Fermat’s Last Theorem

Wow, this article just really gets me pumped up and makes me want to do math.

Pierre de Fermat, a famous number theorist of the 17th century, rarely published his work – instead, he would often write comments in the margins of books. In one margin Fermat proposed that xⁿ + yⁿ = zⁿ has no non-zero integer solutions for x, y and z when n > 2. However, rather than providing a proof, he only offered this taunting sentence: “I have discovered a truly remarkable proof which this margin is too small to contain.”
…
“It was so indescribably beautiful,” said Wiles about the moment he solved the problem. “It was so simple and so elegant, and I just stared in disbelief for twenty minutes.” Thus, in 1994 the final proof of Fermat’s Last Theorem was complete, weighing it at 200 pages, more complex than most people can understand.

That second paragraph I quoted is what really gets me pumped up. The “beautiful”, “simple”, and “elegant” part is something you can really appreciate when you love math.