Possible Proof of P != NP
I’m not sure that this one will break into the public consciousness, but Vinay Deolalikar of HP may have proved one of the major challenges in complexity theory, that P != NP. In addition to being a great intellectual success, this particular problem has very big practical implications. Luckily, though, what may have been proved is what was widely suspected to be true, so the upshot is that, if the proof is correct, the worlds of digital commerce and cryptography will breathe a sigh of relief.
I don’t understand the proof myself, but these guys (with blogs) who are smarter than I am claim that the “proof” has got all kinds of problems, which I also don’t understand. See link: http://rjlipton.wordpress.com/2010/08/09/issues-in-the-proof-that-p%E2%89%A0np/