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.
Does this mean that I win $ one million from the Clay Mathematics Institute (CMI)?
Another contribution to understanding of conceptualization http://menvall.wordpress.com/