Someone already took my favorite theorem, Fermat's Last Theorem. Therefore, I guess I will state my favorite open problem: P = NP
From Wikipedia:
"In essence, the question P = NP? asks: if 'yes'-answers to a 'yes'-or-'no'-question can be verified "quickly" (in polynomial time), can the answers themselves also be computed quickly?"
There are many problems in the NP class that could be solved significantly faster if P = NP were true.
