<story><title>Predicting When P=NP Is Resolved</title><url>https://rjlipton.wordpress.com/2019/12/22/predicting-when-pnp-is-resolved/</url></story><parent_chain></parent_chain><comment><author>joe_the_user</author><text>My pure amateur, possibly muddled understanding is that P=!NP is rather different from most open conjectures.&lt;p&gt;A) It&amp;#x27;s extremely general or even &amp;quot;foundational&amp;quot; in the sense that it&amp;#x27;s asking whether any algorithm at all exists to solve an extremely general sort of problem in polynomial time.&lt;p&gt;B) All of the standard methods used to solve problems of this sort have at least been pronounced exhausted at this point.&lt;p&gt;C) Very few theorems that inherently limit the speed of a class of problems actually have ever been proven. Very few methods for proving these constraints are known.&lt;p&gt;D) A lot of famous theorems have yielded results through being embedded in a larger, different field where they are just one result of many proved with a new machinery (Fermet most prominently). But given P=!NP is so general it can&amp;#x27;t really embedded in a larger, tractible space - lots of things are equivalent to it but all these things are kind of the same.</text></comment>
<story><title>Predicting When P=NP Is Resolved</title><url>https://rjlipton.wordpress.com/2019/12/22/predicting-when-pnp-is-resolved/</url></story><parent_chain></parent_chain><comment><author>AwesomeLemon</author><text>Should we even care for a mathematical proof that P=NP? We know that in practice we haven&amp;#x27;t been able to come up with algorithms that solve NP problems in polynomial time. Suppose we&amp;#x27;ll be told that this is possible (i.e. P=NP): will this help up us to invent such algorithms? I don&amp;#x27;t see how, unless the proof will be by construction.</text></comment>