Kowa and Yasuaki

8/13/2019 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

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Kowa and Yasuaki