Fermat's Last Theorem

Theorem

 * $\forall a, b, c, n \in \Z_{>0}, \; n > 2$, the equation $a^n + b^n = c^n$ has no solutions.

Proof
The proof of this theorem is beyond the current scope of, and indeed, is beyond the understanding of many high level mathematicians.

For the curious reader, the proof can be found here, in a paper published by, entitled Modular elliptic curves and Fermat's Last Theorem, in volume 141, issue 3, pages 443 through 551 of the Annals of Mathematics.

It is worth noting that Wiles' proof was indirect in that he proved a special case of the Taniyama-Shimura Conjecture, which then along with the already proved Epsilon Conjecture implied that integral solutions of the theorem were impossible.