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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

#61

Post by CamperBob2 »

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.

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 thing is, nobody has time for that. Look at Mochizuki's work. It takes years of hard labor by high-level mathematicians to come up with stuff like that, and years of hard labor on the part of other mathematicians to validate it. The low-hanging fruit in math has all been picked, AI or no AI, and Tao doesn't seem to acknowledge that.

The mathematics community needs better tools or they're out of business anyway. Now they're getting those tools... and bickering and complaining about it?

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

#62

Post by gpm »

See also his previous thread from before the result was published (and before he knew it was coming [1]) on how a to this problem seemed increasingly likely to be solved by AI in a way that caused us to miss the insights that would traditionally be associated with solving it: https://mathstodon.xyz/@tao/117207849921390904

[1] https://mathstodon.xyz/@tao/117219101339291693

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

#63

Post by rcxdude »

techas wrote: post #20
Jtariiiii wrote: post #10

Earlier quoted context omitted.

Also Andrew Wiles working in secret for 7 years out of fear of someone scooping him.

I've always found the story of A. Wiles sad and frustrating. He worked in secret for 7 years. He submitted a (incorrect) proof at year 4 or so. Reviewers found a problem, but he decided kept all secret for many years after. He didn't even proof the last theorem of Fermat directly, he proved some conjeture that someone else before him, proved that it implied Fermat last theorem... I found this behavior against healthy…

Eh, it seems like it's pretty necessary for success on such a problem (but obviously not sufficient). These problems gain a reputation, and you either get judged for it or get too much attention for it.

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

#64

Post by dvt »

BeetleB wrote: post #60
dvt wrote: post #52

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…

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 physicists or computer scientists or biologists anymore? I genuinely don't think so.

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

#65

Post by torben-friis »

dvt wrote: post #52

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…

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.

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

#66

Post by throwaway1707 »

bwfan123 wrote: post #58

It is now clear to me why the AI labs are sponsoring these mathathons: https://mathathonchallenge.com/ . They are basically crowdsourcing human researcher data to get access to promising directions possibly later to scoop others.

Not so dissimilar to my first comment on this site (which I got piled on): https://news.ycombinator.com/item?id=48959395

Except way more nefarious than I expected

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

#67

Post by -0_0- »

henryfjordan wrote: post #21
vessenes wrote: post #3

That’s not untrue. But it’s also a misstatement of mathematical history. Many leading mathematicians historically have been highly competitive — Gauss comes to mind. Woe betide the lesser intellect that sent Gauss some ideas. The Newton Leibniz controversy was very serious business at the time in the UK and the continent. It was considered at the least a sin to reveal that sqrt(2) was irrational to those outside Pyth…

The story of the cubic equations is another great example: https://en.wikipedia.org/wiki/Cubic_equation Dudes straight up used to hoard solutions to equations and use them in math battles.

Showing my ignorance, but the only thing I can picture when I hear 'math battles' is akin to the 'street Countdown' scene from the IT Crowd

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

#68

Post by vouaobrasil »

CamperBob2 wrote: post #61
vouaobrasil wrote: post #48

Earlier quoted context omitted.

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.

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 thing is, nobody has time for that. Look at Mochizuki's work. It takes years of hard labor by high-level mathematicians to come up with stuff like that, and years of hard labor on the part of other mathematicians to validate i…

I agree that the low-hanging fruit has largely been picked. But then I think we should acknowledge that and stop innovating, or just work less on new solutions and more on clarifying old ones, and start to work on degrowth rather than useless problem solving. Because I really don't feel that any of this is really necessary or beneficial for the human race in the long-term.

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

#69

Post by _alternator_ »

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 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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