A Brief History of Western Mathematics from 1700 to 1700

Adrian Rice, Randolph-Macon College

It is ironic that, just as Japan began its period of relative cultural isolation in the seventeenth century, western mathematics was undergoing a serious of remarkable developments that would transform the subject into, essentially, the form in which it is studied today. Although some western sciences and techniques (called rangaku, or “Dutch studies”) were assimilated from books received via Dutch traders, Japanese mathematicians of the Tokugawa period remained largely unaware of western innovations, developing their own individual style of mathematics, known as wasan.
To provide some context for the mathematical talks that will follow, this talk will give a brief survey of the chief mathematical developments to occur in the three and a half millennia prior to the start of the Tokugawa period. In addition to giving an overview of the sort of techniques available to Japanese mathematicians in the seventeenth century, it will also provide a glimpse into the era of rapid mathematical change that was just beginning as the period of Japanese isolation commenced.

 

An Introduction to Tokugawa Japan

Todd Munson, Randolph-Macon College

This brief talk will introduce the social, cultural, and historical context of the Edo Period (1603-1868), with a focus on the interplay between the Tokugawa shogunate’s foreign relation policy and the intellectual milieu which gave rise to traditional Japanese mathematics.

 

A Physicist’s Introduction to Japanese Temple Geometry

Tony Rothman, NYU

I give an overview of Japanese mathematics for the nonspecialist by way of my own introduction to the subject. Focusing on the historical peculiarities that gave rise to the tradition now known as Japanese Temple Geometry, I present a few problems found on surviving sangaku, math tablets, and mention several problems that aroused the interest of readers of Sacred Mathematics: Japanese Temple Geometry, by Fukagawa and Rothman.

 

Mathematics and Philology: An Example from Wasan

J. Marshall Unger, Ohio State University

A certain unsolved problem in Fukagawa & Rothman 2008 turns out not to have a solution of the kind demanded, whereas a slightly modified version of the problem does. An examination of the primary source material suggests that the author’s original diagram may be misleading. Both mathematical analysis and attention to the original text play a role in clarifying the situation.

 

Survey of Wasan

Hidetoshi Fukagawa, Daidou and Kogakkan Universities (JP)

Why did traditional mathematics develop in Far East, Japan? Before the 16th century, there were no mathematics in Japan. The government imported many mathematics books from China, but the Chinese mathematics didn’t develop in Japan. When the soroban abacus was imported into Japan, many soroban private schools, jyuku, arose and flourished in Japan since people wanted good calculators in the area. Many books of soroban methods were published and some of them described more difficult problems. The publications are the origin of traditional Japanese mathematics or wasan. Wasan flourished all over the Japan. Ordinary people who had an interest in mathematics would devote a wooden tablet, sangaku, on which mathematics problems were written, to shrines and temples. Mathematicians who liked to travel visited many villages and taught Mathematics and advised for hanging sangaku. In end of Tokugawa era, there were 80,000 jyku over in Japan. Wasan flourished in this era of peace, and then ended in new government Meiji era.

 

The Gion Shrine Problem

David Clark, Randolph-Macon College

Posed on a sangaku in Kyoto’s Gion (now Yasaka) shrine in 1749, this problem rose to some prominence among Japanese mathematicians. While its geometric diagram is simple, the given quantities in the problem statement make it an algebraic juggernaut. We will discuss traditional solutions, including one by the famous Ajima Naonobu, and a modern one.

 

Mon, mathematics, and culture

Felicia Tabing, Rose-Human Institute

Abstract: Japanese heraldry emblems, called mon, are in the form of circular arrangements that feature many designs which resemble geometric or mathematical objects. Some of the designs even feature knots, links, and iterations of fractals. Interestingly, a few mon designs look very similar to sangaku problems. I will describe my exploration in the possible influence of wasan, sangaku, culture and aesthetics on mon designs.

 

Deconstructing Sangaku

Rosalie Hosking, University of Canterbury (NZ)

Sangaku are beautifully ordained tablets from the Japanese Edo and Meiji periods which contain mathematical problems. In this talk I look at these tablets in their entirety by examining not only their mathematical content but their physical makeup, their construction and the parties involved, the language styles they use, their diagrams and the role they play, the religious and artistic functions of the tablets, as well as the kind of mathematics they use and how they may have been created and solved mathematically to provide a deeper understanding of sangaku as mathematical artefacts.

 

The Rediscovery of Wasan

Mark Ravina, Emory University

The term “wasan,” meaning Japanese mathematics, is largely a modern invention. In the Tokugawa era, it was used occasionally to distinguish Japanese math from Chinese math, but the term became common only in the Meiji era, when it was in contrast to “yōsan,” or Western mathematics. In common parlance, wasan became associated with abacus calculation rather than more advanced mathematics, and some defenders of wasan avoided the term, referring instead to specific techniques. Only in the postwar period was wasan re-appraised as a valued part of Japanese culture.