text: what is the most important theorem that has not been prooved?   actually, fermat's last theorem has been proved in 1993 by a mathematician named andrew wiles.  as far as the question goes, it ain't a theorem if it hasn't been proved ;)  but my favorite conjecture is goldbach's conjecture, which states that any even number over 2 can be written as a sum of two primes (14 = 3 + 11, for example). no one's found a counterexample, but no one's proved it either.