Imagine for a moment being in a church where mathematics groups meet regularly to solve geometry problems and to pose new ones, to learn new tools for solving intractable ones, and to celebrate beauty that is intellectual, artistic, and spiritual. It may be hard for you to imagine, for mathematics plays such a different role in our culture. We have to enlarge our understanding of mathematics to admit such a possibility, which is one reason why it is so interesting to study Japanese Temple Geometry (JTG). JTG was a sophisticated mathematics whose development, from the 17th to the 19th century, was centered in Zen and Shinto temples, during the period when Japan had closed its borders to Western influence. As an ethnomathematician trained in mathematics, I have come to believe that mathematics is profoundly influenced by culture. Through this realization (and others), I have lost the dualist faith in the transcendental and absolute nature of mathematics into which I was socialized as a student.
The example of JTG might free us to look at mathematics with more than our logical minds, and see in it aesthetic dimensions of beauty, and spiritual dimensions of deep meaning. We’ll move from the general to the particular. Part I is a historical sketch of JTG with musings on what we can learn from its example. We’ll see how math can develop in other ways, and how such differences can even impact issues of war and peace. Part II takes a close look at three Temple Geometry problems, in an unusual context, meant to encourage you to approach them open to resonances beyond the disembodied intellect of the math classroom. Each problem is introduced through one or two slides from an art project that has occupied me over several years, now called: Japanese Temple Geometry on Beautiful Trees. The art slides are followed by presentations of the problem and of its solution. My hope is that the aesthetic-spiritual dimensions will not get lost if and when you dig into the math.