I'm with @nilesh on this one, and not exactly sure how merely the existence of a solution precludes the advancement of human knowledge. If a problem is "solved" (say, symbolically verified) without any insights gained, it doesn't seem very interesting to the profession.

Navier-Stokes is a bit different (because there's a prize attached, so "scooping" matters), but almost all interesting problems don't have any prizes attached.

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torben-friis 2 hours ago | parent | next [-]

Humanity is very biased for the culmination of work, considering everything that comes before and after busywork for the lower masses.

Replicating a paper is just as valuable scientifically as publishing it, but how many careers advance through replication?

If we move the goal from "find the solution" to "clear up the LLMs work" that doesn't bode well neither for the attractiveness of the problem nor for the career of the professional that takes the challenge.

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derektank an hour ago | parent [-]

>Replicating a paper is just as valuable scientifically as publishing it, but how many careers advance through replication?

I don’t think this is true, especially for novel or unexpected results. I suppose it depends on what you mean by scientifically, and there is a debate in the philosophy of science about what the value of research even is, but a successful replication does not result in substantial updates to one’s beliefs in the way new research does. And if the goal of science is to change our beliefs and bring them closer to what is “real”, successful replications can’t be as valuable as the initial research almost by definition.

	▲	Retric 14 minutes ago \| parent [-]
		From a pure statistical perspective the first scientific paper shouldn’t update your beliefs as much as the independent replication study. People don’t behave this way, but a high percentage of all papers have known flaws and that goes up even higher when you consider unknown flaws. Replication doesn’t own its own solve the underlying issue, but independent replication removes a huge range of potential issues on top of providing more information.

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BeetleB 2 hours ago | parent | prev [-]

Mathematicians will be less likely to work on a problem if there is a solution - even an incomprehensible one.

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dvt 2 hours ago | parent [-]

> Mathematicians will be less likely to work on a problem if there is a solution

Yes, that is Tao's premise, I'm just not sure I buy it. Suppose an oracle existed which could answer any question truthfully. Let's ignore the mechanics of this for now, but it could say things like "the Riemann hypothesis is False" or whatever and we would take it as gospel.

Does this mean that we wouldn't have mathematicians or physicists or computer scientists or biologists anymore? I genuinely don't think so.

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nafey 2 hours ago | parent | next [-]

I think his point is that AI is not creating new problems. It may solve "the Riemann hypothesis" but may completely fail to posit a "Mythos hypothesis" which is vital to advance the field. In fact, achieving the former may make the latter even harder because it will disincentivize production of human mathematics which has till now been the only source of "interesting" problems.

FWIW this is my understanding of his argument and I am not a mathematician.

	▲	gre an hour ago \| parent [-]
		Have we asked AI to create new interesting math problems? XD

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monktastic1 an hour ago | parent | prev | next [-]

But this oracle doesn't just say true / false. It also gives a proof. That makes it much less exciting (not to mention beneficial for your career) to find another one (or even worse, the same one).

	▲	gowld an hour ago \| parent [-]
		The "proof" is merely an appeal (unreadable program) submitted to a different oracle (Lean).

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_alternator_ 2 hours ago | parent | prev | next [-]

I mean, the oracle doesn't really seem so hypothetical right now. And clearly it's going to drastically change these fields, and mathematics, particularly pure mathematics, must change most of all in order to adapt to the existance of a math oracle (or something close to it).

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applicative an hour ago | parent | prev [-]

Yes, the present developments, and the present approach, mean we will not have mathematicians any more.

	▲	dvt an hour ago \| parent [-]
		Your confident re-assertion still doesn't convince me, why do you think so?