Fermat's Last Theorem

[suberatu 0]

Fermat's Last Theorem is (as the name implies) a theorem that (until recently) went unproven mathematicians for centuries. Pierre de Fermat was a 17th century French lawyer who also happened to be especially gifted when it came to mathematics (especially calculus). In the margins of his legal papers (and such related materials) he would often scribble down his thoughts on particular subjects of math, as well as various problems, proofs, theorems and formulas. After his death, mathematicians often tried to solve or prove some of his formulas and theorems. One that consistently baffled mathematicians went something like this (according to Wikipedia):

It is impossible to separate any power higher than the second into two like powers.

In layman's terms, this can be said as:

aⁿ+bⁿ=cⁿ has no integer solution for a, b, c when n >2

The interesting thing to consider about this theorem, is that it is simple and easy to comprehend, yet it is/was nearly impossible to prove. The inherent paradoxial simplicity/complexity of this theorem in essence "pissed off" mathematicians, because while schoolchildren could understand it, they (the mathematicians, being the experts that they were) could not solve it. Adding to their frustration was the following note which Fermat wrote in the margins of his copy of the Arithmetica (an ancient Greek book dealing with mathematics) in which he stated:

I have discovered a truly remarkable proof which this margin is too small to contain.

Despite all of the best efforts put forward by mathematicians, the theorem remained unproven. After a time, it was finally given up on. It was not until recently that Professor Andrew Wiles put forward a proof for the theorem, that the mystery was finally solved. The proof is reported to be over 200 pages, and involves such high level mathematics that the overwhelming majority of the population on earth would probably understand nothing in the proof other than the declaraction of the theorem itself. The proof involved work related to Elliptical Curves and Modular Functions. I'm not even going to pretend that I have ANY expertise in these areas of mathematics, so here I will leave you with links to a documentary put out by UKTV (found on YouTube) which does a great job of explaining the full story behind the theorem and Andrew Wiles's proof. It also gives you an idea as to what exactly Elliptical Curves and Modular Functions are, as well as attempt to inform you about how Andrew Wiles attempted to use them in his proof. The documentary is split into 5 parts and runs about 46 minutes (give or take a few).

Part 1: http://forums.xisto.com/no_longer_exists/

Part 2: http://forums.xisto.com/no_longer_exists/

Part 3: http://forums.xisto.com/no_longer_exists/

Part 4: http://forums.xisto.com/no_longer_exists/

Part 5: http://forums.xisto.com/no_longer_exists/

Edited November 6, 2007 by suberatu (see edit history)

[abminara 0]

Wow. That's pretty amazing. I heard a lot about it, but this is a great gathering of all theinfo about it. Thanks.

[FLaKes 0]

I find it really funny how the mathematicians got pissed off about not being able to solve a simple math problem. What I find really interesting about this guy is that he ended up as a lawyer when deep inside he was a mathematician, which is problably what made other mathematicians get angry, how could a lawyer beat them to some problems? maybe being a lawyer was boring for him so he did that while he was distracted or bored.

[cangor 0]

I just read about this the other day. It's absolutely fascinating... when I see 3^2+4^2=5^2, it's surprising that there isn't anything for higher powers, but I guess that makes sense, because 3^2+4^2=5^2 has two things on the left side because it's squared... I bet there are a bunch of solutions for a^3+b^3+c^3=d^3 has solutions, because that would make sense, three variables for the third dimension... I think I'll look in depth about how he proved it sometime. Or maybe I'll try to prove it on my own.

[bthaxor 0]

we did this in school - our maths teacher was racking our brains for a solution to it. but alas, even my genius couldn't come up with an answer

[hippiman 0]

My Calc teacher was talking about that a couple of days ago. I thought there was something in the guy's quote about the solution being really simple or something, but then he died and no one could figure it out. I don't think he said who it was that finally proved it, though.