Saturday, July 13, 2019

Fermat's Last Theorem

Somehow, I happened across a beat-up, weathered copy of Amir Aczel's Fermat's Last Theorem just before a long airplane trip, and so I happily accepted the gift.

Aczel has written a number of "popular mathematics" books; I think this was one of his first books.

Fermat's Last Theorem, of course, is a wonderful topic, and perhaps one of the best topics for a popular mathematics book, starting from its origin story in Pierre de Fermat's notebooks ("I have discovered a truly remarkable proof of this theorem which this margin is too small to contain") to the marvelous work of Andrew Wiles, who was a great source of quotations himself:

Perhaps I could best describe my experience of doing mathematics in terms of entering a dark mansion. You go into the first room and it's dark, completely dark. You stumble around, bumping into the furniture. Gradually, you learn where each piece of furniture is. And finally, after six months or so, you find the light switch and turn it on. Suddenly it's all illuminated and you can see exactly where you were. Then you enter the next dark room...

(Wiles's evocative quote is pretty much a spot-on description of writing computer software, too, by the way.)

Fermat's Last Theorem is only peripherally about Fermat's Last Theorem. The mathematics in this book stops, more or less, at the level that a strong high school student would encounter. Mostly, it is a sort of history-of-science book, about what the process of "doing mathematics" was like in the second half of the twentieth century.

And, really, the world needs more books about mathematics, of any sort, even if they are just books about mathematicians, rather than books about mathematics. It drives me absolutely crazy when I wander into a magazine rack in a store and I pick up a book full of Sudoku puzzles, and, emblazoned on the cover, it says "No mathematics skills needed!" as if that was something to be happy for. (And anyway they are so wrong: logic and deduction are absolutely mathematics skills. Oh well, what can you do?)

But as it turns out, I already knew most of the story of Fermat's Last Theorem, though perhaps I didn't know quite so much about the individual mathematicians at the heart of the story.

The most interesting part of the book for me, because it was a bit of history that I had somehow never learned, was the discussion of two Japanese mathematicians, Yutaka Taniyama, and Goro Shimura, who together formulated something called the Taniyama-Shimura conjecture when they were both just in their mid-20's; the details of the conjecture turned out to be the critical turning point in "cracking" Fermat's Last Theorem.

If none of this is any interest to you, or if you're not a history of mathematics sort, give Fermat's Last Theorem a pass. But if you think you might find it interesting, it's a fun little book, and perfect for a 6 hour cross-country plane flight!