The answer to the P=NP? problem (ie, whether every problem whose solution can be quickly verified by a computer can also be quickly solved by a computer) is simply no. Not all can.
The reason is that “verification” and “solution” are orthogonal, and thus that there has to be at least one “quick” verification that can’t be solved “quickly” (or one “quick” solution that can’t be verified “quickly”). “Verification” and “solution” simply share no common point, and there thus has to be one more of some of them in “quick” (ie, polynomial) time. The negation emerges in “quick” (ie, finite) time, because time is orthogonal to change (ie, solution).
Does this mean that I win $ one million from the Clay Mathematics Institute (CMI)?