I learned that we sometimes use computers to generate proofs and algorithms for tough problems humans have trouble solving. And ChatGPT seems to suggest one day AIs could generate algorithms.
Has anyone tried to bruteforce search and see if any algorithm solves P = NP, or is there a technical reason we can’t? Do we not have the computer power, or it would take too long? Or would the math be too hard?
It seems like a lot of money could be made and would solve one of the biggest computer problems ever, so could it be worth it if it’s doable? What stops us?
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P = NP is more of a conceptual problem than one we can just plug in and solve.
P is the set of problems that we can easily solve amd easily check the solutions. NP is the set of problems that we can easily check the solutions.
P = NP is the problem of does there exist a problem that exists in NP but not in P.
If we were to brute force the P = NP problem, we would first need to define every problem in NP (which itself is an impossible problem) and then we would need to find a simple solution to all of those problems. Even finding all of the solutions to a single NP problem (by brute force usually) takes an insane amount of time.
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