I’ve fallen down a YouTube/internet rabbit hole of videos on the [P vs NP](https://news.mit.edu/2009/explainer-pnp#:~:text=Roughly%20speaking%2C%20P%20is%20a,actually%20have%20relatively%20easy%20solutions) problem. The content I’ve watched seems to imply that, if it’s finally proven that P = NP, then there will be a common way to solve all NP problems. One of the articles I read said (I’m paraphrasing here) that if P = NP, then there will be a “shortcut” to solve all NP problems.
Examples given of NP problems have varied widely…from figuring out a cure for cancer, to cracking any encryption code known to man, to predicting the weather with 100% accuracy. Those problems are all vastly different, all come from different domains of knowledge/science, and all have radically different solutions.
So if P = NP, how do we know or why do we assume there will be some sort of shortcut that makes solving these problems easier? I totally get that P = NP means that NP problems have a way to make them easier to solve…but that doesn’t mean there’s a universal “key” that magically solves all NP problems in polynomial time. Or…is proving this part of solving the overall assertion?
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There is a group of problems which each of them has been proven that every problem which can be solved in NP time can be converted into that problem in polynomial time.
so if P = NP, you can convert any problem into one of those problems and then solve it in polynomial time.
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