P vs. NP
If you are interested in the implications of P vs. NP, as opposed to a survey of the situation around the problem, check out this excellent essay [1] by Scott Aaronson. He goes into interesting consequences about the nature of quantum computing, simulation of a human mind, and time travel, among other topics.<p>There is also another interesting article [2] by Arkady Bolotin at Ben-Gurion University in Israel, who argues that the lack of macroscopic quantum behavior implies P!=NP. Basically, macroscopic quantum behavior would imply that the universe is computing the solution to a NP-hard problem in violation with currently accepted laws of physics. Also, see this debate between Bolotin and an educated commenter [3].<p>[1]: <a href="http://www.scottaaronson.com/papers/philos.pdf" rel="nofollow">http://www.scottaaronson.com/papers/philos.pdf</a> [pdf]<p>[2]: <a href="https://medium.com/the-physics-arxiv-blog/the-astounding-link-between-the-p-np-problem-and-the-quantum-nature-of-universe-7ef5eea6fd7a#.hybznxnd5" rel="nofollow">https://medium.com/the-physics-arxiv-blog/the-astounding-lin...</a><p>[3]: <a href="https://www.researchgate.net/post/P_NP_and_quantum_nature_of_universe-any_thoughts" rel="nofollow">https://www.researchgate.net/post/P_NP_and_quantum_nature_of...</a>