P ≠ NP

"A mathematical theorem can be proved, yet remain forever uninteresting. And an unproved mathematical conjecture can be fruitful in providing explanations even if it remains unproved for centuries, or even if it is unprovable. One example is the conjecture known in the jargon of computer science as ‘ P ≠ NP’ . It is, roughly speaking, that there exist classes of mathematical questions whose answers can be verified efficiently once one has them but can not be computed efficiently in the first place by a universal (classical ) computer.(‘ Efficient ’ computation has a technical definition that roughly approximates what we mean by the phrase in practice. ) Almost all researchers in computing theory are sure that the conjecture is true(which is further refutation of the idea that mathematical knowledge consists only of proofs). That is because, although no proof is known ,there are fairly good explanations of why we should expect it to be true,and none to the contrary . (And so the same is thought to hold for quantum computers. )"