This question already has an answer here:
- How not to solve P=NP? 5 answers
I have been examining the NP = P problem and I am wondering, why is proving or disproving NP = P hard? For example, why wouldn't a proof such as the following be adequate? Suppose a million doors were in front of me and I had to discover which door had a red ball behind it. In order to verify the solution, one would have to simply open the hypothesized door. But in order to solve, one must check at least one door to solve the problem. However, statistically speaking, that's like guessing an integer zero to an equation. Therefore, it must take more time to solve, then to check statically speaking, proving P != NP. Although one could argue that they could guess the door, the same goes for any solution to an equation. My question is what is wrong with a proof like the one above?