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- Hacker News
- The two-year publication rule is the interesting part. OpenAI doesn't need the million, and the community will judge the result regardless of whether Clay ever accepts it.by Marchant_hq
- The result was never the point.
Clearly the real-world cannot "blow-up" - real-world water vortices do not reach infinite velocity, etc.
The point of having Navier-Stokes as a Millennium prize was to hopefully generate new mathematics and techniques along the way, and auto-generating a sprawling AI-slop proof or millions of lines of Lean does not accomplish that result.
Clearly OpenAI has no interest in the math itself - to them this was just a trophy animal to shoot and stuff. I would be very surprised if they now helped analyze the proof and try to extract the mathematical value out of it, and this would obviously require outside help who are probably not inclined to help OpenAI math-wash their behavior.
- Clay will award the prize (or choose to not award it) when there is an expert consensus that the problem has been solved and the solution is correct. The rules merely state what that would mean in some typical cases. There is always an option that Clay changes the rules to match the reality better.by jltsiren
- What I'm not seeing reported on much is if the result reveals any new techniques or ideas that advance mathematics - which is what we usually hear is the reason to work on these problems. Or does the resolution of NS just add a fact to the list without any new understanding.by stbede
- My understanding is that it’s proof by counterexample, so the main thing to study would be the implications of the counterexample. The technique used to find it sounds like a lot of brute force. But I’m not a mathematician, and maybe the AI used some clever techniques to narrow in on it.by zeroimpl
- I am utterly fascinated by the amount of comments here from engineers that clearly have zero experience with mathematics making utter fool of themselves by claiming to know better than mathematicians what their jargon is/means, how publishing works/should work, etc…
I try not to go down the route of “hn was better before!” but… jeez, do better, people. What happened to this community, there used to be some effort to not be bottom-barrel like this.
by scrollaway - Gell-Mann Amnesia HN version?
- What did you expect? Degree of BS increases together with the population.by aaa_aaa
- It's worth mentioning that OpenAI will not be eligible for the Millennium Prize for quite a while. Per the rules listed https://www.claymath.org/wp-content/uploads/2022/03/millenni... , Clay Mathematics Institute have some requirements to make this process deliberately slow.
1) The solution must be published in a qualifying outlet, i.e. a peer-reviewed math journal. Publishing on your own website (which is what OpenAI did) or posting arXiv does not count.
2) At least two full years must pass after publication in a qualifying journal, before CMI will even consider evaluating it. The intent is to give the maths community time to scrutinize the solution.
Realistically, they'll be eligible for a prize ~2.5 years from now, or around 2029.
by tristanj - It's possible that Clay Mathematics Institute will not award the prize at all. The spirit of the rules seems to be that the result can be attributed clearly to one or more individual mathematicians. If the attribution remains unclear (maybe because the main contributions were made by AI), the rules include an option for not awarding the prize at all.by jltsiren
- Who cares about the prize and the outdated methods?
OpenAI and Anthropic might have 3 millennium problems by December
by vatsachak - > The ultimate decision as to whether a publication qualifies as a “Qualifying Outlet” shall reside in the sole and unfettered discretion of CMI. CMI may, in its discretion, relax or remove one or more of the conditions listed in Section 6(e) above if it has received advice from experts in the field of the Problem, chosen by CMI, that a published solution is likely to be correct.
Looks like even a blog post is good enough, they just need to do the review by themselves.
by tancop - > or posting arXiv does not count
The Poincaré conjecture guy also broke that rule. They wanted to give him the prize anyway but he refused. OpenAI announced they would also not claim the prize.
Looks like no one wants this prize lol
by ngruhn - OpenAI has stated that they will not claim the prize. https://openai.com/index/navier-stokes-solution/
While the scandal is still unraveling, it seems that OpenAI did a rush job to steal other mathematicians' thunder and finish the proof first.
OpenAI released a statement that their work does not relate to the work of the other team, but it clearly does. They use the same niche smooth-forcing mechanism. Altman and Bubeck claim that because the proof used different scaling parameters and analytical steps, it's not related, but it seems that nobody else agrees. Oh, and OpenAI's Bubeck tried to threaten Buckmaster (mathematician working on the proof).
This brings nothing but shame for OpenAI.
by u1hcw9nx - Recent and related. Others?
OpenAI’s Navier-Stokes release included a Lean 4 formal proof - https://news.ycombinator.com/item?id=49650326 - Sept 2026 (179 comments)
More questions about whether researchers can trust OpenAI with unpublished math - https://news.ycombinator.com/item?id=49639408 - Sept 2026 (813 comments)
The Navier–Stokes Millennium Prize Problem - https://news.ycombinator.com/item?id=49621697 - Sept 2026 (237 comments)
Tao: Open math problems being non-renewably mined by AI - https://news.ycombinator.com/item?id=49616968 - Sept 2026 (420 comments)
On the Navier–Stokes Millennium Prize Problem - https://news.ycombinator.com/item?id=49613262 - Sept 2026 (1134 comments)
Navier-Stokes – Tristan Buckmaster [pdf] - https://news.ycombinator.com/item?id=49605915 - Sept 2026 (827 comments)
by dang - In my opinion, I think the Clay Mathematics Institute deserves some criticism for all the drama surrounding these problems. Mathematicians know that you can make problems arbitrarily complex, and declaring problems with large prizes attached to them can lead to a lot of competition and drama. I feel that mathematics should be free from competitions and the pursuit of glory.
However, after reading the open letter signed by 25 Fields Medalists, I became quite concerned. It feels like the mathematical world is changing very rapidly, almost overnight.
I used to think that before AI, you could spend your entire lifetime working on some of the hardest problems in mathematics. If you were an introvert or someone who enjoyed solitude, all you really needed was a pencil, some paper, and an eraser. You could spend years thinking about a problem, and if you were lucky enough to make a breakthrough, it would be your own journey.
Now AI is changing that. I wonder what this means for the kind of mathematics that people have traditionally done.
Mathematics has given us so many stories of lonely geniuses and their passions, people like Andrew Wiles, Grigori Perelman, and Yitang Zhang. Their stories are interesting because they show how deeply personal mathematics can be. They spent years working on problems because they were genuinely interested in them.
I am worried that we might slowly lose some of that side of mathematics as AI becomes more powerful. I do not think change is necessarily bad, but I think it is worth thinking about what mathematics should be in the future and whether it can still remain a deeply personal pursuit of curiosity and understanding.
- > It feels like the mathematical world is changing very rapidly, almost overnight.
...
>Now AI is changing that. I wonder what this means for the kind of mathematics that people have traditionally done.
Mathematics becomes engineering. I think it is great and long overdue. Saying that as a Math PhD dropout :) Of course like manual craftsmen had to adapt to Industrial Revolution, the same would need to be done by the mathematicians. And other scientists too.
by trhway - > Mathematicians know that you can make problems arbitrarily complex, and declaring problems with large prizes attached to them can lead to a lot of competition and drama.
Yes, you can make problems arbitrarily complex. But the prize problems were chosen not just because the solutions appear likely to be very complex (the problem statements aren't necessarily inherently complex--there is a way to restate the Riemann hypothesis that a junior high school student could easily understand, which I'll give below).
They were chosen because they were important problems that mathematicians really wanted solved, top people had worked on them for a long time and progress stalled a long time ago, and it seemed likely that solving them would require major breakthroughs.
Those kind of problems can be discouraging. Enough people who are probably better than you have spent enough time failing to solve them that realistically most researchers are going to focus all their efforts on something they are likely to make progress on.
A nice prize can get more people to at least work on them as side projects.
Here's that restatement of the Riemann hypothesis I mentioned.
The Riemann hypothesis is that the non-trivial zeros of the function ζ(s) occur on the line 1/2 + yi.
ζ(s) is 1/1^s + 1/2^2 + 1/3^s + ... when s is a complex number whose real part is greater than 1, and defined everywhere else except s = 1 by a process called analytic continuation. The trivial zeros are at s = -2, -4, -6, ... .
For a mathematician, or a non-mathematician who has taken complex analysis and hasn't forgotten much of that, that is not too complex a definition. For anyone else the first reaction is probably "Trivial zeros? How the heck does that thing even have zeros? And if it does how the heck can it have zeros at any negative integers! It is obviously infinity at every negative integer!!!".
Here's a different hypothesis that turns out to be exactly equivalent to the Riemann hypothesis. They are either both true of both false, so resolving one of them resolves the other.
Let H(n) = 1 + 1/2 + ... + 1/n for all positive integers n. These are called the harmonic numbers.
Let S(n) = the sum of the positive integer factors of n for all positive integers n. For example S(4) = 1 + 2 + 4, S(6) = 1 + 2 + 3 + 6, and S(17) = 1 + 17.
Hypothesis: S(n) <= H(n) + exp(H(n)) log(H(n)) with equality only when n = 1.
The proof that this is equivalent to the Riemann hypothesis is here [1].
by tzs - I agree. Technological advances can lead to a better world for sure, but I think many people underestimate the human need to create and to find meaning in their work.
If AI can do superhuman math that allows better medicines, cleaner energy etc that is great. But if AI replaces humans in all the creative and intellectual fields that is not only a loss of jobs but also a loss of deeply meaningful activities. This is waved away but I think that is mistaken.
What I fear is really the growing notion that "people shouldn't do math/art/music because machine do it better and cheaper".
by kaffekaka - It's not a large prize though.
OpenAI spent many multiples of the prize money in just a few days to get there and even if one solves a problem in the traditional way, that person is most likely already an accomplished professor at a reputable university where a million dollars doesn't mean as much as the eternal fame that comes with it.
by KeplerBoy - I feel like this is answered in the very second paragraph?
> to elevate in the consciousness of the general public the fact that in mathematics the frontier is open, close at hand, and abounds with important unsolved problems; to emphasize the abiding value of working towards a solution of the deepest, most difficult problems; and to recognize achievements in mathematics of historic magnitude.
Also
> These are not arbitrary puzzles akin to fiendish crosswords. Rather, they are fundamental challenges that mark the frontier of human knowledge and challenge us to develop new structures and methods. They provide foci for the continuing struggle, across generations and cultures, to deepen our human understanding of mathematics and the universe that it describes.
by butterNaN - > In my opinion, I think the Clay Mathematics Institute deserves some criticism for all the drama surrounding these problems. Mathematicians know that you can make problems arbitrarily complex, and declaring problems with large prizes attached to them can lead to a lot of competition and drama. I feel that mathematics should be free from competitions and the pursuit of glory.
Currently 0/2 Millenium problem solvers claimed the prize money so clearly money is not their motivation for tackling the problem.
by drexlspivey - Yes, mathematics has been perhaps the purest human intellectual pursuit. Sure, many theorems turn out to have important applications in science and engineering, but the mathematical community has mostly escaped corporate interests. And for the reasons you mentioned about not needing any resources except your brain, it has been a uniquely human activity which showed us talent can come from anywhere, with stories like Ramanujan and Galois.
I hope that pure mathematics research can retain a strongly human component forever. It would sadden me immensely for human understanding of our mathematical world to wither and die, and for us to become ignorant consumers of wonders beyond our understanding just because our robots can do it better than we can. As far as applied research goes, I hope we will always be able to understand what we want to, but I have less qualms about becoming more scalable and efficient.
- Proving things without comprehending them is a threat to intellectual work.by andsoitis
- No, it is not. Proving things without comprehending them built much of human civilization. Comprehension is a relatively new fad that came along in the 17th century with the scientific method.by Stevvo
- Why is it a threat and not an opportunity? Imagine if in ancient times there was their Oracle that could produce mathematical proofs of any question you asked it, would you burn it or try to understand how it works and use it to ask questions you are stuck on?by alain94040
- >without comprehending
Very on brand with using AI for everything.
by aeve890 - Outside of mathematics, I think it’s very rare for a single human to understand 100% of any complex undertaking, and this was true long before AI.by danenania
- Proving pharmaceutical drugs work on mental health issues has tremendous value even though we don't always (or often) understand the exact mechanisms in brain chemistry as to why it worksby 93po
- No-one cares anymore, OpenAI does not care about the prize either or whatever the Clay institute has to say for that matter. It's about attention, capital and compute. If you can use the result to increase shareholder or company value, that is what matters.by augment_me