A solution to P vs NP could unlock countless computational problems—or keep them forever out of reach. 1. On Monday, July 19, 2021, in the middle of another strange pandemic summer, a leading computer ...

This is a preview. Log in through your library . Abstract We show that there is a structure of countably infinite signature with $P = N_{2}P$ and a structure of ...

A new proof, published to the Web less than one week ago, purports to finally demonstrate that, in complexity theory, P != NP. As fast as the proof went up though, people found some potential issues ...

A diagram showing the relevant complexity classes in the P vs NP problem. “P” problems are solvable in polynomial time; “NP” problems might be solvable in polynomial time, and are checkable in ...

When the Clay Mathematics Institute put individual $1-million prize bounties on seven unsolved mathematical problems, they may have undervalued one entry—by a lot. If mathematicians were to resolve, ...

Has the biggest question in computer science been solved? On 6 August, Vinay Deolalikar, a mathematician at Hewlett-Packard Labs in Palo Alto, California, sent out draft copies of a paper titled ...

Source: Darren Edwards What if one of the biggest unsolved problems in mathematics is not just about numbers or computers, but about observers like you and me? This isn’t a proposed solution to P vs ...