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Tao: Open math problems being non-renewably mined by AI

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Re: Tao: Open math problems being non-renewably mined by AI

#71

Post by gpm »

vouaobrasil wrote: post #48
turtleyacht wrote: post #2

If proofs are tropes, explanations are stories. There won't be an end to stories.

Actually there will because if you've actually ever spent time doing math, you only really get to that level of truly understanding and appreciating the stories if you've actually done the hard work yourself, which in turn will be economically infeasible due to AI. The analogy is interesting but incomplete and misleading.

I've actually spent time doing math and literally everyone I know who knows math learnt it by reproving things that people proved before them. I don't see why AI proving things makes this form of learning any more economically infeasible than the field of mathematics already is - and since it was apparently economically feasible before AI I expect it to stay that way.

Re: Tao: Open math problems being non-renewably mined by AI

#73

Post by dakolli »

This is just the age of slop mathematics, if it doesnt lead to our lives neing improved none of this matters. Math peeps are being nerd sniped by AI in the same way SWEs (the worst ones) got sniped by claude code. Building solutions to problems that dont matter for the sake of doing it just because you can.

You'll ultimately waste a ton of time and get lapped by people doing real world work that actually improves the lives of regular people.

Re: Tao: Open math problems being non-renewably mined by AI

#74

Post by zamadatix »

vouaobrasil wrote: post #46
ModernMech wrote: post #38

Earlier quoted context omitted.

If math is solved then move to an area that’s not. Why do fields need “protecting” from ai?

The reason is because the entirety of society, historically, has been based upon humans using their differential skills to further it, which in turn promotes societal cohesion. If most human endeavours are solved, then we will enter a period of abundance that paradoxically will erode the glue holding society together. In short, endless abundance of solutions and ideas cannot coexist with a healthy society. Only those…

This far into history I don't think many are going to buy a "the next technology is to be the undoing of society itself" pitch until after society is already undone by something. They're as easy to make and hard to concretely evaluate ahead of time as the utopian predictions while offering little in the way of practical approach to preventing the same result from occurring anyways.

Re: Tao: Open math problems being non-renewably mined by AI

#75

Post by jfengel »

I didn't realize that open math problems were a finite resource.

I recall a story about some famous mathematician (Gauss?) dismissing interest in Fermat's Last Theorem claiming that he could crank out problems of equivalent interest.

Clearly Tao knows a hell of a lot more than I do about this, but I'm surprised that math that close to completion.

Re: Tao: Open math problems being non-renewably mined by AI

#76

Post by nafey »

dvt wrote: post #64
BeetleB wrote: post #60

Earlier quoted context omitted.

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

> 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 physici…

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.

Re: Tao: Open math problems being non-renewably mined by AI

#77

Post by CamperBob2 »

20k wrote: post #43

We're having to rediscover in real time the extremely hard way, why enabling mass theft is so incredibly damaging to society. This is literally why we need a functional copyright system If theft becomes more profitable than genuine creation, then nobody will create anything. Then there's nothing to steal, at which point all progress collapses

This is literally why we need a functional copyright system

To block progress. Got it.

Re: Tao: Open math problems being non-renewably mined by AI

#78

Post by p-e-w »

arjie wrote: post #72

Well, we name conjectures after the conjecturer not the (dis)prover so there is some incentive to be the guy who comes up with a hard problems. It is curious that we haven’t had something like this improve OR etc. problems. Perhaps not glorious enough.

> Well, we name conjectures after the conjecturer not the (dis)prover

That’s not universally true. Some conjectures are renamed after being proven. For example, Fermat’s Last Theorem is now sometimes called the Fermat-Wiles Theorem, the Taniyama-Shimura Conjecture is often referred to as the Modularity Theorem now, etc.

Re: Tao: Open math problems being non-renewably mined by AI

#79

Post by dakolli »

ModernMech wrote: post #38
_alternator_ wrote: post #32

This series of posts by Terry Tao is a direct response to the Navier-Stokes results (multiple results!) from the last 24 hours. The question is what is left after the levelling of mathematics, in all its senses, occurs? How can you protect a field that's under this much pressure in the next 6 months? > [I]t is now the identification of a promising problem which is the scarce and precious resource. We have now seen th…

If math is solved then move to an area that’s not. Why do fields need “protecting” from ai?

https://en.wikipedia.org/wiki/Commodity_fetishism

Re: Tao: Open math problems being non-renewably mined by AI

#80

Post by thymine_dimer »

Doesn't this just suggest that the next frontier for powerful AI models is to ask challenging questions, not simply solve them?

Terry even says this: "In fact, it is now the identification of a promising problem which is the scarce and precious resource."

The creativity and insight needed to ask a question that Terry gets excited about is the next step. Perhaps OpenAI should create a set of challenging questions and offer a prize to solve them.

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