Comment by throw-qqqqq

Are you kidding/trolling? The P=NP problem is FAR more fundamental, and if proven true, would basically be a proof that e.g. public key crypto can be broken (NOT a description of how to though).

Basically, it would be a proof that all the REALLY hard (combinatorial) problems out there, have a much simpler solution, if we were able to find it.

EDIT:

NS is used daily in engineering and gas/fluid modeling. We sort of “know it works”. The smoothness proof is “just” formalizing what practitioners assume is true (very coarsely said, no intention to diminish the result!)

It’s a bit like the Collatz function IMO, empirical evidence isn’t proof, but we’ve got a huge amount of evidence for the behavior we’re trying to prove.

I believe P vs NP is a different beast entirely. We don’t even know which way the answer should go.