The P=?NP Poll (2002) [pdf]

Often a "proof" that P does not equal NP is that it would be terribly inconvenient if solvable in n to the second or whatever, and therefore in a sort of cosmic censorship saves us by claiming it clearly can't be the case because it would be so annoying.

A good argument can be provided by an analysis of statistical thermodynamics gas laws. It highly disturbs some people to think that atoms being in motion implies that all the oxygen atoms in the room air might coincidentally cluster into a small corner of the room leaving the victim to suffocate. There is no reason to think that impossible under most thermodynamics theories. However, it is nearly infinitely unlikely and you'd merely have to wait a ten to the hundred times the lifespan of the universe for it to coincidentally happen. I suppose it scales quite strongly with room volume and linearly with air pressure, you have one atom in the ISS airlock and being in one half the air lock at any given moment is a very predictable 50:50 odds...

Likewise if the smallest polynomial solution to a NP problem takes a google's worth of universes to calculate, then even if it is poly you need not worry too much about mere human inconvenience.

I'm not saying its a wise way to go thru life, but there exists a large set of people who get hung up on whats convenient or beautiful must be right, even if whats right turns out to be very ugly or inconvenient, so for them "P=NP but your bank account is still secure" is a very big deal.

Technically, yes, but practically, no.

THEOREMS (the language of correct proofs) is in P; given a correct proof (possibly restricted to being in first-order logic), it can be verified in polynomial time. In the first-order logic case, all you have to do is read the proof from beginning to end and verify that each statement follows from either an axiom or an already-established statement. This is done entirely syntactically, requiring no knowledge of the underlying mathematics.

However, to do this requires formalizing the entire proof in machine-checkable format, which is a substantial undertaking even for relatively simple proofs and will likely take far longer than polynomial time.

Not a lot of mention of AI for CS, even in 2002. What about (2080+, P/=NP, proof techniques completely opaque to humans). And by that I don't mean mechanical exclusion of special cases like for map-coloring. As mentioned already, there's like a handful of people that understand the FLT proof, that situation is unlikely to improve.

You can choose a random oracle by choose a language by random. Here a language means a set of strings.

For those that do not have time to read the whole thing, #29 is worth quoting:

"Stuart Kurtz (University of Chicago, 2050, P!=NP) [on wether and when proof will be found]:

Knowing Ketan Mulmuley, I live in fear that the solution will be via algebraic geometry, and it will come soon enough that I’ll be expected to understand it. An alternative nightmare is that the undergraduate who solves it will publish his solution in French."

But it is by far not the only funny opinion in this paper.