> 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.
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 is sufficient space between air molecules, so that collisions aren't always possible. NS won't be able to predict the state of the fluid in every single point in space.
In practice, when you do CFD, no package uses direct differential simulation of NS equations, you usually have simpler approximations that are good enough for the space you are working for. And if you want accuracy, you usually do something like LBM which simulates particle collisions using probability distributions.
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
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.
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.
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).
I do wonder if perhaps LLMs take credit from some mathematicians working in obscurity in some dark corner of the web, it’s not unheard of for some to be reclusive. Perhaps someone completely unaware that they might have sovled something someone else considers important.
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...
https://www.youtube.com/watch?v=GddkKIhDE2c
Enumeration of syntax patterns when rules restrict legal syntax patterns can be done without LLMs
The data center cartel that sprang up over the last 20 years is desperate to not have their entire social moat go up in smoke
https://archive.is/vlSuj
Discussions:
https://news.ycombinator.com/item?id=49613262
https://news.ycombinator.com/item?id=49605915
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 is sufficient space between air molecules, so that collisions aren't always possible. NS won't be able to predict the state of the fluid in every single point in space.
In practice, when you do CFD, no package uses direct differential simulation of NS equations, you usually have simpler approximations that are good enough for the space you are working for. And if you want accuracy, you usually do something like LBM which simulates particle collisions using probability distributions.
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
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.
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.
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).
I do wonder if perhaps LLMs take credit from some mathematicians working in obscurity in some dark corner of the web, it’s not unheard of for some to be reclusive. Perhaps someone completely unaware that they might have sovled something someone else considers important.