Titles and Short Summaries of the Talks

6 Foundation of Mathematics and History of Mathematics
Final: 2013/2/7
5 Kenshi Miyabe (Kyoto Univ.) ♯ The other history of probability theory · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Summary: The axiomatic approach to probability theory was proposed by Hilbert 1900 and it
made a success. The other approach traces back to the work by von Mises (1919). His theory can be
summarized by his word “First the Collective — then the Probability”. In 1960s–70s, Solomonoff
used complexity for prediction and called his theory “algorithmic probability”. Shafer and Vovk
(2001) constructed probability theory based on unpredictability. All these theories suggest an idea
that “the notion of probability is induced from the notion of randomness”.
6 Setsuo Takato (Toho Univ.) ♯ Consideration of an interpretation of the Fangcheng procedure of the
Nine Chapters on the Mathematical Arts · · · · · · · · · · · · · · · · · · · · · · · · · · 15
14:15–16:30
Summary: Many Chinese and Japanese historians have used Gauss–Jordan elimination to explain
the fangcheng procedure of the Nine Chapters. To put it another way, they have insisted that back
substitution was not used in the fangcheng procedure. Recently Roger Hart, the author of “The
Chinese Roots of Linear Algebra”, pointed out that their interpretation was mistaken and it is
significant that he did it by translating the original draft faithfully and analyzing the procedure
mathematically. In this presentation, we introduce his interpretation and assertion, which seem
more appropriate.
7 Hideyuki Majima (Ochanomizu Univ.) ♯ Some remarks on the calculation of pi by Takebe Katahiro · · · · · · · · · · 20
Summary: We gave some remarks on the calculation by Takakazu Seki a few years. Seki found the
so-called Aitken’s delta-sequenced process in his theory, but there were some errors in his calculation
and he only claimed that his approximate number of pi was a bit less than 3.14159265359. Katahiro
Takebe followed Seki’s method and discovered another method of calculation of pi. We will give
some remarks on it.
8 Hikosaburo Komatsu (Univ. of Tokyo ⋆ ) ∗ On Mikami Yoshio’s study on the theory of determinants in Japan in
the 17th century. Which are justified and which are not? · · · · · · · · · · · · 30
Summary: We give a critical survey of the work of Yoshio Mikami (1875–1950) on the elimination
theory of Seki Takakazu (1640?–1708). It is true that Seki made a mistake in his expansion of
determinants of order 5. But many proposals to correct the errors are also different errors. It is
generally believed that Yoshio Mikami (1975–1950) clarified everything in his doctoral dissertation
and others. However, his statements in those documents are often too ambiguous to distinguish their
mathematical truth or lie. We correct many of his errors and give a rigorous proof of his statement
that Seki’s elimination is attained by the classical method of elimination in the simultaneous linear
equations in China two thousand years ago by Sylvester’s theorem which can be proved by the
knowledge of Japanese mathematicians in the 17th century.