A long time ago, a guy called Fermat said that there are no nonzero integer solutions to the equation a

^{n}+ b

^{n}= c

^{n}for n > 2. He said he had a clever proof that was just too big to fit in the margin he was writing in, and so mathematicians tried for many years to prove what was known as "Fermat's Last Theorem." Then in the middle of the 20

^{th}century, over in Japan two mathematicians called Taniyama and Shimura were doing some seemingly unrelated mathematics, leading to the conjecture that modular forms and elliptic curves were essentially the same thing. Then another mathematician gave a plausibility argument that if Fermat's last theorem were false, it would create a bizarre function that would not fit into the structure of the so-called Taniyama-Shimura conjecture, rendering Fermat and Taniyama-Shimura logically equivalent -- but he couldn't prove it. So Ken Ribet came along and proved it. And then Andrew Wiles proved the Taniyama-Shimura conjecture, which proved Fermat's Last Theorem, which is what all the fuss was about with Fermat's Last Theorem finally being proven.

Here are some pictures of us Williams people with Ken Ribet:

Professor Pacelli, Professor Ribet, Neil, me, and Brian.

Ken Ribet and me.

I talked to the people who were giving a talk on "A Problem Oriented Approach to Geometry." Here was their abstract:

We think it may be possible to organize geometry courses around a set of problems. This approach seems unusual. We have not collected enough problems for a complete course but we have started such a collection. We will share examples of problems we think are interesting, challenging and instructive.So before the conference I e-mailed them and told them that I had learned not only geometry, but also everything else after algebra and all the way up through BC calculus via a problem-oriented approach. I gave them the URL for the Exeter teaching materials and they wrote back and said something like "that's very interesting, thanks, I'll check it out sometime." They did not sound very interested. But when I went to talk to them on Saturday, they were very excited about the curriculum, said it was the best thing ever (an exaggerated paraphrase) and said that they were going to print out the whole thing (no joke, all 400 pdf pages). I told them it was most definitely the best math curriculum ever because people actually learn math, and they don't forget it, even over the summer, even now that I haven't done that math for two years I still remember the problems from ninth grade and the strategies to solve them. It is the best math curriculum ever. Don't waste your time with a textbook. Go straight to the heart of real mathematics and actually learn something. Please.

I also gave my talk on Latin squares. People actually came to watch it. It was astounding. People actually came into the room right before my talk started, to watch it. It was amazing. Who would've though that people actually would come? And the guy chairing the session memorized the number in my talk. That was nice of him, but I felt kind of bad because it was a really long and somewhat useless number. It was actually a pretty engaging and informative talk, if I do say so myself, though not as enlightening as talks that were of a higher level. And 500 people came to the conference. That was a lot of people. And it rained. And Kate Kraft was there. But she didn't come to my talk.

Oh, and the number in the title is the total number of 10x10 Latin squares. I assume you were wondering.

I got into Williams-Mystic! Yay! Take that, Williams-Exeter Programme in Oxford! Take your humanities majors and your stellar GPAs and leave all the engaged mathematical learners back in this country; I'm going to Mystic! (Williams-Mystic site)

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