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Controversy over OpenAI's Maths Breakthrough

scientificamerican.com

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Re: Controversy over OpenAI's Maths Breakthrough

#11

Post by ActorNightly »

runeblaze wrote: post #8
ActorNightly wrote: post #5

The thing about these math proofs is that they really add nothing of value. Its a cool tech demonstration on how LLMS can search the trained space, but fundamentally, LLMS haven't "discovered" anything groundbreaking. For NS equations, they are trying to model something that is discrete (i.e molecules colliding) in a continuous manner. You can easily think of a condition where they fail - imagine a vaccum where there…

I can't wait to tell my pure maths professors that their most of their research adds nothing of value. I mean I am sure most of them would agree to some extent, but like, dude, have some more faith in the utility of pure maths, esp. centuries down the line

There is plenty of work that goes on in the math field that is super important. But any field has research that is irrelevant. So far, all the proofs done by ai have been largely irrelevant.

Re: Controversy over OpenAI's Maths Breakthrough

#12

Post by hliyan »

According to Thomas Wolf:

> Leven and Tristan worked over several months on one of the Millenium Prize Problems with various AIs to reach final interesting results. OpenAI apparently heard about it in the last days and prompted their latest models to work on the direction Leven and Tristan found fruitful. They then tried to push for controlling communication of the result and dropping Leven from authorship with some very bad taste social pressure.

(1) https://x.com/Thom_Wolf/status/2097215782484607029

(2) https://mastodon.social/@tristanbuckmaster/11723341370570119...

Re: Controversy over OpenAI's Maths Breakthrough

#13

Post by runeblaze »

publlus_enigma wrote: post #10
runeblaze wrote: post #8

Earlier quoted context omitted.

I can't wait to tell my pure maths professors that their most of their research adds nothing of value. I mean I am sure most of them would agree to some extent, but like, dude, have some more faith in the utility of pure maths, esp. centuries down the line

My read was that "these proofs" was referring to AI generated proofs specifically, not all mathematical proofs.

sure I get that, but like, my field has plenty of counterexample as proofs. we have had non-constructive proofs like probabilistic arguments. i don't think we can play the game of "oh this proof is useful that proof is not useful" well

Re: Controversy over OpenAI's Maths Breakthrough

#14

Post by ActorNightly »

runeblaze wrote: post #13
publlus_enigma wrote: post #10

Earlier quoted context omitted.

My read was that "these proofs" was referring to AI generated proofs specifically, not all mathematical proofs.

sure I get that, but like, my field has plenty of counterexample as proofs. we have had non-constructive proofs like probabilistic arguments. i don't think we can play the game of "oh this proof is useful that proof is not useful" well

Generally, the proofs that are in the form of "here is a single contradiction to an established statement that proves that its not always true", are generally useless. We can prove that newtons laws don't apply when you start considering relativity, but because they still apply for a large domain, they are still used.

Same with NS equations. Who cares if you can find a singularity.

And if you want an example of something novel that is worth pursuing - Its highly likely that the modern transformer architecture is sub optimal, you probably don't need to do full matrix multiplies in the transformers. There potentially could be a higher level mathematical formulation of minimal math operations that are needed without having to do trial and error - especially because all of the math involves linear combination passed through smooth activation functions.

But coincidentally, there hasn't been any research in terms of point LLMS to self optimize in this way, because there isn't enough human math literature on the LLMs to train on.

Re: Controversy over OpenAI's Maths Breakthrough

#15

Post by ActorNightly »

whoarewethen wrote: post #7
ActorNightly wrote: post #5

The thing about these math proofs is that they really add nothing of value. Its a cool tech demonstration on how LLMS can search the trained space, but fundamentally, LLMS haven't "discovered" anything groundbreaking. For NS equations, they are trying to model something that is discrete (i.e molecules colliding) in a continuous manner. You can easily think of a condition where they fail - imagine a vaccum where there…

There is value in knowing (as opposed to hypothesizing) whether some interesting claim is true or false. Actually, just knowing that a claim is true may motivate people to search simpler proofs, as it happened in mathematics in the past.

There still has to be some logic behind what is the meaning of a proof. Generally, its pointless to explore random equations of numbers and try to prove that this equation holds for every value. That equation needs to have some use, whether its cryptography, or description of a physical process.

For example, look at Poincare conjecture proof. As cool as it is, can you name one area where the derivation of that proof or the proof itself has been used (without asking an LLM)?. Note that the core concept, Ricci flow, is used in lots of places, but the application of the proof is largely irrelevant - the homeomorphism of any 3d shape (say like a surface in Blender) to a sphere can be determined in other ways, more efficiently than what Pointcare conjecture states (i.e that every loop can be tightened to a point).

Re: Controversy over OpenAI's Maths Breakthrough

#16

Post by runeblaze »

ActorNightly wrote: post #14
runeblaze wrote: post #13

Earlier quoted context omitted.

sure I get that, but like, my field has plenty of counterexample as proofs. we have had non-constructive proofs like probabilistic arguments. i don't think we can play the game of "oh this proof is useful that proof is not useful" well

Generally, the proofs that are in the form of "here is a single contradiction to an established statement that proves that its not always true", are generally useless. We can prove that newtons laws don't apply when you start considering relativity, but because they still apply for a large domain, they are still used. Same with NS equations. Who cares if you can find a singularity. And if you want an example of somet…

i really think we are opening a can of worms with these “who cares if you find a single counter example as disproof” arguments. i think the better version is “ok any lemmas or techniques we can generalize from this” or “what did we learn about maths through this” and use this as a basis to say LLM proofs are not useful

like say if god lets me find a single counter example to P=NP and thus disproving it — I think we can learn tons about complexity theory from this counter example by studying it. we should not have the hubris of assuming “oh a single counterexample is generally useless” — why, how. this is the same hubris imo that produced like “number theory is useless” until it is not

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