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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

#141

Post by opello »

johnsmith1840 wrote: post #121
opello wrote: post #96

Earlier quoted context omitted.

No evidence until there's an answer to the question of if prompt data from the other researchers was used to train the internal model. I think the reasonable ethical question to consider when a company has an incentive to prove its value, and learns of the state of the art of a flashy research topic being close to a solution, and then throws loads of resources at trying to solve it first. I agree that "AI" didn't "ta…

Ok so if no plagarism has occured here in any sense then there's no discussion here? I agree though if they did plagarism it's really really bad for OpenAI. They would instantly have evaporated all remaining good will to gloat over a stolen discovery.

I think there's still an ethical question of a business trying to scoop a researcher solely because the business learned of promising progress. It's not a very big leap to consider "multiple discovery" (a la calculus by Leibniz and Newton) and chance that the model that is good at math proofs might have enough ambient context to work faster from a similar knowledge base on the problem for which promising progress was discovered. I think that's not nice at the very least. Surely the above-board way to approach that is "hey researcher, we learned, indirectly, that you might have made significant progress on flashy research topic and would like the chance to throw our vast computational resources in to try to help work toward the conclusion of that effort." But, maybe that's asking too much?

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

#142

Post by bee_rider »

nilkn wrote: post #89
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.

It's easy to come up with new open problems. It's hard to come up with new open problems that seem to teach us something fundamentally new about the world. Our current batch of problems went through a complex selection process over decades (or centuries) based not purely on difficulty but also on perceived insightfulness. I studied math, but I am not a mathematician, so I think I have a slightly different perspective…

I haven’t been following the AI proof stuff very closely, but the impression I got was that these models are producing massive Lean programs that prove the statement one way or another, but are quite difficult to fully understand.

Actually, I have to admit I don’t really know what math is. With physics we suspect there’s a universe, and when we study physics we’re improving our description of the behavior of that universe, right? The universe exists whether or not we know how it works.

Eventually, as you suggest, maybe we’ll hit math that won’t fit in anybody’s head at all. What is the nature of mathematics that doesn’t fit in any human’s head? Does it even exist in some sense?

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

#143

Post by xelxebar »

There is also a large incentive for OpenAI to fold user conversations into the training process. Proving this happened is unduly hard, and given that professionals are using frontier LLMs for daily work, such training would make it easier for labs to scoop said professionals.

I have seen private correspondence between one mathematician working on Navier-Stokes and OpenAI that makes it sound like OpenAI deliberately scooped this Navier-Stokes result. The alleged correspondence also contained veiled threats if said mathematician went public.

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

#144

Post by gpm »

johnsmith1840 wrote: post #126
SpicyLemonZest wrote: post #116

Earlier quoted context omitted.

> Not sure what the point of this argument is. Do we have mathematics for the sake of mathematicians good mental health and career or to solve and discover novel problems? Why should we care if mathematicians can understand proofs if they are correct? Most modern mathematical problems are sufficiently abstract that their proofs or disproofs have no direct application. There's no problem you can fix or invention you c…

So...why can't an AI do the exact same thing? Make AI so it understands math better for future math to understand more math. Unless your argument is that mathematicians are effectively useless? I am assuming that's not your point though.

> 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 that weren't even invented yet at the time of the work.

There's something to be said for the idea that disrupting a system that is working well for no apparent reason is a bad idea.

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

#145

Post by chorizo »

mlyle wrote: post #123
hkalbasi wrote: post #106

Earlier quoted context omitted.

So we can let the ai generate some math problems based on the solutions found? Other fields (computer science, physics, ...) can generate math problems too.

There's an infinite number of possible math problems, but the things that make these open problems worthwhile is they're interesting to people who have worked in related areas. They're good to give to new mathematicians, and they're good to help humans understand the shape of the problem space and relative difficulty with the tools we have. Cheesing these problems with LLMs gets rid of both the training benefit and o…

These open problem solutions often reveal tighter bounds on prior conjectures. Even if the solutions produced are far from elegant and only machine verifiable, we do learn new information. But I agree that just like writing prose and code, brainstorming frontier math proofs is a perishable skill

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

#146

Post by [deleted] »

ryoshu wrote: post #134
porcoda wrote: post #90

Earlier quoted context omitted.

They aren't, but the problem is that open problems tend to emerge when people are working on other problems. If fewer people are spending time deeply thinking about current problems since a handful of labs are solving them with AI without an eye towards understanding and only on verification, the pool of open problems won't be continuously growing. There is a fear that there will be a chilling effect on the community…

tl;dr - it's content creation rather than process and understanding

[deleted]

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

#147

Post by Jblx2 »

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…

Obviously, he was trying to avoid being labeled as a crank for working on a famous problem like that for so long.

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

#148

Post by Retric »

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…

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.

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

#149

Post by johnsmith1840 »

opello wrote: post #141
johnsmith1840 wrote: post #121

Earlier quoted context omitted.

Ok so if no plagarism has occured here in any sense then there's no discussion here? I agree though if they did plagarism it's really really bad for OpenAI. They would instantly have evaporated all remaining good will to gloat over a stolen discovery.

I think there's still an ethical question of a business trying to scoop a researcher solely because the business learned of promising progress. It's not a very big leap to consider "multiple discovery" (a la calculus by Leibniz and Newton) and chance that the model that is good at math proofs might have enough ambient context to work faster from a similar knowledge base on the problem for which promising progress was…

It's a reasonable take.

I think there's an important part which is that the nature of the beast implies there's effectively zero way to do that.

They have no idea what context, triggering this pathway, was from this guys reddit post 4 years ago.

I also assume that if any AI lab could actually do that it'd be an instant pissing context over who gives who credit the mostest. "This software engineer wrote a sick sorting algorthm everyone now uses, thank you random dude for that training contribution"

Maybe we will in the future, maybe we'll learn that the solution to this prize is from 3 peoples schizo rant on reddit a decade ago. Would be kinda sick actually.

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

#150

Post by modemNoises »

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…

Nothing in their comment reads to me as "arguing against"

Reads like nothing but historical context

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