I agree

And let me say, I don't even care about a paper. Sure, it's useful, but it shouldn't be the focus.

A simple implementation that solves any of the NP problems in polynomial time is a much better proof than any article.

(of course, those that prove P != NP can't do that, still)

I beg to disagree with both of you.

You are kinda disrespecting the important of theoretic research, and a big part of any field of interest on research.

Oh the theoretical aspect is important.

But applying it is important as well. Of course, most quantum computing algorithms have not had a chance of being implemented; it's not always possible

Or, as Knuth put it "Beware of bugs in the above code; I have only proved it correct, not tried it."

But if someone comes up with a paper showing a new algorithm but doesn't come up with an implementation of it when it would be straightforward to do so, I begin to doubt this person.

Most other fields don't have the luxury of easy testing.

> A simple implementation that solves any of the NP problems in polynomial time is a much better proof than any article.

That completely misses the point of P vs. NP, which is not about programmability but a problem entirely of theoretical nature (and interest).

- O(n^<Graham's number>) is in P. (If you can solve TSM in that time, you've proven P = NP.)

- Cracking AES-256 is even easier than P: it's O(1).

> "That completely misses the point of P vs. NP, which is not about programmability but a problem entirely of theoretical nature"

Yes, there is an important theoretical background, but IF you prove P==NP you should go for it (of course you can have n^a big number but that's unlikely)

> Cracking AES-256 is even easier than P: it's O(1)

Well, you can take any fixed size subset and say it's O(1), TSP for 100 cities is O(1) as well

But if the 'theoretical work' is merely to win grants and ensure tenure yeah, just don't bother.

A program isn't a proof. It's perfectly possible to solve restricted cases of an NP-problem in polynomial time. Doing so in enough of the test cases people throw at it to fool people for a while would itself be a huge accomplishment, but it would still be entirely possible that P != NP while I'm holding a program that has solved every NP problem I have thrown at it in P time (especially if that P is large).

You would benefit from both, or you might have doubts the NP problem that was solved was ever actually NP.

He does give pseudocode in the paper for transforming an NP problem M<NP> into a P problem. It should be straightforward to apply this with M<NP>=SAT. (Whether it actually works is another matter...)