Saturday, August 2, 2008

The Proof is in the Pudding

I love math books! Real math books, anyway. Books about mathematicians and the math that they discover. I've read books about Descartes, Blaine Pascal, and other mathematicians. I've also read books about code-makers and -breakers from WWII. They all fascinate me. Which I find odd, really, because I don't understand math very easily.

I was hooked on this one right from the start.

There was so much information packed into this one book. I can hardly wrap my mind around it. I don't even know what to focus my essay on!

I read several sections of Fermat's Enigma to Josh, always finishing with: “if that's not a testimony of God, then I don't know what is!” I think one of the reasons I like math is that it's so orderly. My favorite “testimony” parts include the mathematics found in music, the pi ratio of rivers, the perfect number 6, and the friendly numbers. People have drawn such interesting comparisons between math and God. I thought the argument that St. Augustine made in “The City of God” about 6 being a perfect number and the earth being created in six days just fascinating.

One of the things that was new to me was the camaraderie within the mathematic community. I didn't realize that they tend to work so closely together, bouncing ideas off each other.

As much as this book is about a math problem, it's also definitely about the passion that envelops people and the tightness to which they can hold to an idea or a dream. It seems true that those who rise to the top of a field (any field) are the ones who are most passionate about it; who pursue their dream unceasingly. This book was chalk full of stories about people who followed their passion. What great examples they set for us.

Regarding mathematics: the intense concentration involved; the difficulty behind it all, astounds me. At one point, describing Wiles' lecture course on a portion of his proof, Nick Katz says, “There was no way in the world that anyone could have guessed what it was really about. It was done in such a way that unless you knew what this was for, then the calculations would just seem incredibly technical and tedious. And when you don't know what the mathematics is for, it's impossible to follow it. It's pretty hard to follow it even when you do know what it's for” (242-243). This quote, coupled with Nick Katz's explanation of the work required to check the proof (256) shows the huge amount of difficulty behind the math involved. It's just crazy to me that the best minds in the world found it difficult to check his proof!

“If Fermat did not have Wiles' proof, then what did he have?” (284). Wouldn't it be fascinating to find out if Fermat really did have the proof or not? The great thing about this theorem is that even after being “solved”, it's still an enigma because we know that if Fermat solved it, he must have used a different method. When I got to this part of the book, right at the end, I heard dramatic music playing in my head. The problem is still there – how did Fermat reach his conclusion?

I think the concept of hard work and perseverance is demonstrated repeatedly by the many mathematicians who devote whole segments of their lives to one problem. Hard work won't necessarily always be rewarded with success, but when it comes, success is all the more sweet because of the effort taken to get it. Sacrifice and discipline make good work partners. It's a lesson worth learning well.

I want to finish by quoting what I thought was probably the funniest moment in the entire book (and I liked Euler's proof of God, also): “When asked for his reaction to the proof, Shimura gently smiled and in a restrained and dignified manner simply said, 'I told you so.'”(280). I just loved that answer. Finally, to be justified after so many years! It must have felt good.

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