P ≠ NP
Greg Baker mentions a supposed proof from Vinay Deolalikar of HP Labs that P ≠ NP. This is somewhat like the Fermat’s Last Theorem of computer science, with most people believing it to be true, though the proof was elusive. P vs. NP is a more interesting question, however, and the consequences would have been staggering if the result had turned out the other way.
Update (2010-08-11): doespequalnp.com is tracking articles and discussions about the paper.
Awesome, thanks for the link! Of course, I'll only believe it when the wikipedia entry is updated ;-)