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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

#171

Post by wrsh07 »

jfengel wrote: post #75

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.

I'm surprised nobody has stated the obvious: a hard math problem that has been open for ten years (because many serious people have given it serious thought and been unable to make significant progress) is, in fact, nonrenewable.

The only way to renew it is to make a new problem that is so hard systems and humans will be unable to solve it for the next ten years. And, in the spirit of trees, the best time to plant a tree is twenty years ago, the next best is today: we do need to start posing some hard math problems and deciding if they are interesting merely because there are challenging or because of something else (eg busy beaver problems are arbitrarily hard, but does solving them imply anything other than "another busy beaver problem was solved"?)

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

#172

Post by Wissenschafter »

magicalist wrote: post #130
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…

Surprised to see someone on HN arguing against open science. Seems like the opposite of the lessons we should learn from Newton and Gauss, actually, hoarding results for decades at the expense of progress. (the Pythagorean thing isn't really competition either, is ahistorical, and from what we actually do know it's again people hoarding results instead of sharing them). FWIW, your post comes off as a middlebrow dismi…

They aren't arguing against open science, they are trying to educate you on the history of science. It's always been this way.

Also, your third paragraph is highly ironic.

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

#174

Post by blantonl »

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…

Why was there a prize attached to this problem then? What does humanity get out of this being proved?

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

#175

Post by curt15 »

olalonde wrote: post #13

Isn't it safe to say that all famous unsolved math problems will get a "massive amount of AI-powered effort" pointed at them regardless?

A "massive amount of AI-powered effort" costs a ton of money. What's the return on investment for these frontier labs? Do headline-grabbing successes in mathematics translate to expected *profitability* in disciplines with more immediately quantifiable economic value.

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

#178

Post by marcus_holmes »

derektank wrote: post #102
torben-friis wrote: post #65

Earlier quoted context omitted.

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 o…

>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…

I think successful replications are as valuable as the original research because they're not unsuccessful replications

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

#179

Post by pvillano »

The way to tame a profit-maximizer is to make the most profitable choice the one that creates the most societal good.

I would like to see the Clay Institute give zero recognition for formalizations without human-readable proofs. That would incentivize OpenAI to scram or create something that's actually useful.

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

#180

Post by sashank_1509 »

dbmikus wrote: post #158
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…

An AI-generated solution always provides two pieces of info: 1. proof that there is a solution 2. a solution that you can work backwards from to build understanding Maybe the solution is pretty inscrutable, but it's almost always better than nothing. So, both of these pieces of info would be at least marginally useful for advancing human knowledge.

It demotivates mathematicians. That’s a pretty large negative!
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