Vinay Deolalikar from HP Labs claims proof of Millenium Prize problem P=NP, and (potential) $1M prize (pending peer review)! This deceptively simple little bugger (think e=mc^2) has, until now, stumped all suitors—basically it asks whether problems that have verifiable solutions should always be solveable front-to-back, as well as verifiable back-to-front. (Okay, that's massively simplistic, but going any deeper requires some serious CS.)

Deolalikar's solution is a 100-page paper of dense to super-dense CS, which, with the $1M Clay Institute prize at stake, will certainly draw much attention from those with big brains and the time born of tenure to go sifting around in said 100-page paper looking for flaws. If you are one of said big-brained people with time and computing power on your hands, you can find the paper here. The proof is in the pudding, apparently.

Ah, how the mighty are falling! Girgori Perelman proved the Poincare Conjecture in 2002. And now (potentially) P=NP is a mystery of the past. Remaining Clay Institute prizes include the Hodge Conjecture, the Reimann Hypothesis, Yang-MIlls Existence and Mass Gap, Navier-Stokes Existence and Smoothness, and the Birch and Swinnerton-Dyer Conjecture.

Best of Luck.