zlacker

>>qqqqqu+(OP)
Fermat's theorem: a^n + b^n = c^n For n > 2, why are there no integers a, b, and c that satisfy the equality?

>>bjourn+vc
One of my advisors in college said "The proof takes about 10 years of graduate mathematics to understand".

>>ken+Pc
Is there really no intuitive way to communicate the answer to that question without needing 10 years of grad math? I find that to be somewhat hard to believe

>>wesamm+yf
Well, the answer is "simple": It's because the modularity theorem was proven (or better, the Tanyiama-Shimura conjecture was proven)

But why that solves the problem? Because it connects two branches of mathematics (modular forms and elliptic equations) in a way that proves that equations of that form cannot exist (where the exponent is > 2)

Though there probably is an easier way of explaining it, it is strongly suspected that Fermat got the wrong idea there.