Mathematics List of Japanese inventions and discoveries

a page seki kōwa s katsuyo sampo (1712), tabulating binomial coefficients , bernoulli numbers



bernoulli number
studied seki kōwa , published after death, in 1712. jacob bernoulli independently developed concept in same period, though work published year later.


determinant
in japan, determinants introduced study elimination of variables in systems of higher-order algebraic equations. used give shorthand representation resultant. determinant independent function first studied seki kōwa in 1683.


elimination theory
in 1683 (kai-fukudai-no-hō), seki kōwa came elimination theory, based on resultant. express resultant, developed notion of determinant.


hironaka s example
hironaka s example non-kähler complex manifold deformation of kähler manifolds discovered heisuke hironaka.


itô calculus
developed kiyosi itô throughout 20th century, itô calculus extends calculus stochastic processes such brownian motion (wiener process). basic concept itô integral, , among important results change of variable formula known itô s lemma. itô calculus applied in various fields, perhaps best known use in mathematical finance.


iwasawa theory , main conjecture of iwasawa theory
initially created kenkichi iwasawa, iwasawa theory developed galois module theory of ideal class groups. main conjecture of iwasawa theory deep relationship between p-adic l-functions , ideal class groups of cyclotomic fields, proved iwasawa (1969) primes satisfying kummer–vandiver conjecture , proved primes mazur , wiles (1984).


resultant
in 1683 (kai-fukudai-no-hō), seki kōwa came elimination theory, based on resultant. express resultant, developed notion of determinant.


sangaku
japanese geometrical puzzles in euclidean geometry on wooden tablets created during edo period (1603–1867) members of social classes. dutch japanologist isaac titsingh first introduced sangaku west when returned europe in late 1790s after more twenty years in far east.


soddy s hexlet
irisawa shintarō hiroatsu analyzed soddy s hexlet in sangaku in 1822 , first person so.


takagi existence theorem
takagi existence theorem developed teiji takagi in isolation during world war i. presented @ international congress of mathematicians in 1920.




^ selin, helaine. (1997), introduction history of mathematics. saunders college publishing. p. 891, isbn 0-03-029558-0
^ poole, david. (2005), linear algebra: modern introductio. p. 279, isbn 0-534-99845-3 .
^ styan, george p. h.; trenkler, götz. (2007), . journal of applied mathematics , decision sciences, 2007, hindawi publishing corporation, pp. 2
^ howard eves: introduction history of mathematics , page 405, saunders college publishing, 1990. (isbn 0-03-029558-0)
^ hironaka, heisuke (1962). example of non-kählerian complex-analytic deformation of kählerian complex structures . ann. of math. (2). 75: 190–208. doi:10.2307/1970426. jstor 1970426. 
^ bibliography of kiyosi itô
^ http://www.math.clemson.edu/~jimlb/coursenotes/iwasawa.pdf
^ association of american geographers (1911). annals of association of american geographers, vol. i, p. 35
^ rothman 1998
^ teiji takagi . mactutor history of mathematics archive. retrieved 5 july 2016.