P != NP question

Question

Not a \'pure\' programming question, but since it is deeply involved in programming theory, I thought it best to ask here.

Regarding the P NP problem, this excerpt from

Answer 1

Suppose you had tremendous parallelism -- however much you wanted. You could then simultaneously generate all possible solutions, check which of these were correct, and output a correct solution. In the presence of infinite parallelism, this is a method of generating a solution. The set of problems in NP are those for which this procedure would work quickly, because the only interesting computational step it is performing is checking whether solutions are correct, and this can be done efficiently for problems in NP. Note that for some other problems, even this parallelism would not allow us to find solutions quickly, since it requires that checking solutions is easy.

But we don't have infinite parallelism. Can we somehow simulate it, with only a polynomial amount of overhead? If so, we could imagine running the above procedure, and efficiently finding solutions for every problem for which verification was easy. This is the P vs. NP question.

Intuitively, it seems clear that the answer is "no" (i.e. P != NP). How could we possibly simulate infinite parallelism? This is what almost every expert believes. But it is a mystery how to prove it, and one that is worth $1,000,000 in prize money.