Kowa and Yasuaki
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Transcript of Kowa and Yasuaki
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TAKAKAZU SEKI KOWA & AIDA YASUAKI
The most distinguished Japanese mathematician of the Tokugawa
Shogunate (1603-1867) era and perhaps of a time was Takakazu Seki
Kowa (!arch 16"#$ % &cto'er #" 1708) Aida Yasuaki (*e'ruar+ 10
17"7 % &cto'er #6 1817) was one of the most proific mathematicians
of his time This entr+ is not on+ the stories of these two 'ut aso a
'rief description of the ear+ de,eopment
of Japanese mathematics Japan did not 'egin its inteectua de,eopment
unti uddhist missionaries arri,ed from .hina around / 00
Traditiona+ it is 'eie,ed that Japan had a crude s+stem of numeration
dating from 600 .2 and that ear+ in its eistence it produced or
'orrowed a s+stem of measures and a caendar
uring the 8th
centur+ .2 man+ of the .hinese mathematica arts were introduced into Japan Japanese
mathematicians imitated the work of .hinese schoars and when a uni,ersit+ s+stem was esta'ished in
Japan nine .hinese 'ooks were made the 'asis of the mathematica curricuum .hinese mathematics
and Japanese mathematics used the same anguage not 4ust the same .hinese characters Thus if
Japanese mathematicians ac5uired .hinese mathematica 'ooks the+ coud ha,e easi+ understood
.hinese mathematica ideas
uring the Tokugawa Shogunate Japan gradua+ cut itsef off from the western word with this sef-
imposed nationa isoation ( sakoku) officia+ decreed in 163 .itiens were for'idden to ea,e the
Japanese ises foreign 'ooks were 'anned and foreign missionaries and their con,erts were persecuted
Takakazu Seki Kowa
Aida Ysuaki
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e,ertheess during the ate 17th centur+ the countr+ eperienced a cutura renaissance simiar to the
one that had occurred in the pre,ious centur+ in 2urope This period known as genroku saw haiku
poetr+ de,eop into a high art form as did No and Kabuki theater Japanese mathematicians created
their own mathematica word and earned peope of a casses from farmers to samurai produced
theorems in 2ucidean geometr+ !ost of the theorems and answers to pro'ems were presented as
'eautifu+ coored drawings on wooden panes caed sangaku itera+ meaning 9mathematica
ta'et: which were hung under the roofs of a shrine or a tempe: The sangaku 'oth mathematics and
art were 'eautifu in their simpicit+ !an+ of these were ost during the moderniation period of the
!ei4i re,oution ;owe,er a'out nine hundred of these sur,i,ed and can 'e seen nowada+s in rura
Japan
!an+ mathematicians contri'uted significant+ to Japanese mathematics in this period /mong these
are !
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himsef mathematics Seki is known to ha,e coected mathematics 'ooks from 'oth the .hinese and
Japanese cutures and e,entua+ 'ecame so recognied as a mathematica epert that he was caed
Sansei (9The /rithmetica Sage:) a tite car,ed on his tom'stone ;e is genera+ considered to 'e the
founder of Japanese mathematics
Dnder SekiEs infuence a Japanese schoo of mathematics was created ecause of the secrec+ and
ri,ar+ among Japanese schoos it is difficut to identif+ a of SekiEs mathematica contri'utions @t is
known that he introduced age'raic notations in,ented determinants to so,e s+stems of inear
e5uations and e,ident+ made ma4or disco,eries in cacuus ;e created a new mathematica notation
s+stem which he used to determine man+ of the theorems and theories that were aread+ known in
Cestern mathematics /though he anticipated man+ of the disco,eries of Cestern mathematics there
is no e,idence that he was in an+ wa+ infuenced '+ it Dnfortunate+ if the num'er of manuscripts
attri'uted to Seki =owa is accurate then most of these ha,e 'een ost
ecause he was a descendent of the samurai cass Seki was appointed eaminer of accounts for the
Ford of =oshu and when the atter 'ecame Shogun Seki 'ecame Shogunate samurai @n 170" Seki was
made the master of ceremonies in the ShogunEs househod Seki is gi,en much credit for the socia
reform that heped de,eop the stud+ of mathematics in Japan and make it wide+ accessi'e
/ida >asuaki produced as man+ as fift+ to sit+ works a +ear of which near+ #000 ha,e sur,i,ed ;e
was a distinguished teacher of traditiona mathematics which is caed 9wasan: (od Japanese
!athematics) in order to distinguish it from 9+osan: (western mathematics) >asuaki studied under the
mathematician >asu+uki &kaaki @n 176 /ida went to 2do (now Tok+o) to work for the shogunate of
Tokugawa @eharu The shogunate which asted from 11# to 1867 was etreme+ powerfu
controing the emperor administering the ands and making foreign poic+ /ida was empo+ed as a
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ci,i engineer 'ut his dream was to 'ecome the 'est mathematician in Japan
Through a series of unfortunate e,ents >asuaki earned the animosit+ of Sadasuke *u4ita one of JapanEs
eading mathematicians @n 1781 *u4ita pu'ished a mathematica work Seiyo sampo upon which his
reputation rested /ida wrote Kaisei sampo a work 'ased on that of *u4ita 'ut critica of it perhaps in
retaiation for *u4ita pointing out errors in ta'ets inscri'ed with mathematica pro'ems that /ida had
donated to a reigious tempe This fanned the fame of the feud 'etween the two mathematicians
which soon in,o,ed man+ others who took sides in the dispute
Chen the shogun Tokugawa @eharu died in 1786 to 'e succeeded '+ Tokugawa @enari /ida ost his
position and chose to spend the rest of his ife working on his mathematics @n 1788 he compied a
'ook of geometr+ pro'ems caed Sampo tensi shinan @n it he epained the use of age'raic
epressions and the construction of e5uations and contri'uted to num'er theor+ /ida was the founder
of the Saijo schoo one of the most acti,e groups in the mathematica sciences in the atter haf of the
2do period @n 181 =au Catana'e edited and pu'ished the mathematica 'ook Kinsensanpo in
honor of his master /ida >asuaki @t incuded much of the traditiona mathematics of the period that
in,o,ed so,ing compicated geometrica pro'ems featuring chains of circes
uring the 1th centur+ the wasan was gradua+ suppanted '+ +osan This transformation introduced
h+'rid manuscripts written in Kambun with Cestern mathematica notation Chen .ommander Gerr+
opened Japan to the Cest in 1867 cose+ foowed '+ the coapse of the Tokugawa shogunate the
new go,ernment ordered that the stud+ of nati,e mathematics 'e repaced '+ +osan
Quotation of the DayH 9I the Japanese mathematics did not eist as a science 'ut as art &n that
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account e,er+thing studied in Japan had 'orne the character of speciat+ acking in generait+ ut the
Japanese were '+ no means wanting in the scientific spirit the+ were on the contrar+ endowed strong+
with the eaous +earning after truth and knowedge which pre,aied throughout the whoe histor+ of
the Japanese mathematics: % >oshio !ikami