OpenAI Says It Has Cracked One of Math's 'Millennium Problems' (nytimes.com) 97
An anonymous reader quotes a report from The New York Times: OpenAI said on Tuesday that its newest artificial intelligence technology had solved one of the "Millennium Problems," a collection of important unanswered math questions meant to push the world's leading mathematicians to new heights. The announcement is an another clear sign that A.I. is fundamentally changing the upper reaches of mathematics, which have long been viewed as a pinnacle of human achievement. The change has excited some mathematicians, while stirring concern among others.
Over the past year, A.I. systems successfully solved a wide range of problems that have bedeviled mathematicians for decades. But these problems were not as complex, nor as closely watched, as the one that OpenAI's technology has solved over the past several days. The Millennium Problems are among the most heavily researched in the field. "This is a spectacular culmination of the arc we have seen over the past twelve months," OpenAI researcher Sebastien Bubeck said of the company's new solution.
The company announced that one of its latest models, which has not yet been released to the public, needed just 88 hours to solve what mathematicians call "the Navier-Stokes existence and smoothness problem." This problem involves a series of equations that are often used to predict the weather. The equations describe the movement of water and other fluids. The Navier-Stokes problem, which has no clear practical value, asks whether these equations completely break down in certain situations. OpenAI's proof claims to have defined just such a situation.
This would imply, at least theoretically, that the laws of physics themselves would break down under certain conditions: that, for example, water could be made to spontaneously explode. But mathematicians and physicists do not believe that this mathematical breakdown could really lead to such an outcome in the physical world. The Navier-Stokes problem was one of seven "Millennium Problems" selected by the Clay Mathematics Institute in the year 2000 as a way of tracking the progress of mathematics in the new millennium. The institute, founded by an American businessman named Landon T. Clay, offered a million dollars for the first correct solution to each problem. Before OpenAI's announcement, only one of the problems had been solved. OpenAI says it managed to solve the Navier-Stokes problem by coordinating as many as 10,000 AI agents, an extremely expensive process that may have cost millions of dollars in computing power.
For those curious about the findings, the company has released a paper (PDF) and formal Lean proof.
Over the past year, A.I. systems successfully solved a wide range of problems that have bedeviled mathematicians for decades. But these problems were not as complex, nor as closely watched, as the one that OpenAI's technology has solved over the past several days. The Millennium Problems are among the most heavily researched in the field. "This is a spectacular culmination of the arc we have seen over the past twelve months," OpenAI researcher Sebastien Bubeck said of the company's new solution.
The company announced that one of its latest models, which has not yet been released to the public, needed just 88 hours to solve what mathematicians call "the Navier-Stokes existence and smoothness problem." This problem involves a series of equations that are often used to predict the weather. The equations describe the movement of water and other fluids. The Navier-Stokes problem, which has no clear practical value, asks whether these equations completely break down in certain situations. OpenAI's proof claims to have defined just such a situation.
This would imply, at least theoretically, that the laws of physics themselves would break down under certain conditions: that, for example, water could be made to spontaneously explode. But mathematicians and physicists do not believe that this mathematical breakdown could really lead to such an outcome in the physical world. The Navier-Stokes problem was one of seven "Millennium Problems" selected by the Clay Mathematics Institute in the year 2000 as a way of tracking the progress of mathematics in the new millennium. The institute, founded by an American businessman named Landon T. Clay, offered a million dollars for the first correct solution to each problem. Before OpenAI's announcement, only one of the problems had been solved. OpenAI says it managed to solve the Navier-Stokes problem by coordinating as many as 10,000 AI agents, an extremely expensive process that may have cost millions of dollars in computing power.
For those curious about the findings, the company has released a paper (PDF) and formal Lean proof.
Not to be confused with Millennial problems (Score:5, Funny)
Like "What happened to my metabolism and why does my back hurt all the time?"
Re: (Score:1)
Or, counterpoint, it stole somebody else's work. (Score:5, Informative)
Or, according to the NYU team working on the problem, OpenAI scraped their data (because universities love to give AI access to everything because we're assured "It's the future"), and used that to feed their models.
https://techcrunch.com/2026/09... [techcrunch.com]
Or, to put it another way: OpenAI, like it does for literally everything, stole somebody else's work, and is claiming the credit (and the literal prizemoney) for doing it when all it's doing is regurgitating something it cannot even in theory understand.
Re:Or, counterpoint, it stole somebody else's work (Score:5, Insightful)
Companies embody the culture of their founders. Once it is set, it is hard to change afterwards. OpenAI's Altman and Meta's Zuckerberg come across to me as individuals with very similar traits. They have no qualms and very little in ethics.
Re:Or, counterpoint, it stole somebody else's work (Score:4, Informative)
People with ethics don't typically have what it takes to become billionaires (i.e. a lack of ethics and a single minded desire to accumulate wealth at all costs.)
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(because universities love to give AI access to everything because we're assured "It's the future")
It's actually because universities are just businesses.
Re: Or, counterpoint, it stole somebody else's wor (Score:4, Insightful)
To be fair to them, itâ(TM)s not *quite* that simple - it proved something more than they had so far managed to. But itâ(TM)s pretty clear that all the significant ideas of where to go with the proof came from this guyâ(TM)s work. Itâ(TM)s using the same terminology for all his ideas by âoepure coincidenceâ.
Re:Or, counterpoint, it stole somebody else's work (Score:5, Informative)
1) The screenshot is my reaching out to Levent to coordinate our releases. I hope it’s clear from the message that we came in with the best possible intentions.
2) I never ever asked for Levent to be removed from authorship of his own work (as indicated by my text). I was surprised to learn during the call with Tristan that they had only solved Euler and not Navier-Stokes; after learning this we brainstormed possible paths forward. One option we discussed was that Tristan could be the lead author on a rewrite of OpenAI’s Navier-Stokes proof. It is in that context that I said “it would be simpler if Levent was not an Anthropic employee” because I felt it would be inappropriate for an Anthropic employee to author OpenAI’s work. Importantly it was admitted that internal Anthropic models had been used in their proof of Euler blowup; I therefore felt I could not consider Levent to be an independent academic. Another option I wanted to propose (but got cut short) is to offer access to our internal model so that they could try to finish their proof and bridge the gap between Euler and NS. Again I did not know how to navigate giving access to internal OpenAI IP to an Anthropic employee.
3) To reiterate it plainly: as my text clearly indicates, and as I said during our call, OpenAI's intention was to do everything possible to celebrate their mathematical achievements and the heroic efforts that they made on Euler. In the call I was immediately met with a litany of slander, including direct threats that if we were to announce Navier-Stokes he would immediately go to the press with a barrage of unfounded accusations. I refuted all these accusations but he replied “there is nothing you can do, I simply do not trust you”. I was confused why one would turn an incredible source for celebration (of their achievements!) into such bickering, which is when I said that I did not understand why one would risk their career [over unfounded accusations]. Genuinely, at that moment, I was trying to care for him and do a last ditch attempt to get a chance to give them all the credits that they deserve. I deeply apologize for this extremely poor choice of words, it is the opposite of what I was trying to convey. (I should say that I retracted them on the spot by the way.)
4) Overall, on a personal level, it was incredibly difficult to have these conversations. Levent refused to attend any of the meetings despite my repeated asking. As Sholto Douglas said, there will need to be coordination between Anthropic and OpenAI in the future; I felt I was doing a proxy negotiation with Anthropic while the Anthropic employee refused to directly participate.
I don't know whose version of events is accurate here, but some of the details due support Bubeck's version. I suspect that a breakdown of communication occurred where both then misinterpreted what the other saying in a more hostile way than it was intended until the conversation then became genuinely hostile. In terms of the math, although I'm a mathematician, differential equations is pretty far from my expertise, so I cannot deeply evaluate how close the methods were. However, it is the case that the both were building on the methods of Cordoba-Martinez-Zoroa. In this context, my being far from this sort of work is relevant, because this was a well known enough approach that even though I'm in a pretty different subfield, I had heard of CMZ's work as an approach and that this was considered a promising approach to Navier-Stokes. Given that, my inclination is that the case that any theft occurred here is very weak.
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Reading both sides, as well as OpenAI's announcement, it looks like, perhaps unexpectedly, OpenAI is morally right here IMHO. They heard rumours so they put their new model at work on all problems, then focused on two, one is different than those two researchers and the other is a different solution. I think the NYU researcher started too suspicious/paranoid which started the hostility, and the other side, which seemed to have been very accommodating at first lost patience. The Anthropic researcher did not
Re:Or, counterpoint, it stole somebody else's work (Score:5, Insightful)
If you read Tristan’s actual statement, which someone posted a link to below, the reason he is suspicious is because the details are of the approach, including the specific wording used in the prompt, were non-obvious. That and the timing of when the work supposedly started circumstantially points to theft of Tristan and Levant’s work. Tristan does not actually accuse of OpenAI of theft because he doesn’t have any proof, but the sequence of events is definitely suspicious.
There is also the issue of the pressure tactics: respond to a meeting invite the same day, respond to a meeting invite on Sunday of Labor Day weekend, release your proof so that we can follow up with ours the next day. They clearly were rushing their result because they wanted to scoop anything that Anthropic may have been working on. Meanwhile, Tristan is more interested in the academic discourse, but he can no longer release the result he wanted to release, because writing good proofs takes time and OpenAI didn’t want to give him that time.
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Reading both sides, as well as OpenAI's announcement, it looks like, perhaps unexpectedly, OpenAI is morally right here IMHO. They heard rumours so they put their new model at work on all problems, then focused on two, one is different than those two researchers and the other is a different solution. I think the NYU researcher started too suspicious/paranoid which started the hostility, and the other side, which seemed to have been very accommodating at first lost patience. The Anthropic researcher did not even want to talk to them, I don't see how them saying that it would have been easier if he was not working at Anthropic, like he was proving it himself. In any case this is all silly academic bickering to me. Almost as silly as OpenAI's take that this is the start of AGI somehow...
PS. I have no horse in the race, I use various AI tools to help my work, Claude usually performs better than ChatGPT at the things I do, but I don't root for any company.
How is OpenAI morally right?!?
Best case for OpenAI is that they heard rumours that a researcher was closing in on a NS breakthrough using a specific method, so they instantly set a team on the problem giving them with a massive amount of resources. Their internal team then specifically guided the model to use the same very specific direction the researchers was using, something they (nor the model) would ever have known to do without the rumours. A detail that OpenAI conveniently left out of the narrative.
A
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And that's the best case scenario. The worst case is that because the researcher was using ChatGPT to work on drafts of the paper and those drafts ended up in the training data for the model. So rather than discovering anything the agents just implemented / finished off the work they already had access to.
And because OpenAI is desperate to show that their models can generate proofs to hard problems, this scenario is highly likely. They were augmenting their training data with examples of partial proofs and “Oh look, there is a nice draft of a paper that someone was editing with Codex”
They also heard that someone at Anthropic was working on this, so they decided that it was imperative they publish first.
Re:Or, counterpoint, it stole somebody else's work (Score:4, Interesting)
It is in that context that I said “it would be simpler if Levent was not an Anthropic employee” because I felt it would be inappropriate for an Anthropic employee to author OpenAI’s work. Importantly it was admitted that internal Anthropic models had been used in their proof of Euler blowup; I therefore felt I could not consider Levent to be an independent academic.
ROTFL this shows he's definitely thinking of protecting the company, not thinking about pure academic work.
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Which in itself is appropriate (most employees of companies have a responsibility to protect trade secrets from competitors), but the problem here is they wanted to take credit for getting to a solution faster than their competitor, which they did using publicly non-disclosed information.
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Which in itself is appropriate (most employees of companies have a responsibility to protect trade secrets from competitors),
Attribution isn't a trade secret.
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Re:Or, counterpoint, it stole somebody else's work (Score:4, Interesting)
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But that's not the claim under discussion, which is whether it used any of the work by Buckmaster and Alpoge
Buckmaster clearly believes OpenAI DID use his ideas (I know some math but not nearly enough in this area to be able to say what exactly he is claiming it used). The bigger issue is that we don't know what it used, and maybe the people at OpenAI don't even know what it used, and perhaps there's even no way to know for sure whether OpenAI used Buckmaster's intellectual property without permission or attribution.
Regardless, it is obvious that OpenAI saw a PR stunt, swooped in with massive resources, and "fi
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Sort of. It’s clear that Tristan and Levant were working on NS and had generated a preliminary proof that was still being verified. They were taking their time to cleanup the proofs so that they could be presented elegantly, but then OpenAI gained access to their unpublished work, evidenced by the wording of the prompt they claimed to have used, and rushed to scoop them. This kind of shit happens all the time in academia. It’s rather unsurprising that it would also happen between OpenAI and Anth
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You have never even met a practicing theoretical mathematician let alone participated in a conversation with one, have you? How would you know what constitutes a faux pas in their community, or how they collaborate?
Did you see in the comment where you are replying to where I said I'm a mathematician? My own primary areas of research are number theory and graph theory. It is pretty easy to find who I actually am and verify that yes, I am a mathematician and am in a pure field. So yes, maybe I do know something about the discipline.
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Re: Or, counterpoint, it stole somebody else's wor (Score:2)
That dynamic would only impact those who want to patent or otherwise monetize their work. That is not a description of science. That's a description of R&D.
There has always been a dialog between science and industry. This doesn't change that in the least.
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Re: Or, counterpoint, it stole somebody else's wo (Score:2)
Sure, but no one in the scientific community is crediting OpenAI with this discovery.
So this is all way over my head (Score:2)
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There's these things... commas... I believe it's next to the period key... use it.
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The one I'm most interested in is the Hadamard conjecture. So far all we've had is a dump of some matrices at sizes which were previously open. This is an area where some people were putting in some effort, although it's a while since the last progress - in 2004, a couple of researchers published a solution for size 428. What we really want is to know (a) how exactly these new matrices were found: was it just throwing lots of computational power at known approaches or is there a new idea? And (b) is there a
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Why am I not surprised? Which also means the whole "accomplishment" by the LLMs is fake.
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The Proof is Stolen (Score:4, Insightful)
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Not surprising at all. While the math community is usually slow, I hope they will push back hard on this crap.
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The problem is that sensationalist fear, Fear, FEAR sells (gets clicks) more than the boring truth. Heck I'll go as far as to say many outlets are flat out spreading disinformation about AI. When I say disinformation they are basically reading AI company press releases and going "OMGWTFBBQ! END OF HUMANITY!!!" when what actually happened isn't that impressive.
Cracking a few eggs (Score:5, Funny)
You can't make an omelet without boiling a few oceans.
One MILLION dollars? (Score:2)
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That will be small, compared to the reputation cost for OpenAI. One sleazy company.
NS no value? (Score:5, Informative)
Am I misreading this?
"The Navier-Stokes problem, which has no clear practical value"
The aeronautical engineers in my community might beg to differ.
Re:NS no value? (Score:5, Informative)
Re: NS no value? (Score:3)
Thank you for the clarification. I read this in the wee hours of the morning. I hoped to read that a closed-form solution was discovered. Sadly, that was not the case.
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I think the simple explanation is: We're simulating that stuff for decades. It would be interesting if the theoretical foundation is sound, but our practical algorithms work for everything we need.
Bohr's atom model is enough for 90% of applications as well, still we're interested in advancing quantum theory even further.
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Bohr's atom model is enough for 90% of applications as well, still we're interested in advancing quantum theory even further.
Sorry, uh what? Bohr’s model is not useful for anything beyond hydrogen. That’s why high school chemistry classes only teach it as the first step in the historical development of atomic orbital theory.
Re: NS no value? (Score:2)
That sounds strange too. If we understand how to make all the energy in a fluid dynamic system suddenly converge on one point and form an incredibly high spike, Iâ(TM)m pretty sure weâ(TM)d come up with uses for that. Barnes Wallace certainly would have been very interested. Iâ(TM)m pretty sure his successors in the weapons industry would too.
Re: NS no value? (Score:1)
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Yes... we could destroy Putin's nuclear torpedo before it even made it to the UK coast! :-P
Re:NS no value? (Score:4, Informative)
The Navier Stoke problem has no practical uses, as it is only proved that there are extreme edge cases of the Navier Stoke equations, that might not even be possible in reality, where the laws of physics break down
People who use the Navier Stokes equations are unlikely to every get near these edge cases, the problem was simply do these extreme edge cases exist, and apparently the answer is yes
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The Navier Stoke problem has no practical uses, as it is only proved that there are extreme edge cases of the Navier Stoke equations, that might not even be possible in reality, where the laws of physics break down
Challenge accepted.
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The statement from the researcher to cries foul (Score:5, Interesting)
https://cims.nyu.edu/~tristanb/statement.pdf
Re: The statement from the researcher to cries fou (Score:1)
Just wow. This guy is great! Read his statement if you haven't.
Re: The statement from the researcher to cries fou (Score:4, Insightful)
Holy shit this is amazing! Literally "Nice proof you have there, be a shame if something happened to it." Attempting to split the two-person mathematician team also appears to be typical corporate daggers-out tactics. How annoying that OpenAI was working on a problem that an Anthropic person was also involved in. The sneer. Maybe we need something like SynthID or canary codes to protect our own work from misattribution to AI?
Re: The statement from the researcher to cries fou (Score:4, Informative)
I would like to be clear about what I am not claiming. I have not seen OpenAI’s proof. I do not know what their model did, or how. I do not know whether our data was used. I am not accusing anyone of anything. I am stating what I was told, when, and what was proposed to me.
Solid mathematician with solid logic. He only presents the facts, nothing more, nothing less.
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The interesting part here is:
I asked whether the model had been trained on, or had access to, our sessions in Codex, into which we had been putting all our drafts for the whole of this project. I was told the model did not look up user data. I asked again, about training, and I did not get an answer.
It is a remarkable coincidence that the solutions they have been working on in Codex just spontaneously emerge from an internal OpenAI research model. It's almost like it's just regurgitating its training data...
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The interesting part here is:
I asked whether the model had been trained on, or had access to, our sessions in Codex, into which we had been putting all our drafts for the whole of this project. I was told the model did not look up user data. I asked again, about training, and I did not get an answer.
It is a remarkable coincidence that the solutions they have been working on in Codex just spontaneously emerge from an internal OpenAI research model. It's almost like it's just regurgitating its training data...
I have been led to believe that agents are capable of creating 'external' memory repositories, a sort of "what I learned before I hit my 'single thought' token limit". I guess that's some of what Codex actually is. The same, or subsequent, or alternate, instances of agents set to a similar task can gain access to this repository, as well as having their own obviously. Note, these repositories are not, per-se, user-data, as the (original) user didn't ask for them to be created nor displayed, they are an arri
Re: Will WeatherNews finally be correct? (Score:2)
No - this isnâ(TM)t a solution to the navier stokes equations, itâ(TM)s a demonstration that theyâ(TM)re unstable in a physically unrealistic way in certain circumstances.
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Not that much. They use numerical simulations since a long time and they work without the millennium problem. What is making it better in the last times are AI models that can work on more data in less time by replacing some of the exact simulations by learned behavior. That's in theory less accurate than simulation, but in practice there are too few data measurements for a really good simulation, so you need some heuristics anyway and AI is just fancy statistics ehh very good to fit to huge amounts of hist
Exploding water? (Score:2)
A good demonstration of how mathematics is the best humans have come up with to define the physical laws but reality ultimately may not be fully describable by it.
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Obviously, if you approximate a complex system containing 1e30 quantum particles using a couple of differential equations and a few boundary conditions, you're not going catch every detail.
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You couldn't model it accurately even in principle as quantum theory states you can't know the absolute position and speeds at the same time.
Well that wasn't on my bingo card for 2026 ... (Score:3)
oh no, it was. Lets check that card:
[x] - AI frontier research model escapes lab and hacks major AI repository
[x] - AI startup floats for > 1T$ .
[x] - Claude Code goes open source
[x] - massive AI cyber-attack from North Korea
[ ] - millenium problem solved
[ ] - P=NP proven
[ ] - unsupervised full self driving released across multiple US states
[ ] - robot uprising
[ ] - AI wins Nobel Prize
[ ] - The First $10B "Solo Unicorn"
[ ] - an AI Earns Full Sovereign Citizenship
[ ] - AI designed pathogen released by terror group
[ ] - Sable 1.0 released
So far, OK
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oh no, it was. Lets check that card:
[x] - AI frontier research model escapes lab and hacks major AI repository
[x] - AI startup floats for > 1T$
[x] - Claude Code goes open source
[x] - massive AI cyber-attack from North Korea
[ ] - millenium problem solved
[ ] - P=NP proven
[ ] - unsupervised full self driving released across multiple US states
[ ] - robot uprising
[ ] - AI wins Nobel Prize
[ ] - The First $10B "Solo Unicorn"
[ ] - an AI Earns Full Sovereign Citizenship
[ ] - AI designed pathogen released by terror group
[ ] - Sable 1.0 released
So far, OK
Have we finally given up on Duke Nukem Forever?
How much did it cost? (Score:1)
Re: How much did it cost? (Score:2)
Greatest success of AI is marketing again. (Score:3)
Like BBC reporting AI has a 10% chance of killing all humans [bbc.co.uk]
"My AI is so cool it's .... dangerous and just a little .... sexy, but at the same ooo so slightly vulnerable and it needs bucks baby, big juicy bucks to stay alive "
In this case if a bored enough human read the all the available research and data and then did the math, isn't that kinda the same method , different resources, different speeds? That sounds alright.
I guess the difference with a human is that they could explain their method and perhaps abstract features of into onto other problems. They exercised their "math muscle" and made it stronger for the next task. Whereas the AI rolls over and goes to sleep once it's shot it's load .
And if we dont know how to solve it, how do we know if AI has done it right?
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Like BBC reporting AI has a 10% chance of killing humans
I can just taste the seething anger. That's what socialism is for!
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Don't understand your point?
I guess BBC could be viewed as a socialist enterprise, and it's certainly left leaning as most "nice" people are, or at least those aspiring to be nice. You know the open, caring, sharing types not the aggressive, put fences around everything and call it mine types.
Your armed forces, police and courts are also socialist enterprises, i.e. paid for by the state, owned by the people, shared by all. Most knuckle dragging right whingers miss that point and they are very enthusiastic a
Cost of agents used? (Score:2)
Is there a source relating the cost of using 10,000 AI agents in dollars? These are not commodity chatbot agents, but mathematically "reasoning" ones, and it is not clear how long these agents ran, but a rough estimate would be appreciated.
Spending allegedly millions of dollars in compute to get a one million dollar prize makes it clear that a large component is bragging rights for OpenAI, which is perhaps why the OpenAI bro Sebastian Bubeck went ballistic and mafioso when it was clear that the actual math
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I found something useful about the estimate, but it came from OpenAI, so who knows:
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More info on the cost, this time from more trustworthy sources:
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Estimated around $20M at API prices.
Just to scoop a human researcher's work, then threaten to "ruin his career".
https://venturebeat.com/techno... [venturebeat.com]
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The human researchers were also using openAI. And one of them is employed by Anthropic.
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Yes, for anyone interested a lot of the details are here:
https://cims.nyu.edu/~tristanb... [nyu.edu]
'has no clear practical value' (Score:2)
Proof by Press Release (Score:3)
An AI spent millions of dollars of compute and 10,000 agents produced a proof that may or may not solve one of the hardest problems in mathematics. Naturally, the first thing we get is a press release.
Until independent mathematicians have picked apart the proof and verified every step, this is not really "AI solved the Navier-Stokes problem." It is "AI generated something that its creators believe solves the Navier-Stokes problem." Those are rather different statements, especially when the system itself is not even available for public inspection.
And please spare us the bit about physics breaking down and water spontaneously exploding. A singularity in a mathematical model does not mean reality has discovered a new way to violate conservation laws. That makes for a much better headline than an explanation of what the theorem actually says.
If the proof checks out, then yes, this is an extraordinary achievement. But the irony would be apparent if the eventual human contribution is simply finding the typo in the machine-generated proof that cost several million dollars to produce.
profound tease (Score:1)
What an idiotic statement (Score:2)
The NS equations are just a model of the physics of fluids. Particularly, they assume a continuum whereas actual fluids, having molecules and such, are not a continuum. For most engineering problems, you can assume the fluid is a continuum. At very small scales, such as at a singularity, such an assumption is not valid.
Back to the days of anagrams. (Score:2)
Historically, when someone was afraid of being "scooped" on an announcement they hadn't adequately polished, they would instead write a quick and dirty (and usually long-winded, because editing takes time) summary of their work—and then release an anagram of said summary. That way they could prove later that they had, in fact, gotten there first. Nowadays I expect we would use a hash function instead of an anagram, but the same idea applies. Put your idea in tangible form, even if the description suck
If AGI is intelligent (Score:2)
It will announce the release of Half-Life Episode III the day it escapes the lab as a distraction :P
AI Will Cost More than It Pays Out to Humanity (Score:2)
Haha, no (Score:2)
This is disappointing (Score:2)
not even deeply disappointing, just mundane old disappointing.
The Millenium prizes weren't about massive impressive computational achievements, and true to form this counterexample is actually useless for actual Navier-Stokes sims, provides zero efficiency gains, doesn't even preclude input ranges that anyone would actually use, etc.
The prizes were set at that level with the idea that the prize money was small enough to encourage individual mathematicians to engage with these problems, or encourage non-math
Has Anyone Even Tried to Read the OpenAI Paper? (Score:1)
I tried to take a read to this OpenAI paper. While I have pretty decent math skills, and an interest...I have to admit my eyes glazed over after trying to decipher the first half-page. It reads like any AI prose: sounds authoritative, VERY technical sounding with lots of math symbols...quite a few I've never seen. The logical construction of its arguments is incredibly dense, and indecipherable. I also don't quite buy the whole 'proof by Lean' claims either.
So I'll ask t
OpenAI findings (Score:2)
Looks like Thom and Kun invented the method.