http://ephermata.livejournal.com/190880.html?mode=reply David Molnar (ephermata) wrote, @ 2008-10-04 01:59:00 Current music: Crystal Castles - Air War What does knot theory have to do with P^#P != NP ? I didn't know, but Michael H. Freedman has an answer - by assuming that the complexity class P^#P is not equal to NP, you can prove a new theorem in knot theory! Complexity Classes as Mathematical Axioms M. Freedman (Submitted on 30 Sep 2008) Abstract: Treating a conjecture, P^#P != NP, on the separation of complexity classes as an axiom, an implication is found in three manifold topology with little obvious connection to complexity theory. This is reminiscent of Harvey Friedman's work on finitistic interpretations of large cardinal axioms. http://arxiv.org/abs/0810.0033