This reminds me of an excellent short story by Ted Chiang, "Division by Zero", which deals with a mathematician's deteriorating mental state and attempted suicide as a consequence of proving the inconsistency of mathematics.

The whole thing (http://www.fantasticmetropolis.com/i/division/full) seems to be temporarily offline, but here's a pretty good summary: http://kasmana.people.cofc.edu/MATHFICT/mfview.php?callnumbe...