Solving the problem of P=NP? implies that you would also be able to write an algorithm for such a task that currently we don't know the answer to (whether a tas

Solving the problem of P=NP? implies that you would also be able to write an algorithm for such a task that currently we don't know the answer to (whether a task can be completed in polynomial time, just as it can be verified) -- once this algorithm is written, basically every other problem in that category (class) would also be pretty much solved. We're talking about thousands of such problems.