[philwelch]

Assuming P provably != NP, banks and online retailers win (certain forms of encryption even theoretically can't be broken in P time), NSA supercomputer contractors might lose (certain forms of encryption even theoretically can't be broken in P time). UPS and FedEx likely lose (traveling salesman problem is NP-complete). Any other business that hinges on solving hard problems might lose, though counterintuitively, some might win--firms that do a really good job at approximate solutions to NP problems (is ITA an example?) are extremely talented at doing something really hard, whereas if P = NP, it would be easier for any old firm to develop a perfect solution.

But considering the fact that we've all been operating under the assumption that P != NP, the losers don't lose much (if anything) and the winners don't win much (if anything). If P = NP was proven, it's possible but not guaranteed that bank robbers and whatever software firms can pivot fast enough to exploit P = NP get huge windfalls, internet retailers would be ruined, banks who didn't shut off their data links fast enough would be ruined, etc. This worst case scenario hinges on a proof that took the form of a proof by counterexample, which happened to neatly solve an NP-complete problem in efficient P time. In better case scenarios, where other proof forms were used or the P-time solution was a horrific factor like O(n^100,000), online retailers would still lose a little if only based on media hype about the discovery scaring grandmothers away.