Does solving "P=NP?" require filling every hole ever left in math?

I think the answer is that solving it would then successively fill every hole in math. It seems that the answer is not P=NP.

If I knew what it took to solve P=NP then I certainly wouldn’t tell!

There’s an artificial intelligence technique that models the functions of nature (specifically related to reproduction) to make use of the concept of P=NP to solve problems. The technique is generally referred to as the formation of a “genetic algorithm” whereby the computer starts with a random collection of “DNA” (just a collection of bits, 1s and 0s) called a gene. The information encoded in a gene can be anything, a video stream, a series of characters, a series of numbers, whatever. The algorithm checks each gene to see if it contains a correct solution to the problem being solved and assigns it a score. A certain percentage of bits are then randomly selected from two of the highest scoring parent genes and joined to create a new child gene. This process is repeated a predetermined number of times. Random changes like frame shifts or mutations are also introduced to inject a little change into the process so the algorithm doesn’t get stuck. The resulting child genes are then given scores of their own. If one of the children is scored highly enough, then it can be considered to contain a solution to the problem. With enough repetition, genetic algorithms can find solutions to problems that we never thought of. Consider this: a genetic algorithm (a program) that writes programs!

Genetic algorithms are kind of an answer to the P=NP problem because the scores are usually easy to calculate. The solutions themselves, however, can’t necessarily always be found quickly, so it’s not really a correct P=NP solution. If some mathematician proves P=NP, AI will move forward in leaps and bounds because it will prove that things like genetic algorithms can work to solve literally any computer-related problem given enough computing time and memory. It’s not so much that we haven’t invented the math for it yet – we just don’t know if it’s even possible because all the math that we do know hasn’t shed any light on an answer.

P and NP are two classes of problems. They are problems that are easy to solve (N) and problems that are hard to solve (compared to the size of the problem) but easy to prove weither the answer is correct or not (NP). If N=NP, then all problems that have solutions that are easy to prove also have simple ways to solve the problem. If P=NP, problems that are normally hard (like finding the prime factors of very large numbers) can actually be done relatively easily. This would mean that math problems will become much simpler and easier to solve. There are downsides, though. For example, it would be possible to easily decode almost all modern cryptography, with the exception of the one-time pad and quantum cryptography. The simplest way to prove P=NP is to prove just one NP-complete problem to be a P problem. A problem is NP-complete is if is possible to encode all other NP problems into a form of that problem. However, is is very unlikely that P=NP. Trying to prove the statement incorrect is much more of a challenge.

If I knew the answer, I wouldn’t tell you. Clay Math Institute has a one million dollar prize for solving this problem.

__It is rumored that whoever proves P=NP will walk away with not just one, but every prize.__

Yeah I saw about the prize. Probably easier ways to get that money though.

I read a lot about this on wikipedia today and had actually read all that earlier. But thanks for your opinion, haven’t there been supposedly unsolvable problems before?

Might the assertion that P=NP be in the category of theorems that are true but unprovable? This is in reference to Kurt Godel’s undecidability theorem, which shattered the dream of some mathematicians to derive everything bottom-up from one consistent logical system.

I think solving this is harder than passing the Turing test and collecting the final Loebner Prize.