3 ms·
A mathematician can write an equality without anybody raising an eyebrow, but as soon as someone suggests that we can choose the optimal answer on the first "gu
by sova 5y ago
A mathematician can write an equality without anybody raising an eyebrow, but as soon as someone suggests that we can choose the optimal answer on the first "guess" everyone wants to rekindle the Spanish Inquisition. If we can go from "guess" to "obvious solution" then it stands to reason that P=NP. Of course, this is a debate that likely has no clear path without some stroke of insight, because the axiomatic "truth" that confirms it one way or the other is not reachable by induction alone.
There is likely an island of consistent axiomatic logical statements that we must not only wait for someone to reach by happenstance, but to decipher and know what to do with them. According to Fermat, his proof was omitted due to lack of space in the margin. I suppose it's good to let others share in the glory now and again, if on centuries-delay.
- mdoms 5y agoWhat?
- bawolff 5y agoSo what you're saying is: If there exists an algorithm that always guesses correctly then we can solve NP problems? That's just the definition of NP restated. One of the definitions of NP is all the problems that can be solved in polynomial time if at every choice we had a method of always guessing correctly. The question of NP=P is if such a method can actually be implemented in polynomial time on a Turing machine. So yes, you are correct, it stands to reason that if NP=P, then NP=P.
- hnfong 5y agoI don't know whether the GP intends this, but one fun way of understanding the GP's comment is: If you believe really so strongly that P!=NP without actual proof, you're actually just making a guess, and then saying you can make good guesses. But the process of doing so implies you actually believe P=NP.