LogFAQs > #884959361

Norbert Blum claims that he has proven that P != NP.

https://lucatrevisan.wordpress.com/2017/08/15/on-norbert-blums-claimed-proof-that-p-does-not-equal-np/

The proof: https://arxiv.org/abs/1708.03486

stackexchange discussion: https://cstheory.stackexchange.com/questions/38803/is-norbert-blums-2017-proof-that-p-ne-np-correct/

I'm not totally up on what this would mean. From my understanding, there are certain applications of computer science that rely on the assumption that P != NP, such as modern cryptography algorithms. If the opposite were the case (i.e. P = NP), this would potentially allow these algorithms to be cracked (although there may be weaknesses in these algorithms anyway), which would have major implications for cyber security, so we can rest a bit easier in that regard.

More widely, I think it would mean that many common problems cannot be solved efficiently, so attention could be directed elsewhere.