It is fairly new, but very relevant for daily life, like many others are not. Thousands of people have tried to write smart algorithms to solve NP problems and many have thought they found an algorithm in P only to be disproven later.

Whether the Riemann hypotesis is true or not, is not going to have any practical effect, accept for a small group of mathematisians who are working on it. Most people do not know what a Field medal is nor care about it.

> A new "math" might be needed, but an answer (affirming or not) will be found.

What if there exists a proof that P!=NP, but the shortest possible proof of that proposition is a googolplex symbols that long? Then P!=NP would be true, and provable and knowable in theory, yet eternally unprovable and unknowable in practice

Maybe I should have written: "Many have tried to find algorithms in P to solve NP problems and failed to find them." Even now, many people are working on algorithms to find solutions for NP problems. I understand that it has been proven that it is not possible to proof P=NP? using 'algorithms'. That might mean that even when a proof is found that P=NP that there still will be no P algorithm to solve NP problems.

My philosophy of math muscles tingle at both sentences at about the same rate.

P=NP and P=!NP are both proven nor disproven. (There is redundant information in this sentence.)

History shows us that the historical / ‘effort’ argument is not applicable to mathematics. All proofs were unproven once until proven successfully for the first time. Harder problems need bigger shoulders to stand on. Sometimes this is due to new tools, sometimes it is a magically gifted individual focusing on the problem, usually some mix of both. All we know is that all before have failed. It’s one of the beauties in math.

It needn’t be a “free lunch” at all. An O(n^1000) algorithm for an NP-complete problem would constructively prove that P=NP yet be completely useless for solving any NP problems in practice

Nah, cranks post inscrutable incorrect proofs (and/or bizarre unified theories) to math forums regularly. They often lack the vocabulary to even format it in a way the community can read and correct.

I recall there was a mathematician that was cataloging all the 'squaring the circle' methods people kept mailing him (it's been proven to be impossible).

If their idea were legitimately revolutionary and they had the vocabulary to express it, they could simply publish.