Someone needs to prove that P != NP. Want to understand why that's important? Read this: http://cacm.acm.org/magazines/2009/9/38904-the-status-of-the...
Or, if you just happen to find an error, send that back. But the service is free if you don't!
These faculty complain about getting e-mail spam and sometimes even visits and phone calls out of the blue from people who claim to have solved it and want their proofs checked.