaloka, 48Maga Brahmin, 86Magic square, pandiagonal, 87Magnetism, terrestrial, 228Magnetohydrodynamics, 416Mahabharata, 38Mahabhaskariya, 86, 108Mahakshobha, 110Mahayuga, 42Maitrayana, 40Majority decisions, 213Male and female, both, 55Manava, 40Manchester Mark I, 28Mango fruits, 110Manhattan Project, 349, 367, 398, 422Mannheim, Baden, Germany, 294Man, primitive, 3–5Man, small, 162, 176Manyakheta, 109Maps

conformal, 284, 297, 301, 325, 379weather, 276

Maragha, 121Marbles, gravity-driven, 28Markandeya (9,000 verses), 38Markov chains, 308, 327Marriage and morals, 334Mars, occultation of, 190Martyrs, 163Marvelous Merchiston, 148Maryland, 29, 210, 363, 397, 398, 440Massacre, St. Bartholomew’s Day, 142Massless rod or cord, 174Mathematical Analyzer, Numerical Integrator

and Computer (MANIAC), 398Mathematical art, 8, 93Mathematical Explorations and Excursions,

404Mathematical proof, 19–21, 25, 34, 36, 93,

131, 205, 299Mathematical puzzles, 342Mathematician(s)

blind, 194hyper-pure, 370and machine, 32Vedic, 46, 365

Mathematicscomputer, 413faulty, 14, 300prince of, 184, 230queen of, 4, 230Sanksrit sutras in, 364uncivilized continent of, 4

488 Subject Index

Mathematics in War Perspective, 334Matrimony, 156Matrix algebra, 273, 358, 428Matsya (14,000 verses), 38Matter, first principle and basic form of, 54Maxima, 12, 13, 200, 336Mayan ziggurat, 402Meat broth, 73Mechanics, quantum, 273, 276, 287, 295, 348,

367, 395, 397, 412Medallist, youngest gold, 450Medical imaging, 11Medication, potency of their, 109Medicinal plants, 53Meditation, 39, 161, 184, 322, 364, 379Melancholy temperament, 298Memory, photographic, 396Memory, re-circulating mercury-delay line, 29Meningitis, 368Mental calculation, 170, 279Mental illness, undiagnosed, 318Mercator charts, 151Merchants, three, 110Mercury, 29, 77, 155, 156, 190, 191, 198, 206,

348Meridian at Greenwich, Prime, 247Meruprastaara, 60, 61Metalanguage, 394Metal insert, 147Metals to gold, 184Metaphysics, 14, 121, 122, 185, 186, 203, 299,

311, 317, 335, 364Metempsychosis, 59Meteor shower, Leonid, 269Method, “chakravala” (cyclic), 7, 101Method, least squares, 219Methods, heuristic (self-educating) search, 433Metric spaces, 346, 389Microscope, reflecting, 182Microwave ovens, 33Migraine headaches, 173Milky Way, 152Millennium BC

first, 3second, 5

Mimamsa (rituals and spiritual philosophy), 39Minds as vital tools, 37Minerals and plants, properties of, 67Minimal cost telephone networks, 442Minimal surfaces, 444, 447Minute arc, 130, 151, 158Mirror, Burning, 83, 84, 99, 149Misnomers, historical, 365Mlechchas, 87

Mobile phones, 448Molding, 38Molecular Computation of Solutions, 446Monads, 186

monas, One, the, 55Mongol invasion, 120Monk, 69, 104, 109, 127, 133, 135Monsoon season, rainy, 5Moon

mountains on the, 152waxing and waning of the, 4

Morality, victorian notion of, 334Motion

elastic, 224laws of planetary, 147, 191six types of, 70

Motorized pogo stick, 425Mountaineering accident, 327Movie Sneakers, 447Mozambique, 2Mridangam, 377Mug, quart, 180Mule, 51, 77, 119, 442Multimedia authoring tools, 438Multiplication, rules for the, 143Muscle contraction, 193Muses, 44, 56, 72Mushrooms, poisonous, 198Music therapy, 59, 109Mustard seeds, 46Myriad, 79, 102Mystery, unsolved, 365Mystic, number, 155Mythological monster, 80

NNaked, stripped, 97Namagiri, family goddess, 369Naming convention for large numbers, 142Napier’s bones, 29, 148Narada (25,000 verses), 38Narayaneeyam Dinam, 150Natural inheritance, 276Natural Knowledge, Principles of, 317Nature, Concept of, 317Nature, good, lucky celestial, 55Navaratnas, 86Navayoni Chakra, 39Navigation, 11, 141, 147, 148, 150, 217, 414Navigation instructor, 414Nazi years, 305Nearsightedness, 192Nebulae, 4, 189

Subject Index 489

Necklace, beautiful pearl, 101Negative wealth, 441Neomartyr, 360Neoplatonism, Syrian, 94Neo-positivist, 361Nephritis, 275Neptune, 153, 227, 231, 262, 268Nerve action potential, 311Netherworld, 3Neural networks, 443Neurosurgery, 432Newton, Correspondence of Isaac, 366Newton’s work, plagiarized, 183Nile, periodical inundations of the, 50Nirukta (etymology), 39Nitrous acid, 214Nomad, academic, 362Nonconstructive proof, 23Non-deterministic polynomial time (NP)-hard

problem, 34Nose, prominent, 162Notation, good, 318Notion of compactness, 346Nuclear fission, 282Nuclear fusion, 393Nude, 285Number(s)

of atoms, infinite, 66decomposition of, 260distribution of prime, 444feminine, even, 55first masculine, 56irrational (illogical or unreasonable), 3law of large, 189, 233not a, 55, 134perfect, 57, 105, 131, 163theory

computational, 4, 449probabilistic, 4

transfinite, 318, 319Numbering rods, 148Number: The Language of Science, 363Numerical calculations, lacks any, 76Nursing, modern medical, 263Nyaya (law of nature), 39

OOath not to reveal, 55Objects beyond our world, 4Obscurity of the subject, 64Occultation, 90, 190Octahedron, 56, 58, 70, 155Octave, 119, 174

Oil stoves, 286Old Testament, 44, 132Olive crop, 51Olympic soccer (football) player, 367One-third man, 66Ontology, 353Operating systems, 437Operations, fixed- and floating-point, 29, 34Opinion, two stood for, 56Opium, overdose of, 176Optical illusions, 348Optics, physiological, 180, 214, 278Orbits of Jupiter and Saturn, 207Organisms, 177, 417Origin, “barbaric,” 236Orphic philosopher, 60Overheated room, 223Oyster shell, 97, 110

PPadma (55,000 verses), 38Paganism, twilight of, 163Painter, mathematical, 234Paleontology, 177Palm leaves, 2Panava, 86Panchangam, 43Pancha-Siddhanta, 87Paper tape, punched, 29Parable, 17, 253Parabola, focal properties of a, 83Parabolic reflector, 80Paradox

liar’s, 308Russell’s, 14, 333

Paradoxes of the Infinite, 234Parallax, 107, 129, 152, 234Parallel zero-knowledge proof, 448Paralysis, 150Paramour Pink, 191Paranoia, 184Parody of the metric system, 442PASCAL, 31Pascaline, calculating machine, 25, 186Patiganita (Mathematics of Procedures), 100Patrimony, 372Peashooters, 247Pebble, common, 116Pellets, pierced, 25Pendulum in a resisting medium, 232Pensees (Thoughts), 173Pentagram, the beautiful star, 55Periodical, world’s first, 248

490 Subject Index

Persecution, 37, 64, 175, 340, 389Personality, vivacious, 176Person of the century, 349Perturbations of the planetary orbits, 232Pharaonic practice, 81Philosopher, Neoplatonist, 97Philosopher’s death, 82Philosophy

experimental, 197founder of, 163of science, 51, 361

Photoelectricity, 347, 349Photons, 349, 367, 378, 386Physical weakness, 161Physicochemical phenomena, 291Physico-mathematics, 208Physics, elementary particle, 446Physiological optics, 180, 214, 278Piano keyboard, 119Pipe organ, 81Pirates, 176Plagiarism, Leibniz of, 183Plague, bubonic, 181Plague, Great, 181Plane Loci, 83Planet(s)

innermost, 155latitudes of the, 101longitudes of the, 86, 104, 113

Plant genetics, 361Platonic realm of objects, 353Platonist school, 97Plato’s Academy, 69, 72, 81Pleuritis, 281Plimpton 322 (a Babylonian clay tablet), 6Pneumonia, 162, 250, 265, 267, 334Pocket compass, 347Points, infinitely close, 12Poisoning, methods of, 53Polarization of the sunlit sky, 415Polio, 355Polish notation, 346Polish underground army, 383Polyhedron, 155Polymath, 129, 206, 340Polynomial-time, 32–34, 449Polytope, 315Population

dynamics, 351flour beetle, 252fruit fly, 252

Porcelain, inventor of, 188Postulates, three, 76Potato, 150

Potential infinity, 12, 73Power, French unit of, 237Prakrit language, 300Pressure, barometric, 191Prime, Mersenne, 32Primes, infinite number of, 24, 77, 219Primordial female, 39Primordial male, 39Princeton Cemetery, 401Principle of Maximum Plastic Dissipation,

361Principles of Analytical Calculation, 224Prisms, volumes of, 11, 45Prism, truncated triangular, 11, 93Probability, negative, 395Problem

birthday, 361intractable, 32kissing, 443traveling salesman, 446–447

Problem, Cattle, 79Processor speed, 33Prodigy, child, 255, 342, 396, 411, 450Programming as a scientific discipline, 437Progression

arithmetic, 48, 49, 96, 144, 195, 254, 385,405, 451

with fractional numbers, 100geometric, 41, 96, 144harmonic, 96

Projective transformation, 32, 34, 303, 449Proof

direct, 21, 22, 90fallacious, 302geometric, 143methods of, 70and program verification systems, 438of the transcendence of e; 276ugly, 25

Proportion, rule of, 164Proposition

false, 19, 35infinite list of, 24

Protestant sentiment, antipsychic, 155Psychology, differential, 26, 60Psychometrics, 277Pump

hydraulic, 165piston, 81pressure, 81suction, 81

Puranic view, 88Putha-gorus, 59Puthumana Illam (Kerala), 165

Subject Index 491

Pyramid, volume of a, 11Pythagoreans, fanatic, 61

QQuadrivium, 55, 56, 69, 102, 114Quantities, impossible, 215Quantum computing, 441Quarrel, acrimonious, 193Quartan fever, 177Qubits, 441Quicksort, 441quipu (an Inca word meaning “knot”), 26

RRaasi-gola-sphuta-neeti, 149Rabbit, pair of, 118Radical group, 261Rajju, 48Raleigh’s ship, 150Raman effect, 378Rao Paradox, 429Rarefied gases, 246Rasa, 53, 377Rasi, 300Reality, 4, 17, 66, 69, 70, 175, 253, 267, 268,

317, 334, 344, 347, 349, 441Reasoning through a process, 55Rebirth, 105Rectangle

square equal to a, 6, 40triangle equal to a, 6, 40

Reductio ad absurdum, 23, 65, 90, 300Refraction, atmospheric, 43, 115Regression, linear, 226Reincarnation, 59Relativity priority dispute, 322Religion of the Soul, Eternal, 364Religious cults, 54Renaissance, 112, 121, 122, 144, 164Respiration, 179Retardation, equatorial, 190Revelation, whole, 149Revolution, French, 211, 213, 217, 219, 220,

222, 235Rheumatic fever, 426Rhombus, triangle equal to a, 6, 40Right-angle triangle, archetypal, 56Rigveda, dictionary for the, 257Rise of divorce, 381Rishis, 19, 87Ritual sacrifice, 5, 40Robotics, 438

Rocket-powered Frisbee, 425Roman numeral, 118Romantic era, 308Rooster, psychic, 149Roots, recomposition of imaginary, 160Rope stretchers, 6, 41, 67Rotating mass of fluid, 307Rotating universes, 406Rotation, diurnal, 104Rote learning, 347Rounding and truncation, 35RSA data security, 447Ruler and compasses, 66Russia, invasion of, 236Russian cipher, 375

SSadhu (saint), 364Sadratnamala, 127Sages and Rishis of history, 19Saint of computers, patron, 103Saint of the Internet, patron, 103Sakhas (recessions)., 38Sakti, 39Sam (United States), 420Samadhi, Maha, 364Samaveda, 38Samhita

Brihat, 87Charak, 53Sushrut, 53

Samhitas (hymns), 38Samuha, 300Samurai warrior, 180Sanatana Dharma, 39, 87Sanatorium, 406Sand Reckoner, 78, 170Sand-Reckoner, Archimedes, 78Sangamagramma, 13, 126–127Sanitation in hospitals, 263Sanskrit scientific manuscripts, 106Sanyas, 364Satan, Cantor, and infinity, 427Satellite-artificial, 43Satkhandagama, 48Saturn’s rings, 304Savior, tomb of the, 163Scarlet fever, 426Scattering of x-rays by liquid, 378Scholastics, first of the, 100School, Digambara, 48School of astronomy and mathematics, Kerala,

127, 137, 149, 150

492 Subject Index

School of Economics, London, 333School of Mathematics, Jain, 14, 300Schools of thought, 14, 300Science and Humanism, 371Science, molecular and microscopic, 231Science of love, 110Science of measurement and number, 15Science of nonexistent things, 372Science of self-evident things, 15Sciences

exact, 52, 173, 312queen of the, 230

Scientific computing, 27Sea-Mirror of the Circle Measurements, 120Secretiveness, 192Secrets-military, 327Seismology, 11, 70Self-realized saint, 364Self-replicating spacecraft, 398Semitic Babylonians, 43Sequences, fourteen types of monotone, 14Series

divergent, 249, 315, 332Nilakanthan’s arctangent, 179, 186summability of, 315

Series of functions, infinite, 13Series of squares and cubes-summation of, 42SETL programming language, 438Set-omniscient, 14, 300, 301Set-perfect, 317Sets-transfinite, 14Set topology, 317Setun-70, 31Sexagesimal (base 60), 108Shankaracharya of Sharadapith, 364Shanku-yantra, 42–43Shastras, 50Shiksha (phonetics and phonology), 39Shirsa prahelika, 46Shishyadhividdhidatantra, 104Shiva (24,000 verses), 38Shock waves, 284, 340, 434Siddhanta

Aryabhatta, 42Paitamaha, 87Paulisa, 87Romaka, 87Siromani, 13, 100Surya, 9, 87Vasishtha, 87

Siddhanta of Brahmagupta, 107Siddhantasekhara, 116Siddhanta Siromani (Crown of Treatises), 100Sifr, 118

Sightless, 203Signal processing, 226, 450Silicon chip, 31Sine table, construction of a, 87, 108Singular value decompositions, 291Skanda (81,100 verses), 38Skating, ice, 235Slavery, 210Slaves to women, 67Slide rule, principle of the, 164Smallpox, 200, 253Smoker, inveterate, 176Smoking cigars, 325Smoothing of Stationary Time Series, 384Snake, black, 110Soap, film analogy, 341Socrates, pupil of, 68Software, 25, 27, 33, 103, 408, 436, 438Solar year, Length of the, 89, 111Solids, perfect tetrahedron, 70Solitonic physics, 434Solutions-existence and uniqueness of, 286Son

drowning, 315illegitimate, 208

Sorcery, 146Sorting algorithms, 441Soul

parting of the, 282purification of the, 55

Sound, ranging equipment, 358Sour, 53, 183, 353Space-filling curves, 325, 375Space Shuttle Columbia, 416Space-time continuum, 273, 324Space–time–matter, 366Spectroscopy of gases, 246Spheres

celestial, 113, 156gravitational, 290

Spherical harmonics, 270, 287Sphuta-nirnaya, 149Spider-black, 149Spiral

equiangular, 189logarithmic, 187, 197

Spirits, departed, 3Spiritual philosophy, 39Spyglass, 152Square equal to a rectangle, 6, 40Square n times in area to a given square, 5, 40Squaring a figure, 61Srichakra, 39, 40, 43Sriyantra, 39

Subject Index 493

Stabilityin a chaotic system, 439hydrodynamic and hydromagnetic,

415–416of orbits, 307

Starbinary, 234dead, 234

Starvation, 82State of silence, the ultimate state, 379Statistical mechanics, 291Statistics

Bose, 386Fermi–Dirac, 395

Statistics and Truth, 428Stellar atmosphere, 385, 415Stellar Interiors, 418Sterility of a cow, 271Sticks-notches cut on wooden, 2Stones-scratches on, 2Storage and control, separation of, 28Story, apocryphal, 205Strange dreams, 140Street brawl, 193String

knotted, 26vibrations of, 198

Strip of carbon and oxygen atoms, 240Stroke, 2, 3, 42, 179, 204, 255, 362, 407Structured programming, 437Student, rowdy, 263Submarines, German, 414Suicide by taking cyanide, 417Sulbasutra, 40Sun

annual eclipses of the, 113diameter, 78distance, 190equator of the, 206true longitudes of the, 113true positions of the, 107

Sunya, 42Super, computer, 408Supersonic nozzle, 341Supersonic shock waves, 340Superstitious, 54Supper, Last, 160Supreme Fascist (God), 420Surfaces, minimal, 444, 447Surgical operation, 407Surveying, 5, 11, 50, 89, 90, 114, 117, 145,

241, 295, 337Surya Prajnapti, 45Sutra, Buddhist Diamond, 94

Switches, telephone routing, 29Switching circuits, 425Symbol of health, 55Symbol of the mathematics, 55System

caste, 116heliocentric, 85Hindu–Arabic decimal, 86Hindu place-value, 106limitations of the Greek numbering, 78of weights and measures, 3

System of Numeral, Sanskrit, 108

TTables, nautical, 178Tablets, 2, 4, 6, 7, 11, 23, 43–45Talismans against evil, 87Tangents, for drawing, 12, 166Tasso, critique of, 152Tata Institute of Fundamental Research

Research Automatic Calculator(TIFRAC), 30

Telescopeaerial (tubeless), 174Gregorian, 178

Tensor analysis, 227, 284Ternary computer, 31Tetrahedral, congruent, 319Tetrahedron, 12, 56, 58, 70, 93, 136, 155Theorem

of algebra, fundamental, 7, 160, 226, 238Aryabhatta, 21, 22binomial, 24, 114, 117, 123, 179, 182of calculus, fundamental, 13, 128central limit, 271, 310, 373, 416Chinese Remainder, 98divergence, 228, 245famous false, 239Fermat’s Last, 166, 219, 231, 244, 254, 344four colors, 36, 302Gödel Completeness, 405prime number, 219, 226, 272, 326, 328, 343proof of Fermat’s last, 231, 260, 305, 344

Theories, undecidable, 394Theory

algorithmic complexity, 400Bohr–Kramers–Slater (BKS), 367of Brownian motion, 289, 415of the circulation of blood, 163of complex iteration, fundamental, 345of errors, 251of the evolution of the sex ratio, 381fuzzy set, 14

494 Subject Index

Theory (cont.)Maxwell’s electromagnetic, 347measure, 330, 332, 336, 389, 397proof, 321of recursive functions, special, 404, 414of relativity, general, 348, 355, 371, 416of relativity, special, 154, 307of the structure of the human brain, 399of superconductivity, 412

Theory for Metamathematics, Recursion, 427Theory of Error-Correcting Codes, 443Theory of Numbers, History of the, 337Thermometer

alcohol, 198mercury, 198

Thyagaraja Keerthana, 376Tiger of Bengal, 377Time, sharing computer systems, 435Tomato picker, automatic, 155Toothache, 173Topology, chemical, 240Tragedies, 37, 66, 327Trajectories, orthogonal, 183Trakeacheda, 47, 48Transformations, infinitesimal, 295Transistors, 31Transmigration, 59Transmission control protocol/internet protocol

(TCP/IP), 32Transmutations, 52Tree, Steiner, 244Triad, three the, 56Triangle, 5, 6, 9–11, 20, 22, 24, 39–41, 45, 50,

51, 56–58, 60, 65, , 75, 77, 85–87, 90,91, 96, 114, 119–121, 123, 125, 130,136, 147, 148, 153, 160, 166, 172, 202,219, 242, 297, 359

Triangle Pascal’s, 24, 114, 119, 123, 125Trilokaprajnapti, 48Triloko Sara, 48Truth

subjective, 19universal, 19, 405

Tuberculosis, 53, 124, 161, 201, 248, 281, 289,298, 331, 338, 369

Tubes, vacuum, 29–31, 246Turing-complete, 28, 29Turing machine, 28, 417Typhoid fever-plague of eruptive, 71

UUlcer, bleeding, 407Uncertainty principle, 392, 395

Universal Automatic Computer (UNIVAC), 30Universal Truth Machine, 405Universe

center of the, 45, 130infinitude of the, 268

Unshaken foundation of science, 15Upangas, 39Upanishads (philosophies), 38Uparagakriyakrama on lunar, 149URAL (a big-bodied Russian Computer), 387Uranus, 80, 231, 262, 268Uttaradyyana Sutra, 45

VVacuum tubes, 29–31, 246Vaisampayana, 38Vamana (10,000 verses), 38Varaha (10,000 verses), 38, 40Vayu (24,000 verses), 38Vedanga Jyotisha, 50Vedangas, 39Vedas, 38–40, 50, 364Vedic meters, 60Vedic Sulvasutras, 48Veena, 376Vegetarianism, 369Vehicle, tank-like, 149Venn diagram, 14, 288Venus, transit, 178, 192Vietnam War, 439Vikalpa, 45Violent way, 67Violin, acoustics of the, 328Virginity, 56Virtual private networks, 448Viscosity of liquids, 378Vishnu (23,000 verses), 38Vishnu Purana, 38Vitamin B12, 295VLSI design, 447Void, 67von Neumann

architecture, 28, 398bottleneck, 398

Vyakarana (grammar), 39Vyasa, 38–40

WWandering stars, seven, 56War, Trojan, 59Waterclock, 181Wavelets, 222

Subject Index 495

Web browsers, 448Western drums, 377Whales, 50Whispering gallery, 377White Jew, 392Windmill (for grinding grain), 242Wind tunnel, 341Wisdom, static, 39Witch’s spell, 171Wolf, young, 2Woman-rugged, tireless, 162Wood-apples, fragrant, 110Work, three types of, 72World, map of the ancient, 92, 107, 141World War I (1914–1918), 309World War II (1939–1945), 305World wide web (www), 32

XX-machine, 421

YYajurveda, 38, 50Yasti-yantra, 43Year, length of the, 42, 43, 116Yoga-sadhana, 364Yojana, 46, 48Yuktibhasa, calculus text, 13

ZZ1, 28Z3, 28Zeeman effect, 309Zeno’s paradoxes, 62, 63, 74Zero

division by, 88repeated, 88the void, 186

Zodiac, signs of the, 113Zoology, descriptive, 179