[khawkins]

I'm very confident that orders of magnitude more man-hours have been spent thinking about P=NP in the past 20 years than were spent in the whole 358 years on Fermat's theorem. The number of people in academic situations to work on hard problems has increased exponentially.

I think it's fair to assume that there are potentially asymptotic limits to what can be achieved, but it's not that we default to one conclusion or the other, but that we conclude that whatever might be the real solution, the complexity of the proof is insurmountable or doesn't exist.