Suppose an oracle tells us the Riemann Hypothesis is correct. There are a vast number of results of the form:
If RH is correct then A.
It would be very useful to have an oracle tells us whether or not RH is correct.
We all believe it. It's a magic oracle. Now what?
But one can already study the consequences of P=NP right now. You don't need to know that it's provably true in order to do that.
Knowing an actual proof would be useful, but an oracle revealing merely that it's true (or even provable) without telling you the proof does not let you do anything you couldn't do before.
For what? Which product becomes better if it is correct?
I have published mathematics so I do value knowledge, but for most of mathematics the value of the knowledge isn't the thing you try to prove it is all the things you learn as you try to prove it. p = np is one such thing.
So the whole interesting bit about it is the proof, not the fact.
For what? Which product becomes better if it is correct?
This sentiment is anti-thetical to the whole point of pure math and theoretical science. No product became better when Euler proved the fundamental theorem of algebra.
Somebody, eventually, somewhere would understand it, or at least aspire to understand it. And even if he doesn’t, what have they learned in the process? About themselves, about their environment? About failure? I would bet a lot. How useful then, can we say that it is, not because we can understand it, but because we can try? That is useful. This is about the journey. Sometimes the journey is the point.
This is like if math was fascist, this is what would happen. When you start controlling the flow of knowledge like this, it will be bad news all around. And who is to say whether or not something can be understood?Aside from the math nazis.
If we are going to dictate what gets published like this, why bother publishing anything? This feels like a gatekeeping…that’s exactly what it is. Ya’ll getting nervous?
In any case, I think it's better to read PP as somebody would find a practical, albeit incomprehensible, algorithm for solving NP complete problems.
Although I probably disagree with PP, because even a candidate algorithm that mysteriously works without proof would have practical value, so this case is not predicated on proving.
I think a better example of genuinely practical but rather uninteresting (YMMV) mathematical proofs are proofs of convergence of numerical methods, FEM for example. (I have been through it in school, it was a torture.)
It would not not necessarily be practical, even if it ran in polynomial time. It may have cost O(n^c), with a totally out of order exponent like c=A(5,5) or whatever.