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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

#91

Post by layman51 »

_alternator_ wrote: post #55
olalonde wrote: post #49

Can't mathematicians still gain novel insights by reverse-engineering AI-generated proofs? Just like chess players learn new concepts by studying what engines play.

Yes, and they will. But what's happening here is that the system that cultivates mathematics (and mathematicians) is recieving likely the biggest shock of its history. How do you reward merit and identify talen when people can't absorb the number of proofs being generated, much less understand them? Perleman's proof of the Poincare conjecture took several years for the mathematical community to digest; the proof of N…

This reminds me of the time an AI was taught how to play a racing sim game (Gran Turismo if I remember correctly). The AI was able to race its car very well, but it took a lot of risks that a human player probably would not. A human player might be able to copy the approach the AI took, but they would probably crash.

Going back to chess, I think the situation is similar where you can’t expect an amateur player to get better by trying to play like a strong engine. I think even professional chess players mainly use engines to prepare or memorize variations that are counterintuitive for their opponent. In other words, getting into situations that look wild, but that part of one player’s preparation.

I’m not sure how it is in math, but in chess, it seems like top players can play just like engines when they are in “normal” positions, so that is where I get a bit confused as to where the direction of insight is coming from because it’s been my view that AI is able to make leaps that we would never think of taking and I’m not sure that anyone could actually learn how to do that on their own unless they were willing to keep failing over and over.

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

#92

Post by senordevnyc »

ltbarcly3 wrote: post #5

I think he's suffering from a sort of static-universe fallacy. People aren't going to keep doing what they are doing, but secretly. What is going to happen is a complete revaluation of things like "finding a counter example to a famous problem". Even if someone finds a solution to a problem like this with pencil and paper, nobody will believe it, and they will assume that there was an AI involved. Further, sitting an…

People who work hard to build intuition and also use AI effectively will dominate the field.

This will be literally every field, sooner or later, at least until the human and their intuition is just slowing the AI down. There’s no scenario where humans without AI beat humans with AI in the long run, unless there are fields where the “alien intelligence” somehow hurts more than it helps (like artistic pursuits perhaps?)

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

#93

Post by monktastic1 »

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…

But this oracle doesn't just say true / false. It also gives a proof. That makes it much less exciting (not to mention beneficial for your career) to find another one (or even worse, the same one).

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

#94

Post by hackinthebochs »

vouaobrasil wrote: post #46
ModernMech wrote: post #38

Earlier quoted context omitted.

If math is solved then move to an area that’s not. Why do fields need “protecting” from ai?

The reason is because the entirety of society, historically, has been based upon humans using their differential skills to further it, which in turn promotes societal cohesion. If most human endeavours are solved, then we will enter a period of abundance that paradoxically will erode the glue holding society together. In short, endless abundance of solutions and ideas cannot coexist with a healthy society. Only those…

>endless abundance of solutions and ideas cannot coexist with a healthy society.

This really cuts to the heart of the problem with AI. Not only does AI undermine the monetary economy, it undermines the intellectual economy. What is humanity without the need for collaboration for survival or for intellectual progress, ultimately providing the impetus to build something greater as a result? I don't know, and I'm not looking forward to finding out.

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

#95

Post by johnsmith1840 »

_alternator_ wrote: post #55
olalonde wrote: post #49

Can't mathematicians still gain novel insights by reverse-engineering AI-generated proofs? Just like chess players learn new concepts by studying what engines play.

Yes, and they will. But what's happening here is that the system that cultivates mathematics (and mathematicians) is recieving likely the biggest shock of its history. How do you reward merit and identify talen when people can't absorb the number of proofs being generated, much less understand them? Perleman's proof of the Poincare conjecture took several years for the mathematical community to digest; the proof of N…

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 understand proofs if they are correct?

If this is V0.5 of AGI/ASI then by V1 the only system that will be understanding any of this is the AI itself. If AI creates a new field of mathematics month 1, then solutions to new problems in month 2, then another field of mathematics on top of that at month 3 there's no human who will ever keep up with that.

Or the alternative is a flattening of abilities, the AI cannot proceed further than the collective intelligence of humans and in that case this is correct. We'd be in a future where nobody wants to work in a field with an AI dominating it and when AI hits the limit of no useful training data input we'd have this giant gap of nobody know wtf it's done for years and nobody willing to figure it out and advance it.

Ooo here's a dytopian story: - AI gets better at everything humans do - humans stop trying - AI cannot improve anymore than its input data + human support - AI slowly degrades itself (model collapse) for decades, it slowly hallucinates little by little until its hallucinating entire scientific fields losing quality over time - there's a mass population of people in the future who never learned to do anything and now have to relearn and figure out the equivalent of 100k years of AI work in order to prevent its slow degredation while all the systems they've come to rely on start failing around them. The AI has solved every problem but every real solution is saturated with 1000 false ones. - humanity starts from scratch?

I love the idea of an archive of every solution to every problem existing but it's impossible to figure out the correct one. Infinite library like!

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

#96

Post by opello »

johnsmith1840 wrote: post #59
calf wrote: post #35

Earlier quoted context omitted.

The difference is no one writes punchcards so the comparison is inapt. It is more like supposing AI eats everything humans attempt to do. They will take your work as you are working on it, any interaction at all. It is meta-plagiarism, on another level.

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 "take" but it's not an incomprehensible shortcut of criticism of the aforementioned behavior, not that precision should be avoided here.

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

#97

Post by [deleted] »

CamperBob2 wrote: post #57
colinhb wrote: post #50

Seems like in current cultural and economic context, short term extraction is what we’re going to do > In short, the indiscriminate use of powerful solution-extraction tools can achieve the immediate short-term goal of solving problems at hand, but at the cost of sustaining the ecosystem for the next wave of progress, or in understanding the progress already obtained.

The "ecosystem" is dead. Tao should be thinking about what will replace it. I don't understand why he's taking this tack.

[deleted]

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

#98

Post by jijji »

The lack of reasoning traces in frontier model output is hurting science and progress... thats my take away from reading that, and why open source models are so critical and so needed, because they actually do expose the chain-of-thought reasoning traces recently missing from the frontier models (openAI, anthropic, etc). By encrypting and purposely hiding this important information from public inspection, it makes for a world where people lack the true understanding of how a problem gets solved.

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

#99

Post by pizzly »

coliveira wrote: post #83

This to me is another level of dishonesty. Imagine if a company producing math software starts to hear "rumors" someone is using their software to prove an important result and start massive runs of that software to beat the team. That may not be illegal per se but it is incredibly deceitful. I wonder if the original mathematicians should start a lawsuit for theft of intelectual property.

I would expect this for service providers that provide their "free" services but the mathematicians said they paid OpenAI to help generate this result. This is a clear conflict of interest. Similar to inside trading. Or the same lawyer being hired from two opposing sides which is a big no no. There are rules and laws that already deal with this in other industries and I expect that there will have to be regulation developed for cases where there is a conflict between AI customers and AI provider interest.

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

#100

Post by srcreigh »

ModernMech wrote: post #38
_alternator_ wrote: post #32

This series of posts by Terry Tao is a direct response to the Navier-Stokes results (multiple results!) from the last 24 hours. The question is what is left after the levelling of mathematics, in all its senses, occurs? How can you protect a field that's under this much pressure in the next 6 months? > [I]t is now the identification of a promising problem which is the scarce and precious resource. We have now seen th…

If math is solved then move to an area that’s not. Why do fields need “protecting” from ai?

Math can never be fully solved by a computer, if only for lack of computational resources.
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