x^n+y^n=z^n

First for those that don't know the basics on Fermat's last theorem:
Back in 1637 Fermat wrote down a conjecture (or theory depending on if you believe what he wrote next or not) in the margin of a book and then wrote: "I have discovered a truly marvelous proof of this, which, however, the margin is not large enough to contain". For the next several hundred years many mathematicians worked on proving the conjecture. In 1993 Professor Andrew Wiles presented the proof he came up with after working in near isolation for 7 years. Soon after people realized the proof had an error. Then he spent a year trying to figure out how to fix it and eventually did.

Fermat's last theorem says that the equation x^n+y^n=z^n does not have whole number solutions for n > 2. An example of a solution for n=2 is x=3,y=4,z=5 since 3^2+4^2=5^2.

The book Fermat's Last Theorem starts in 2000 BC and tells the stories of the key mathematicians that led up to the conjecture and then those that led to the proof. It is actually an interesting way of taking brief (4000 years is a long time to cover in 150 pages) snapshots of the development of math across time. For the very early stuff, when the math is more understandable, the book goes into it a bit, but it does a good job of shifting its focus to the people as the math gets harder. It also does a good job of dispelling the idea that it was one guy in a 7 year stint that created the proof when really it was the build up of hundreds of years of effort. Also he wasn't unabomber isolated - he had a family and near the end even worked with two other professors, but he did spend a lot of those 7 years in his attic and kept his work secret the whole time. One of the interesting aspects of the proof is that it is actually done by proving a correspondence between two ideas in completely different areas of math. So rather than being a pure number theory proof it actually involves ideas about curves and other modern areas of math.

One thing the book reminded me of is that my math education cuts out somewhere in the early 1800s (except a small amount of very specific applied stuff). I'm not saying I know a lot up to then, but that is the point where I'm lucky if I recognize the name of a field, much less an actual concept. Which I guess is a combination of math being really old and thinking that I know something about math even though I've never taken an actual pure math class.

Anyway, the book was surprisingly interesting, although considering the topic is 4000 years of math building up to a single proof it didn't have to do much to exceed expectations.