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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

#191

Post by kccqzy »

twotwotwo wrote: post #167

This is worsened by OAI/Ant's strategy of grabbing the glory and running rather than spending effort trying to to advance understanding of math. Tao, who is quite sophisticated in use of AI, has said a lot about this, including in meme form: https://mathstodon.xyz/@tao/117068266026618494 The AI labs' approach to math is immature in a way they can't get away with in coding. In coding, they realize that a pile of code…

Besides Sendov’s Conjecture, Terence Tao has also shared his AI-assisted digestion of the counterexample to the Jacobian conjecture. In simple words, digestion just means full human understanding of the results. It could come from understanding the result from a different perspective, or perturbing the result and seeing what breaks.

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

#192

Post by sdenton4 »

torben-friis wrote: post #65
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 o…

In mathematics, finding novel proofs of a given result is often valuable; it may be a shorter proof (demonstrating better/expanded understanding of the problem) or a translation of the problem into a new domain, setting up more cross-domain advances.

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

#193

Post by dayjah »

sashank_1509 wrote: post #180
dbmikus wrote: post #158

Earlier quoted context omitted.

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!

* current mathematicians

Were early in this cycle, we will learn to do more, and exercise our new capabilities more fluently, which in turn will create more skilled practitioners

Consider the abacus, calculator, computer, etc, each of these enhanced mathematicians’ capabilities and thus outputs.

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

#194

Post by magicalist »

drivebyhooting wrote: post #160
gpm wrote: post #144

Earlier quoted context omitted.

> Unless [...] mathematicians are effectively useless? It's always been a bit bizarre that this isn't the case. Mathematicians are almost always working on problems that there is no good reason to expect to have utility in the real world... problems they selected because of their elegance or whatever... yet there is a strong historical trend of their work having huge importance after the fact. Sometimes in fields tha…

Math academia was not working well at all. Almost every single graduated from my PhD program wound up working in ads or finance. The gatekeeping in math academia is extremely unfair, or should I say objectively fair but personally unfair. I won’t cry crocodile tears.

> wound up working in ads or finance

Because there's lots and lots of money in that and there's not in funding pure math. It sounds like your problem is with the people holding the purse strings.

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

#196

Post by itemize123 »

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…

this is not untrue but it's a pendulum swinging back to ancient times man

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

#197

Post by evenhash »

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.

> An AI-generated solution always provides ... proof that there is a solution

This is only true in the most trivial sense. A solution is a solution, sure... but how do you know it's a solution, and not an incoherent jumble of words? A human has to review and vouch for it.

Just because the AI gives you an arxiv-worthy PDF, or a Lean proof which compiles, doesn't mean it proves what the AI says it does. The AI could give you the same PDF/Lean code and says it proves the opposite, how would anyone know the difference?

You can't advance human understanding unless you produce things that humans can understand.

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

#199

Post by traes »

matherial wrote: post #186
traes wrote: post #161

Earlier quoted context omitted.

> Now, Tao is a sort of a celebrity of the quarter on HN, but I promise you that outside this forum, almost no one has ever heard of him. This is an absurd thing to say. Hacker news is not the only place that knows about the most famous mathematician in the world. Glancing at Google Trends he seems to be roughly as famous as Linus Torvalds. Not exactly a household name but by no means obscure.

I'm going to charitably assume that you forgot to include quotes around the names in your query, because that's absolutely not what Google Trends shows. Stop 100 people on the street in NYC or Berlin or Tokyo and I bet none of them will be able to name any living mathematician. A few of them might know Linus, though.

Yes, it absolutely is what it shows[0]. I have no idea what data you're looking at that suggests otherwise. Worldwide or in the US, as public individuals or as search terms with quotes or without quotes, over any reasonable timespan, they get roughly the same amount of searches.

[0]: https://trends.google.com/explore?geo=US&q=%2Fm%2F047mjr%2C%...

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

#200

Post by paxys »

_alternator_ wrote: post #169
paxys wrote: post #166

Earlier quoted context omitted.

What theft? LLM output has never been copyrightable.

I'll give you the benefit of the doubt. GP was referring to the use of copyrighted material to train LLMs.

1. using copyrighted material to train LLMs is fair use, not theft

2. The topic we are dissussing concerns LLMs being trained on logs from previous LLM chats. If you're prompting a model and it spits out some unique mathematical insight, you do not have copyright on that.

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