A Purdue University mathematician who goes by the name de Branges claims that he's proven the Riemann hypothesis.
The Riemann hypothesis, first formulated by Bernhard Riemann in 1859, is a highly complex theory about the nature of prime numbers - those numbers divisible only by 1 and themselves. More technically, it's a conjecture about the distribution of the zeros of Riemann's zeta function ζ(s). It's considered to be one of the most important open problems of contemporary mathematics; a $1,000,000 prize has been offered by the Clay Mathematics Institute for a proof.
De Branges has posted a 23-page paper detailing his attempt at a proof on his university Webpage. Called, "Apology For The Proof of the Riemann Hypothesis," it's actually an interesting read, even for those of us who are mathematically hopeless.