Fermat's Last Theorem

ln(dx/dy)

How will this Theorem effect math in any way? I mean, it's nice to know there are no solutions for $x^{n}+y^{n}=z^{n}$ , where $n \ge 3$ . But it seams kind of pointless for Wiles to virtually kill himself over this problem, it didn't really change things that much. Or am I missing something Question

Did you know that Fermat wrote he had found a "wonderous proof" to his theorem, but he didn't have enough room to write it down in the margin of a book were he wrote the famous(or infamous) equation?

**Posted:** Sun Jan 30, 2005 6:09 pm

LynnelleYe

Shouldn't this be in 'other topics' rather than MathCounts?

**Posted:** Sun Jan 30, 2005 8:14 pm

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yif man12

Good point. Moved.

**Posted:** Sun Jan 30, 2005 8:16 pm

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Magnara

He connected elliptic curves and modular forms by proving the Taniyama-Shimura conjecture, which has serious implications for the study of both. FLT was just a consequence of the theorem (essentially because a solution "could be" one, but not the other).

**Posted:** Sun Jan 30, 2005 9:13 pm

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-Erdos

blahblahblah

Strictly speaking, he didn't prove Taniyama-Shimura.

Perhaps there are not any great applications to FLT, but Wiles discovered several things of significant mathematical interest en route to his proof, which may or may not have applications (most likely in cryptography)

**Posted:** Sun Jan 30, 2005 9:35 pm

Magnara

**Posted:** Mon Jan 31, 2005 1:04 am

_________________
The game of life is to keep the SF's score low. If you do something bad in life, the SF gets two points. If you don't do something good that you should have done, the SF gets one point. You never score, so the SF always wins.

-Erdos

blahblahblah

Uhh, I think he only proved the semi-stable case, whatever that means.

**Posted:** Mon Jan 31, 2005 2:00 am

ComplexZeta

Wiles did not actually prove Taniyama-Shimura. He only proved a special cases that is equivalent to Fermat's Last Theorem. The full Taniyama-Shimura was finally proven in 1999.

**Posted:** Mon Jan 31, 2005 6:51 am

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shake9991

all of what I will say is from: Fermat's Enigma (great book)
as said above, Wiles didn't prove Taniyama-Shimura... he proved special case... and to the pt. about Wile's pratically killing himself for the proof: it's like what they say about people climbing mt. everest; they do it because it is there.
Also, there about500 - 1000 mathematicians in the world who actually understand every part of Wiles' proof and the mathematics surrounding it.

**Posted:** Mon Jan 31, 2005 5:13 pm