52 3. MATHEMATICAL CULTURES IIWasanists were men of fine arts rather than men of mathematics in the European
sense."
According to Murata (1994), tne stimulus for the development of wasan came
largely from the two Chinese classics mentioned above, the 1593 arithmetical trea-
tise Suan Fa Tong Zong and the algebraic treatise Suan Shu Chimeng. The latter
was particularly important, since it came with no explanatory notes and a rebellion
in China had made communication with Chinese scholars difficult. By the time this
treatise was understood, the Japanese mathematicians had progressed beyond its
contents.
Sangaku. The shoguns of the Tokugawa family (1600-1868) concentrated their for-
eign policy on relations with China and held Western visitors at arms length, with
the result that Japan was nearly closed to the Western world for 250 years. During
this time a fascinating form of mathematics known as sangaku (mathematical study,
the "study" being a physical plaque) arose, involving the posting of mathematical
plaques at sacred shrines (see Plate 2). These problems are discussed in detail in
the book of Pukagawa and Pedoe (1989).
Yoshida Koyu. Mori Shigeyoshi trained three outstanding students during his life-
time, of whom we shall discuss only the first. This student was Yoshida Koyu
(Yoshida Mitsuyoshi, 1598-1672). Being handicapped in his studies at first by his
ignorance of Chinese, Yoshida Koyu devoted extra effort to this language in order
to read the Suan Fa Tong Zong. Having read this book, Yoshida Koyu made rapid
progress in mathematics and soon excelled even Mori Shigeyoshi himself. Eventu-
ally, he was called to the court of a nobleman as a tutor in mathematics. In 1627
Yoshida Koyu wrote a textbook in Japanese, the Jinkd-ki (Treatise on Large and
Small Numbers), based on the Suan Fa Tong Zong. This work helped to popularize
the abacus (soroban) in Japan. It concluded with a list of challenge questions and
thereby stimulated a great deal of further work. These problems were solved in a
later treatise, which in turn posed new mathematical problems to be solved; this
was the beginning of a tradition of posing and solving problems that lasted for 150
years.
Seki Kdwa and Takebe Kenko. One figure in seventeenth-century Japanese math-
ematics stands out far above all others, a genius who is frequently compared with
Archimedes, Newton, and Gauss.^6 His name was Seki Kowa, and he was born
around the year 1642, the year in which Isaac Newton was born in England. The
stories told of him bear a great resemblance to similar stories told about other
mathematical geniuses. For example, one of his biographers says that at the age of
5 Seki Kowa pointed out errors in a computation that was being discussed by his
elders. A very similar story is told about Gauss. Being the child of a samurai father
and adopted by a noble family, Seki Kowa had access to books. He was mostly self-
educated in mathematics, having paid little attention to those who tried to instruct
him; in this respect he resembles Newton. Like Newton, he served as an advisor
on high finance to the government, becoming examiner of accounts to the lord of
Koshu. Unlike Newton, however, he was a popular teacher and physically vigorous.
He became a shogunate samurai and master of ceremonies in the household of the
(^6) His biography suggests that the real comparison should be with Pythagoras, since he assembled
a devoted following, and his followers were inclined to attribute results to him even when his
direct influence could not be established. Newton and Gauss were not "people persons," and
Gauss hated teaching.