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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

#121

Post by johnsmith1840 »

opello wrote: post #96
johnsmith1840 wrote: post #59

Earlier quoted context omitted.

AI didn't "take" anything. An openai researcher did? The solution is also different to theirs? Literally no evidence of plagarism?

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.

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

#122

Post by magicalist »

nomel wrote: post #41
enraged_camel wrote: post #11

Earlier quoted context omitted.

So let me get this straight: you're saying that Terrence Tao, one of the most prominent mathematicians alive today, doesn't know math history? And me pointing this out is merely an appeal to authority? Get outta here.

Soldiers rarely know the history of war, and war historians are rarely soldiers.

> Soldiers rarely know the history of war, and war historians are rarely soldiers.

I mean, besides the empty platitude that we have no reason to assume applies here, we can easily search and find Tao commenting on the history and philosophy of mathematics.

This is a really weird subthread.

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

#123

Post by mlyle »

hkalbasi wrote: post #106
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…

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 our ability to create good related problems. There's an aesthetic part of this, too, that LLMs do not capture.

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

#124

Post by roywiggins »

gowld wrote: post #115
roywiggins wrote: post #113

Earlier quoted context omitted.

If AI can generate questions and then answer them, what are the people for?

If humans can shovel dirt, then what are the ants for?

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

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

#125

Post by 20k »

CamperBob2 wrote: post #77
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.

This is the literal opposite of progress: stealing from people genuinely creating, and stealing the money they should earn

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

#126

Post by johnsmith1840 »

SpicyLemonZest wrote: post #116
johnsmith1840 wrote: post #95

Earlier quoted context omitted.

So what happens to this world view when AI not only clears the forest of problems we couldn't solve but also in the future discovers more forest with trees bigger than anything we've ever seen before? 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 understa…

> 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.

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

#127

Post by pictureofabear »

thymine_dimer wrote: post #80

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…

I think the problem with AI asking questions is that it will ask questions that are interesting to it but not necessarily us. AI, as a model, will never be a perfect copy of a human. It will always be a simulation, and thus to some extent, will ask questions that humans find irrelevant and solve problems that humans find irrelevant.

For anyone facing an existential crisis on AI, your ace in the hole is your humanity. Only you have it, and only you will be the best judge of what is good and interesting (to a human at least).

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

#128

Post by samwise99 »

soundworlds wrote: post #86

I think this is where people will have to let go of the ego of being the "sole author" of a solution for us to move into the next era of human flourishing.

The future sole owners of half of San Francisco’s mansions thank you for your enlightened stance.

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

#129

Post by dvt »

applicative wrote: post #110
dvt wrote: post #64

Earlier quoted context omitted.

> 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…

Yes, the present developments, and the present approach, mean we will not have mathematicians any more.

Your confident re-assertion still doesn't convince me, why do you think so?

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

#130

Post by magicalist »

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 dismissal, surface level and not actually engaging with the substance of the comment. It's also just wrong. You claim "it’s also a misstatement of mathematical history", but don't specify which part. That there's "centuries of traditions of open science"? But your examples are from centuries (and millennia) ago, and there was never any claim that these traditions are universal.

But more fundamentally, competition doesn't mean you can't also have open science. And the very long, damaging events like the Leibniz/Newton feud are exactly what make many mathematicians work to maintain a spirit of collaboration and attribution even when they're competing on approaches.

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