OpenAI Says It Has Cracked One of Math's 'Millennium Problems' (nytimes.com)
- Reference: 0185540200
- News link: https://science.slashdot.org/story/26/09/08/2228220/openai-says-it-has-cracked-one-of-maths-millennium-problems
- Source link: https://www.nytimes.com/2026/09/08/science/openai-proof-millennium-problem.html
> OpenAI [1]said on Tuesday that its newest artificial intelligence technology had [2]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.
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> 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.
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> 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.
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> 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. [3]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 [4]released a paper (PDF) and formal Lean proof.
[1] https://openai.com/index/navier-stokes-solution/
[2] https://www.nytimes.com/2026/09/08/science/openai-proof-millennium-problem.html
[3] https://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_existence_and_smoothness
[4] https://cdn.openai.com/pdf/32d9f210-8b73-45e0-91bc-82a30aef8a9a/navier-stokes.pdf
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.
[1]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.
[1] https://techcrunch.com/2026/09/08/openai-fought-dirty-on-career-making-math-problem-says-nyu-mathematician/
Re: (Score:2)
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: (Score:2)
> (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.
The Proof is Stolen (Score:5, Insightful)
Someone in the company [1]more or less admitted it was stolen from the original authors by trying to bully the actual authors into accepting 'partial credit'" [engadget.com]. It's unshocking to hear OpenAI will steal anything and everything you throw into and then claim that stolen property as its own publicly, but more or less just admitting that publicly in such a high profile case while trying to file an IPO claiming anyone anywhere at anytime should pay OpenAI with literally anything even close to valuable is a next level stunt.
[1] https://www.engadget.com/2253393/whats-going-on-with-openai-and-the-navier-stokes-controversy
Cracking a few eggs (Score:2)
You can't make an omelet without boiling a few oceans.
One MILLION dollars? (Score:2)
I hope the prize covers the electricity and hardware costs.
Re: (Score:2)
That will be small, compared to the reputation cost for OpenAI. One sleazy company.
NS no value? (Score:2)
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: (Score:3)
The Navier-Stokes problem is not the same as the Navier-Stokes equations. The equations have uses. The problem is a question about the equations, but apparently, there's no practical benefit to knowing the answer.
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.
Re: (Score:2)
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
The statement from the researcher to cries foul (Score:3)
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: (Score:2)
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?
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.
Well that wasn't on my bingo card for 2026 ... (Score:2)
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 ter
Not to be confused with Millennial problems (Score:2)
Like "What happened to my metabolism and why does my back hurt all the time?"