“There is a strong connection between epiphanies
in mathematics and epiphanies in religious
experience.”
I
n 1998, Professor Matthew Scott happened to pick up
a copy of Scientific American, attracted by a story entitled
“Japanese Temple Geometry”.
The story described Sangaku, exquisitely illustrated
geometric results drawn on wooden tablets and left as
offerings in Shinto shrines and Buddhist temples in Japan.
The results were typically presented without proof and
people of all ages would flock to the temples to work on the
problems.
Scott was hooked. He spent the summer working on
Sangaku problems and they have been a hobby of his ever
since. Almost twenty years later, he shared the story of the
Sangaku tradition in his Bridges Lecture at the University of
Waterloo.
Though it may seem odd to work on mathematical proofs in
religious temples Scott says that there is a strong connection
between epiphanies in mathematics and epiphanies in
religious experience.
“If you work through a mathematical problem, there is a sort
of enlightenment that doesn’t occur if the answer is simply
presented to you.”
He compares it to the koan in the Japanese tradition of Zen
Buddhism. A koan is a story, dialogue, question, or statement
presented to a student by a Zen Master. It is meant to
provoke thought and potentially lead to enlightenment, but
you have to work through it yourself – no one can explain
it to you. A koan can be as simple as, “what is the sound of
one hand clapping?”
The Sangaku served a similar purpose. Each Sangaku tablet
begins with a preamble explaining who wrote it and why
they left it there. In many cases, the connection between
mathematics and religious belief comes through.
Mathematics is the origin of everything in the universe…
If visitors would look at my sangaku, then I would be very
happy (Ogura Yoshisada, 1817)
When I had questions, I visited and asked mathematician
Ono Eijyu. I appreciate my master’s teachings.
For his kindness I will hang a sangaku in this temple (Saito
Kuninori, 1828).
The Sangaku were part of a larger phenomenon of
recreational mathematics that developed during Japan’s
seclusion in the Edo period (1635-1838). With the end of the
period came the end of the Sangaku tradition, though many
of the problems remain unsolved. It is now up to enthusiasts
like Scott to solve them.
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