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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/uplo

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/millennium_prize_rules_0.pdf 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.

ngruhn 22d ago
> 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
- tristanj 22d ago
  You might be right. At this rate, if AI solves the remaining five problems, we're heading towards a hilarious situation where all the Millennium Problems are solved, but nobody wants to claim the prize money.
  - jtpmath 22d ago
    I did and was intending to claim the prize, that is why I worked with GPT-4 and GPT-5 to program the algorithms that lead to the breakthrough. You think NS is a surprise? Wait until you see that my NS counterexample was based on my RH disproof.
  - seanhunter 22d ago
    That’s a big if. In the maths community, there has been a feeling that Navier-Stokes was close to being solved for a while now. I don’t know of anyone credible who feels that way about the Riemann hypothesis. Here’s what Terrence Tao had to say about it https://youtu.be/vuT-2_e4NHg https://youtu.be/vuT-2_e4NHg Edit to add: The fun part about the RH since people mentioned lean in a sibling thread is that in lean’s mathlib4 there is verified statement of the Riemann Hypothesis with a comment that says something like “instantiating an object of this type will lead to a prize of a million dollars”
    - famouswaffles 22d ago
      It's really not that big. Yeah Navier-Stokes was easier than Riemann but that's not really the issue. AI has and will improve at a much greater rate than human mathematicians. So it's really a question of if AI gets good enough to tackle it before any human does. It doesn't look like humans will be solving it anytime soon but where will AI be in 2 years ? Hell, it looks like at least one other result will be announced soon too.
      - xanderlewis 22d ago
        Has and will. Are you going to back that assertion up at all, or just repeat it like that other viral thought-terminating cliche: ‘this is the worst the models will ever be’?
        famouswaffles 22d ago
        Yes. This is the worst the models will ever be. Perhaps you should start paying attention to that now.
        fragmede 22d ago
        No it isn't. Best and worst and ill-defined anyway but the chess ELO score of various LLMs has fluctuated up and down, it's not been montonically increasing. What is the best answer to "how do I make cocaine"? The models are getting larger, with more compute and RAM backing them, but that doesn't automatically make them better if you don't define how you're measuring better-ness.
        famouswaffles 22d ago
        None of the frontier labs care about Chess as it's already a solved problem. If they did, the models would be much better. It's really not that hard. Google has a paper on grandmaster level chess without search from transformers. Better obviously means better, like how they became better than they were 6 months and a year ago.
  - fc417fc802 22d ago
    TBF a company the size of openai claiming a prize of this sort would be a pretty bad look. If they did accept it I expect they would inevitably redirect it to charity for PR reasons. I'm surprised perelman turned it down though. Seems straightforward enough to offer half of it to the other guy if you feel strongly about it.
- ncruces 22d ago
  Perelman posted to arXiv in 2002/3. The prize was offered to him in 2010, after multiple others had digested his work and published elsewhere.
  - kzrdude 22d ago
    But if I remember correctly, he gained recognition for his achievement rather quickly after posting.
tancop 22d ago
> 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.
- noodletheworld 22d ago
  My opinion is that it is pretty clear that they’re not going to do that. > The rules governing the prizes describe the process for evaluating what has been achieved and for assigning credit. The process is deliberately unhurried, but we will provide updates. I think “you don’t get anything straight away for rushing your AI into the maths problems, not even credit” aligns pretty fairly with what the fields medalists are concerned with.
- tristanj 22d ago
  Interesting. It seems this carve-out was added when they rewrote the rules in 2018. In the original rules [0], it says: Before consideration, a proposed solution must be published in a refereed mathematics journal of world-wide repute, and it must also have general acceptance in the mathematics community two years after that publication. Following this two-year waiting period, the [Clay Mathematics Institute] will decide whether a solution merits detailed consideration. There's no option for CMI discretion. They probably rewrote the rules to avoid another Poincaré conjecture situation, where the paper was only published on arXiv and not in a mathematics journal. [0] https://web.archive.org/web/20000622023328/http://www.claymath.org/prize_problems/rules.htm https://web.archive.org/web/20000622023328/http://www.clayma...
vatsachak 22d ago
Who cares about the prize and the outdated methods? OpenAI and Anthropic might have 3 millennium problems by December
- crowfunder 22d ago
  https://xkcd.com/605/ https://xkcd.com/605/
  - tristanj 22d ago
    Relevant, but it's already rumored that OpenAI and Anthropic have made very significant progress on two more Millennium Prize problems. They're in a race to solve the next problem. OpenAI needs to solve another to shut down the (baseless) plagiarism allegations. Anthropic wants blood because OpenAI sniped the last one from one of Anthropic's researchers. It's a matter of pride for both companies. More results will come out soon.
    - HarHarVeryFunny 22d ago
      Given that the math community (incl. those 25 Fields medalists) has come out strongly against this trophy hunting of their unsolved problems, to the detriment of mathematics, I don't think these companies are going to be getting positive press if they ignore this plea and continue with this, nor is this going to help turn public sentiment pro-AI. Presumably the people that OpenAI and Anthropic are trying to impress with these trophy kills are potential IPO investors, but I would have thought investors would also be concerned about the growing public backlash against AI.
      - famouswaffles 22d ago
        They aren't going to sit on millenium solutions regardless (so if Hodge and /or BSD is really done it will get announced especially because of the baseless accusations), and they aren't going to stop trying to solve P/NP and Riemann. The letter doesn't really matter. It's not the first time, and I don't think AI's dramatic ramp in capabilities ever had positive reception from the bulk of mathematicians anyway.
u1hcw9nx 22d ago
OpenAI has stated that they will not claim the prize. https://openai.com/index/navier-stokes-solution/ 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.
- tristanj 22d ago
  1) OpenAI and Buckmaster did not solve the same problem. Per https://x.com/IlinVasily29521/status/2097554700321329393 https://x.com/IlinVasily29521/status/2097554700321329393 , here is a breakdown of who solved what. Tristan + Levent: 3D incompressible Euler with forcing OpenAI: 3D incompressible Euler without forcing OpenAI: Navier-Stokes with forcing No one: Navier-Stokes without forcing Euler equations = Navier-Stokes without viscosity. Forcing means external force. Absence of viscosity and presence of external force make blowup easier to construct. Tristan+Levent ticked the weakest case, OpenAI ticked the two next weakest, then the final case is unsolved. Only the last two are eligible for the Millennium Prize. The Navier-Stokes general case remains unsolved. Navier-Stokes has an extra viscosity term compared to Euler, which makes the problem noticeably harder to find a blowup. They are not the same problem. 2) The approach both chose to use (by Luis and Diego) was published in 2023 and is included in every frontier model's training dataset. An AI model could independently choose the same route as Luis and Diego, without access to Buckmaster's work. 3) You mischaracterized OpenAI's statement. They issued a blanket denial on using Buckmaster's Codex data from after July 3. "We can say categorically that it is impossible for Dr. Buckmaster’s Codex prompts over the last two months to have influenced the system in any way, including training. After investigating, we can say with full confidence that no user inputs past July 3rd could have influenced this system in any way.” July 3 was the training cutoff date for the model that solved Navier-Stokes. No user data after that date influenced the model. 4) Buckmaster and Alpöge found their blow-up for 3D incompressible Euler with forcing on August 15 https://cims.nyu.edu/~tristanb/statement.pdf https://cims.nyu.edu/~tristanb/statement.pdf , over a month after the model training cutoff point. They stated they did not have real progress prior to this point.
jltsiren 22d ago
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.
- glimshe 22d ago
  Wouldn't the proof be attributed to the people who operated the AI? After all, it took more than writing a "prove the navier Stokes Clay problem" prompt.
  - holowoodman 22d ago
    > After all, it took more than writing a "prove the navier Stokes Clay problem" prompt. Yes, but it took far less than using your meat brain to prove the Navier-Stokes Clay problem.
    - glimshe 22d ago
      It will be tough to draw the line, as the meat brains trying to prove it were also using AI. I assume that the mathematicians outside Anthropic were hoping to publish an actual human-understandable paper. That could be one way to draw line: you can use AI, but you must also have an intelligible explanation at the end.

ngruhn 22d ago

> 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

tristanj 22d ago
You might be right. At this rate, if AI solves the remaining five problems, we're heading towards a hilarious situation where all the Millennium Problems are solved, but nobody wants to claim the prize money.
- jtpmath 22d ago
  I did and was intending to claim the prize, that is why I worked with GPT-4 and GPT-5 to program the algorithms that lead to the breakthrough. You think NS is a surprise? Wait until you see that my NS counterexample was based on my RH disproof.
- seanhunter 22d ago
  That’s a big if. In the maths community, there has been a feeling that Navier-Stokes was close to being solved for a while now. I don’t know of anyone credible who feels that way about the Riemann hypothesis. Here’s what Terrence Tao had to say about it https://youtu.be/vuT-2_e4NHg https://youtu.be/vuT-2_e4NHg Edit to add: The fun part about the RH since people mentioned lean in a sibling thread is that in lean’s mathlib4 there is verified statement of the Riemann Hypothesis with a comment that says something like “instantiating an object of this type will lead to a prize of a million dollars”
  - famouswaffles 22d ago
    It's really not that big. Yeah Navier-Stokes was easier than Riemann but that's not really the issue. AI has and will improve at a much greater rate than human mathematicians. So it's really a question of if AI gets good enough to tackle it before any human does. It doesn't look like humans will be solving it anytime soon but where will AI be in 2 years ? Hell, it looks like at least one other result will be announced soon too.
    - xanderlewis 22d ago
      Has and will. Are you going to back that assertion up at all, or just repeat it like that other viral thought-terminating cliche: ‘this is the worst the models will ever be’?
      - famouswaffles 22d ago
        Yes. This is the worst the models will ever be. Perhaps you should start paying attention to that now.
        fragmede 22d ago
        No it isn't. Best and worst and ill-defined anyway but the chess ELO score of various LLMs has fluctuated up and down, it's not been montonically increasing. What is the best answer to "how do I make cocaine"? The models are getting larger, with more compute and RAM backing them, but that doesn't automatically make them better if you don't define how you're measuring better-ness.
        famouswaffles 22d ago
        None of the frontier labs care about Chess as it's already a solved problem. If they did, the models would be much better. It's really not that hard. Google has a paper on grandmaster level chess without search from transformers. Better obviously means better, like how they became better than they were 6 months and a year ago.
- fc417fc802 22d ago
  TBF a company the size of openai claiming a prize of this sort would be a pretty bad look. If they did accept it I expect they would inevitably redirect it to charity for PR reasons. I'm surprised perelman turned it down though. Seems straightforward enough to offer half of it to the other guy if you feel strongly about it.
ncruces 22d ago
Perelman posted to arXiv in 2002/3. The prize was offered to him in 2010, after multiple others had digested his work and published elsewhere.
- kzrdude 22d ago
  But if I remember correctly, he gained recognition for his achievement rather quickly after posting.

tancop 22d ago

> 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.

noodletheworld 22d ago
My opinion is that it is pretty clear that they’re not going to do that. > The rules governing the prizes describe the process for evaluating what has been achieved and for assigning credit. The process is deliberately unhurried, but we will provide updates. I think “you don’t get anything straight away for rushing your AI into the maths problems, not even credit” aligns pretty fairly with what the fields medalists are concerned with.
tristanj 22d ago
Interesting. It seems this carve-out was added when they rewrote the rules in 2018. In the original rules [0], it says: Before consideration, a proposed solution must be published in a refereed mathematics journal of world-wide repute, and it must also have general acceptance in the mathematics community two years after that publication. Following this two-year waiting period, the [Clay Mathematics Institute] will decide whether a solution merits detailed consideration. There's no option for CMI discretion. They probably rewrote the rules to avoid another Poincaré conjecture situation, where the paper was only published on arXiv and not in a mathematics journal. [0] https://web.archive.org/web/20000622023328/http://www.claymath.org/prize_problems/rules.htm https://web.archive.org/web/20000622023328/http://www.clayma...

vatsachak 22d ago

Who cares about the prize and the outdated methods? OpenAI and Anthropic might have 3 millennium problems by December

crowfunder 22d ago
https://xkcd.com/605/ https://xkcd.com/605/
- tristanj 22d ago
  Relevant, but it's already rumored that OpenAI and Anthropic have made very significant progress on two more Millennium Prize problems. They're in a race to solve the next problem. OpenAI needs to solve another to shut down the (baseless) plagiarism allegations. Anthropic wants blood because OpenAI sniped the last one from one of Anthropic's researchers. It's a matter of pride for both companies. More results will come out soon.
  - HarHarVeryFunny 22d ago
    Given that the math community (incl. those 25 Fields medalists) has come out strongly against this trophy hunting of their unsolved problems, to the detriment of mathematics, I don't think these companies are going to be getting positive press if they ignore this plea and continue with this, nor is this going to help turn public sentiment pro-AI. Presumably the people that OpenAI and Anthropic are trying to impress with these trophy kills are potential IPO investors, but I would have thought investors would also be concerned about the growing public backlash against AI.
    - famouswaffles 22d ago
      They aren't going to sit on millenium solutions regardless (so if Hodge and /or BSD is really done it will get announced especially because of the baseless accusations), and they aren't going to stop trying to solve P/NP and Riemann. The letter doesn't really matter. It's not the first time, and I don't think AI's dramatic ramp in capabilities ever had positive reception from the bulk of mathematicians anyway.

u1hcw9nx 22d ago

OpenAI has stated that they will not claim the prize. https://openai.com/index/navier-stokes-solution/ 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.

tristanj 22d ago
1) OpenAI and Buckmaster did not solve the same problem. Per https://x.com/IlinVasily29521/status/2097554700321329393 https://x.com/IlinVasily29521/status/2097554700321329393 , here is a breakdown of who solved what. Tristan + Levent: 3D incompressible Euler with forcing OpenAI: 3D incompressible Euler without forcing OpenAI: Navier-Stokes with forcing No one: Navier-Stokes without forcing Euler equations = Navier-Stokes without viscosity. Forcing means external force. Absence of viscosity and presence of external force make blowup easier to construct. Tristan+Levent ticked the weakest case, OpenAI ticked the two next weakest, then the final case is unsolved. Only the last two are eligible for the Millennium Prize. The Navier-Stokes general case remains unsolved. Navier-Stokes has an extra viscosity term compared to Euler, which makes the problem noticeably harder to find a blowup. They are not the same problem. 2) The approach both chose to use (by Luis and Diego) was published in 2023 and is included in every frontier model's training dataset. An AI model could independently choose the same route as Luis and Diego, without access to Buckmaster's work. 3) You mischaracterized OpenAI's statement. They issued a blanket denial on using Buckmaster's Codex data from after July 3. "We can say categorically that it is impossible for Dr. Buckmaster’s Codex prompts over the last two months to have influenced the system in any way, including training. After investigating, we can say with full confidence that no user inputs past July 3rd could have influenced this system in any way.” July 3 was the training cutoff date for the model that solved Navier-Stokes. No user data after that date influenced the model. 4) Buckmaster and Alpöge found their blow-up for 3D incompressible Euler with forcing on August 15 https://cims.nyu.edu/~tristanb/statement.pdf https://cims.nyu.edu/~tristanb/statement.pdf , over a month after the model training cutoff point. They stated they did not have real progress prior to this point.

jltsiren 22d ago

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.

glimshe 22d ago
Wouldn't the proof be attributed to the people who operated the AI? After all, it took more than writing a "prove the navier Stokes Clay problem" prompt.
- holowoodman 22d ago
  > After all, it took more than writing a "prove the navier Stokes Clay problem" prompt. Yes, but it took far less than using your meat brain to prove the Navier-Stokes Clay problem.
  - glimshe 22d ago
    It will be tough to draw the line, as the meat brains trying to prove it were also using AI. I assume that the mathematicians outside Anthropic were hoping to publish an actual human-understandable paper. That could be one way to draw line: you can use AI, but you must also have an intelligible explanation at the end.