From talking to the mathy-side CS faculty in my department (UofC), the crackpots all think they've solved it. Genuinely, honestly, and completely.
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.
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.