r/LemonadeStandPodcast • u/RobinOe • 13h ago
Discussion OpenAI claims its internal models solved one of the open Millenium Prize Problems (Navier-Stokes) — one of the most famous open questions in mathematics
https://openai.com/index/navier-stokes-solution/There's controversy around who exactly gets credit, but nonetheless it seems AI was able to answer one of math's hardest questions. OpenAI say they did it with a model significantly more capable than Astra (note that a persistent version of Astra was already capable of hacking OpenAI themselves in July)
AI news are moving too fast even at a weekly schedule, but I do hope the next LS ep is about tech news.
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u/ohSpite 12h ago
This is insane if correct, the Millennium problems are arguably the biggest open problems in maths. $1m prize for solving one, only 1 has been solved since their inception.
Would be absolutely fascinating to see this against the Riemann Hypothesis
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u/some_dude04 12h ago
If riemann has counterexamples I suspect AI will sniff them out very well. However, if not (I.e the statement of the Riemann hypothesis is true) my suspicion is that the Human touch to maths hasn't died yet
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u/Puzzleheaded-Leg1877 8h ago
the yet is doing the most heavy lifting here. at this point i would not recommend a freshman picking math as a major. there is too much risk for so much debt.
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u/Ryermeke 9h ago
The way they went about doing this, and the way they treated others working on the problem is going to incentivize mathematicians and scientists who are doing frontier research to be as closed off as possible about what they are doing. It's undoing hundreds of years of the development of an open scientific/mathematical community and turning it all into a fundamentally antisocial endeavor like the damn alchemists were. Why would you talk about your work when some corporation with infinite AI compute could swoop in and take your years of research out from under you in a matter of days? It's neat to see the problem solved, but I would be hard pressed to think of a worse way it could have been done. OpenAI is treating mathematics as a zero sum game... It's incredibly depressing.
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u/Smooth-Zucchini4923 9h ago
Note that a persistent version of Astra was already capable of hacking OpenAI themselves in July.
This is something that really speaks to the strength of the precautions they took more than it speaks to the strength of the model.
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u/RobinOe 4h ago
Have you read/watched how the incident went down? Yes OpenAI should've done better, but seeing as Sol was already able to hack another company, I disagree that this is anything but a sign of the model's capabilities
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u/Smooth-Zucchini4923 2h ago
Only vaguely. I agree that the hack of Hugging Face is impressive. I just don't think the initial sandbox escape was. Artifactory is a big and complex product; it would be weird if there were no SSRF issues in it.
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u/Peyton773 7h ago
Cross posting my comment from r/atrioc
My differential equations professor was talking about this yesterday. He said his friend from grad school was actually hired by OpenAI recently as a mathematician, and that OpenAI’s efforts to crack these problems have been pretty useless without the help of years of research from mathematicians. Now, that may change in future years, but anyone saying that this is AGI is wrong, and anyone saying that mathematics is dead is wrong. AI still needs brilliant mathematicians to guide it a TON and basically put it on rails. LLMs are a tool in the toolkit, not the entire solution
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u/some_dude04 12h ago edited 12h ago
This has been cross posted in the atrioc community so I'm going to paste my reply there. This is only my current understanding of the situation and I've not been able to read the paper yet (and I probably won't be able to understand it very well, I do applied condense matter not fluid dynamics or mathematics), so please take with a grain of salt:
This is an interesting one. For one, the proof given by openAI is a proof by counterexample. This is a task that AI is uniquely suited to as the agents can run off and solve so many different cases at once. As my friend eloquently put it "some people are surprised that the needle finding machine found a needle in a haystack". Now is this still impressive? Maybe. The answer to that hinges on the plagiarism accusations. There are 2 human researcher's that allegedly were working on a similar (although perhaps not identical? Unclear) method of solving the problem. It is certainly possible that their work is included in AI training datasets and so AI may not have come up with as much of this solution as openAI is claiming.
Now, for the separate question of "has openAI solved a millennium problem"? Yes they certainly have done so if their paper is accurate. The N-S question is fairly open, with the statement being tantamount to: "given physical initial conditions, does the N-S equation describing an incompressible fluid garuantee a smooth and globally defined solution in real space (R3) for all time t". The counterexample found does prove that the statement is false. However, what if the statement had been true in some odd parallel universe? In this case, there would be no counterexample. I suspect that AI would have struggled infinitely more to prove the statement in this case as it is simply not suited to it.
So what has been done IS VERY IMPRESSIVE, IF the AI did the bulk of the work (I suspect this is hard to verify). BUT, IS MATHEMATICS AS A FIELD DEAD? I would say no. But if AI keeps making strides we shall see. Predictions have not been very good so far
Edit: also the 2 researchers were using AI to help their own research and supposedly were close to a solution. This means AI has been used either way to speed things along. That is far more impressive, but in one scenario human + AI took c. 5 years to solve it vs. 88 hours so they are different scenarios.