If 3SAT is solvable in polynomial time, then P=NP. Which means that any problem that can be solved by brute-forcing an exponential number of possibilities (and

If 3SAT is solvable in polynomial time, then P=NP. Which means that any problem that can be solved by brute-forcing an exponential number of possibilities (and doing a polynomial amount of checking for each) can also be solved with an asymptotically much smaller (polynomial) amount of work. This includes anything from complicated optimization problems, to theorem proving, to inverting cryptographic hash functions, to any other NP algorithm that hasn't been thought up yet. Whether this would have any practical use would depend on the polynomial exponents and constant factors, of course. But even in a theoretical sense it would be very, very surprising to a lot of people if it were true.