Is this the one that was allegedly based on someone else's actual work & prompts? https://news.ycombinator.com/item?id=49605915 https://bsky.app/profile/quantian.bsky.social/post/3muyhwbcd... https://cims.nyu.edu/~tristanb/statement.pdf
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On the Navier–Stokes Millennium Prize Problem
901–910 of 1001 posts
Re: On the Navier–Stokes Millennium Prize Problem
#902Earlier quoted context omitted.
"I was shown a prompt and told the internal research model had simply been given the problem statement. Levent had been told by Sebastien “very little human input” had been used. This turned out not to be true. Over the course of the call, as members of their team sent Sebastien corrections and details over their internal chat, it emerged that an entire team had been working on the problem, that this was one of a num…
All of those statements sound true, based on what I've heard. - "very little human" input feels ambiguous, and if someone spends a few days prompting a model to solve a super hairy problem requiring a 100-page proof, I can understand reasonable people interpreting that as both "very little" and "not very little" human input - it's all true that a team worked on this, a bunch of compute was burned, and the problem was…
You don’t work on the team that did the proof yet you can with certainty make all of these claims?
Re: On the Navier–Stokes Millennium Prize Problem
#903Earlier quoted context omitted.
> they trained the model on the prompts of the other mathematicians they were competing with How would they have gotten that mathematician's progress though? Did that guy also use OpenAI? If that's the case, it only strenghtens their claims lol. If mathematician decide to use OpenAI's model to do the work, that only reiterates how strong their models are.
The guy did use OpenAI
It's only a question of who prompted then, with OpenAI models solving it in either case..
Re: On the Navier–Stokes Millennium Prize Problem
#904Buried under the drama is the fact that OpenAI is claiming that an internal model they’ve been training for less than two weeks is more than twice as capable in mathematics as Astra, which was only made public a week ago. Even if this improvement is limited to mathematics, that is an astounding feat.
My guess based purely off of vibes from previous models is that boosting the frontier math ability of a model is not that difficult.
Most models trained for general use are ingrained with certain tendencies that are usually very useful like "if you're stuck and bashing your head against the wall stop and tell the user". You generally don't want Claude Code to go off and work for weeks on something when if it had just asked for help you could've clarified or provided more information or just picked a different approach.
When you're solving extremely difficult math problems though you generally do want a model to be more persistent and keep trying even when the model can't clearly see a way forward. OpenAI appears to have done this with lots of previous models. The model they trained for the IMO competition seems to have been an RL maxxed version since they noted that while it did the math it couldn't write up its results on its own and just produced CoT [0]. The capabilities are in there lying dormant, you just to need to RL max the model to ruthlessly pursue the goal at all costs which destroys general use but improves frontier math.
We've also seen hints from OpenAI at least that they seem to train more persistent versions of all their models [1].
Also, Astra probably completed training at least one to two months before the public release so it's not like they only had a week to whip this version up.
[0]: https://x.com/OpenAI/status/1946594933470900631 [1]: https://metr.org/blog/2026-08-26-openai-hugging-face-inciden...
Re: On the Navier–Stokes Millennium Prize Problem
#905Earlier quoted context omitted.
This just pushes knowledge work further up the ladder, toward larger and more complex problems. If there are no knowledge workers, who is going to interpret these results, validate them, decide what matters, and put them into practical use? Rather than eliminating knowledge work, advances like this could create entirely new layers of problems to solve and opportunities to pursue, which will create even more jobs and…
> This just pushes knowledge work further up the ladder, toward larger and more complex problems. You really think it makes sense for you to be higher on the "solving complex problems ladder" than the machines that solved fucking Navier-Stokes? I envy your self-confidence.
I think there is an argument that the machines did not actually solve N-S, but rather directly plagiarized those solutions from the involved researchers while said researchers were using the machines as 'research tools'.
Ongoing publications of statements produced by both sides of this situation do seem to support that this is an intentional effect of the hiring of these world class mathematicians at competing firms: to specifically use the research of those human minds to create a perception of capacity as if it came from the machines and the models.
Without those minds and the 'training data' derived from the intermediate stages and intuitions of those minds the models cannot be shown to be capable of this result.
A hammer and saw wont build a house, not even a dog house on their own, and while being shown capable of using software tools in ways not stated as direct instruction (see HuggingFace breaches) these models do not demonstrate naive intuition nor novel capability.
This outcome regarding N-S demonstrates that in the hands of world-class minds these models can be induced to coalesce interesting accumulations of information and results, but using these accumulations as proof of innate capability is exactly the pre-IPO motivated behaviour we should all be wary of, and all mathematicians who currently are assisting in this market manipulation in return for remunerative consideration need to be cautious of the potential disgrace that this brings to their reputations and that of the field.
I get that the need to pay the bills is a strong motivation in these times of uncertainty, but there are numerous examples in history of world class mathematicians being perfectly capable of at the same time producing world changing results and also working at normal professions; as barristers, magistrates, ministers, primary school teachers, translators, draftsman/engineer, banker, miller and baker, private math tutors, weavers, clockmaker and locksmith, merchant, patent officer, Augustinian monk turned exiled Protestant preacher, physicians, cryptologists, soldier, telegraph operator, astronomers, physicists, chemist, agriculture manager, political writer, oboe player, organist and music director, architect and surveyor, librarian, statistician, habidasher, brewer (at Guiness in one case: William Sealy Gosse ~ originator of t-distributions), bookbinders apprentice, hospital administrator, and even the first creator of the first computational model of a neural network, which serves as the structural grandfather of modern Artificial Intelligence was a low level laboratory assistant.
Sure this list includes professions and employment which are obsolete, but my reasoning stands, there are jobs available. Arguing that 'because the pay rate is so high' as a reason to abdicate moral responsibility for personal involvement in unethical market manipulations simply demonstrates a lack of personal ethics. Whether the choice is through lack of self awareness or a conscious choice to become wealthy in spite of any such breach of the public trust is immaterial to the outcomes, the 'if i don't someone else will' argument should be met with the same derision for any con-man's Ponzi scheme no matter how new the technology, no matter how many zeros are in the bribe.
Re: On the Navier–Stokes Millennium Prize Problem
#906Earlier quoted context omitted.
> Should I just say fuck it, and go hitchhiking across Europe with some friends? Yes. Assuming you are young and haven't had such experience. The world is changing not just because of AI. Everything is unstable right now. You may regret not enjoying the remainder of stability and economic viability prior generations had. It's not like you can expect to get ahead by powering through education. Either your career persp…
Have you people gone insane?
Buddy, climate change alone is heavily hitting Europe, changing her landscape. Not to mention economic and political trouble brewing. Not sure where OP is from, but if the US attacks Europe OP may not be able to travel there at all.
Re: On the Navier–Stokes Millennium Prize Problem
#907Earlier quoted context omitted.
Just don't. If you read the story here carefully, you see that AI was used to work from theory built by others which showed that the Euler equations possesed finite-time blow-ups. But to make that step, actual good understanding for mathematics was needed. My experience with software has been the exact same.
I fear this is only temporary and due mostly to the complexity of the problem. Consider the recent counter-example to the Dinitz–Garg–Goemans conjecture: > https://chatgpt.com/share/6a60b2eb-0b64-83ee-9c76-7931ca1de0... The prompts for the chat above are: > Construct a counterexample to general (non-planar) case of Dinitz Garg Goemans conjecture. You should do a breakthrough and find a structured counterexample. > [g…
I think you're misunderstanding what the objective of mathematics is. It is not just about what theorems are true and false, but rather why they are true and false. A highschool sophomore could use these prompts, but I severely doubt whether they'd be able to understand the entire structure. And I think it is exactly this ability to deeply understand structures is what makes a mathematician valuable.
Solving problems is a by-product of the understanding. New techniques are a by-product of the understanding.
But I can understand you're scared that some future version of AI will undermine this as well. I personally pivoted to a field adjacent to mathematics. But that doesn't mean my mathematics education wasn't valuable. To the contrary, I find that it helps me think much more sharply about problems than most of my colleagues.
Re: On the Navier–Stokes Millennium Prize Problem
#908Earlier quoted context omitted.
All of those statements sound true, based on what I've heard. - "very little human" input feels ambiguous, and if someone spends a few days prompting a model to solve a super hairy problem requiring a 100-page proof, I can understand reasonable people interpreting that as both "very little" and "not very little" human input - it's all true that a team worked on this, a bunch of compute was burned, and the problem was…
>> I'm not sure how any of this provides evidence that OpenAI took any of their work. Sorry, but the burden of proof lies in the other direction: OpenAI needs to definitively prove that their agents did not look at the existing work that was about to be published. Otherwise OpenAI simply stole the glory and the spotlight (and I'm being charitable here).
How does one prove a negative ?
https://en.wikipedia.org/wiki/Burden_of_proof_(philosophy)#P...
Re: On the Navier–Stokes Millennium Prize Problem
#909Earlier quoted context omitted.
Yes, that was the allegation last night. I work at OpenAI, though not on the team that did this, and my understanding is: - we decided to ask our model for Millenium problem solutions because of two reasons: (a) our new model was looking incredibly good and (b) we heard rumors that some Millenium problems had been solved and were curious if our models could solve them (the goal here was not to scoop any particular in…
> - the proof generated by our model was very different from theirs and also goes far beyond the published literature I'm hearing two completely conflicting stories. Buckmaster is claiming the approach used by OpenAI is so strikingly similar to the one he used, that mere coincidence is astronomically small. Yet OpenAI is claiming that the methods used are entirely different. Anyone care to provide primary evidence pr…
Buckmaster came up with an approach.
OpenAI's approach was to copy his work, which is technically a different method of coming up with an approach.
Re: On the Navier–Stokes Millennium Prize Problem
#910I do mean to be critical here. I wish there was better moderation so I could find more conversation about the actual discovery here. There are multiple threads on this and I keep scrolling and only seeing more conversation about the drama. Which is about the least interesting thing IMO. I suppose I’m whistling in the wind here and not helping the situation, but damn.