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The statement is not about AI but about the behaviour of AI companies. OpenAI have put vast resource into solving open maths problems: many millions of dollars

The statement is not about AI but about the behaviour of AI companies. OpenAI have put vast resource into solving open maths problems: many millions of dollars of compute just on the Navier-Stokes result, plus whatever they spent on the broader Millenium Prize problems initiative and the other results they have published. Anthropic are doing the same. The statement is asking them to stop doing this. AI companies are investing these resources primarily as a marketing exercise. There is no near term commercial value to a 100 page Lean proof of blow up in an extreme special case of Navier Stokes, besides the bragging rights. As the statement says any commercial value in this stuff comes a very long time later after new insights and techniques have been digested, integrated into the mathematical canon, expressed in ways that don't take a lifetime of study to understand, etc. (things that AI is not yet capable of doing itself). The bragging rights, on the other hand, are massively valuable. There is a mystique to maths that makes "our AI solved a Millenium Prize problem" an irresistable headline for a company like OpenAI. What the mathematicians are saying is stop pouring resources that most mathematicians can only dream of accessing into projects that are actively damaging to their field. They face a massive challenge of figuring out how maths can evolve in the face of this new technology, and this is not helping.

dominotw 15d ago
yeah beacuse no one trust any of their benchmark results now they are scrambling to find a signal thats undeniable
- pfdietz 15d ago
  I expected this. They prove a millenium result, but it doesn't count because they are bad people. It's this sort of thing that motivates people to burn down the institution you might be trying to defend.
  - magicalist 15d ago
    > It's this sort of thing that motivates people to burn down the institution you might be trying to defend. lol, yes, this sort of thing is what many people who voted for Trump were saying, and things are going great for them. > They prove a millenium result, but it doesn't count because they are bad people. OpenAI has only themselves to blame for this, and they know it. They could have handled this so much better. I'd bet there's more meeting time right now going into how to unveil future math results than on meeting about the actual math research.
mosura 15d ago
> What the mathematicians are saying is stop pouring resources that most mathematicians can only dream of accessing into projects that are actively damaging to their field. They face a massive challenge of figuring out how maths can evolve in the face of this new technology, and this is not helping. Is it reasonable for any field to make such demands? If this were doctors objecting to AI becoming good at medical practice would you have the same concerns? While any idea of OpenAI spying on people to pursue their goals is disgusting, the rest of this is par for the course, as Kasparov experienced with IBM in the 90s. Humans still play chess after all.
- drivebyhooting 15d ago
  Chess is even more mainstream and accessible now!
- omnicognate 15d ago
  It's not a simple matter of "becoming good at", and yes, I could very well have similar concerns, depending on how it impacts the field. The statement itself mentions that such concerns exist in many other fields. I doubt OpenAI will take such a combative stance and accuse these mathematicians of "demanding" things, as you do. As I said, the purpose of this is marketing and the statement simultaneously undermines the value of that marketing (showing these projects as irresponsible) and gives these companies an even better piece of marketing in its place: "our AI got so good at maths the mathematicians begged us to stop". It's entirely possible they will stop pouring millions into these projects.
  - mosura 15d ago
    So let’s say OpenAI cure cancer and put every cancer researcher out of work depriving them of intellectual satisfaction, this would also be a problem? It would certainly impact the field. The fact is these fields are supported by society because of the benefits to everyone else. Once the same results can be achieved in a cheaper and faster way that is what will be done. We should mourn this in the same way we do buggy whip manufacturers. Again people still ride horses.
sobellian 15d ago
That solution (stop pouring resources in to proofs, stay in your lane) works today. How does it work 5, 10, 20 years from now? The software and hardware advances will continue.
causalmodels 15d ago
What do we do about the problems that don't require many millions of dollars in resources? Last weekend I spun up a small agent swarm and pointed it at a field of math I have some affinity towards. Within four hours I had settled three conjectures, one of which is rather famous (for the field, not in general). It cost me about four hundred dollars. I am at a loss about what to do with these results. On one hand I feel like the mathematicians working on these should know about them, but on the other I feel a bit like a barbarian who suddenly finds themselves sacking Rome.
- lasersox 15d ago
  How do you know the proofs are correct?
  - causalmodels 15d ago
    The numerical results are trivial to check. I wrote the analytical results in Lean by hand before asking a former professor to confirm after asking him to keep this private. They're valid.
    - ardme 15d ago
      It's really tough to come to terms with it but making academic contributions in general from the outside (with or without AI tbh) is not often welcome and the whole process feels very gate-kept.
      - FartyMcFarter 15d ago
        If that's the case, that makes me much less sympathetic, even though I can understand how it's very disturbing to see the field suddenly changing like this.
      - gammarator 14d ago
        (academic.) Unfortunately the overwhelming majority of outsiders are missing core knowledge (or are cranks), so the optimal prior from a time management perspective is to ignore them. AI just makes engaging more costly because there’s more volume and it’s harder to get signal on whether they know what they are talking about.
adastra22 15d ago
Humanity is better off for knowing these proofs. This strikes me as academic NIMBYism.
- Panoramix 15d ago
  Your point is largely addressed in the article, did you try reading it? "In many fields and activities, years of training have traditionally served not only to produce a final answer or product, but also to develop understanding and the ability to formulate new questions and ideas. However, building on a vast body of previous human work, AI systems are becoming increasingly capable of producing the results of such work directly, and these goals cease to align." The point is that these proofs are largely useless without the insights. The value of a proof is largely in the travel, not so much in the destination.
  - yieldcrv 15d ago
    Different person here, I read the article and they are all wrong. Hope that helps. Okay, to elaborate, substantively, their point is that the people using these AI models are not doing it for the love of the game, but for marketing. And instead of them - and nobody - spending millions of dollars to solve the problem, successfully, they want every problem of their academic industry to persist because even though they never solve the problem, they synthesize and solve lots of other problems nobody asked for. And get to boost their egos? Yeah, stop that. Actual alignment is on the humans themselves, if they want to remain relevant as academics and mathematicians, they need to learn how to replicate the proofs and the steps that alluded humans for decades and don't worry about the narcissistic elements that slow their industry down.
    - SpicyLemonZest 15d ago
      Their claim is only indirectly related to the motivations of the people using their models. What they're saying is that doing math in this way does not produce the same value as traditional mathematical research, and the people using these AI models aren't concerned about that because their marketing objectives don't depend on whether their results produce mathematical value. If people doing valuable work are made irrelevant by people doing a larger volume of non-valuable work, that's not a positive outcome.
deleted 15d ago
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mypalmike 15d ago
I suspect that beyond just marketing, these pursuits yield plenty of useful information about model design that will likely lead to model improvements and optimizations for both mathematics and general reasoning going forward.
soerxpso 15d ago
Are they claiming that the only value in solving these problems was for their field's personal development process? I thought Navier-Stokes (and some of the other millenium prize problems) actually had implications for useful technology. It would be insane to demand that people avoid making progress on technology that can save lives or improve general quality of life, just to protect the sanctity of your karate belt system. Perhaps in lieu of open problems left to solve, mathematicians should be welcome to take up chess or sudoku to keep their minds spry.
- Sharlin 15d ago
  No, there's most likely zero practical benefit of having found a pathological edge case in which the Navier-Stokes equations do not work. We're most assuredly not talking about "saving lives" here. Unless advanced aliens show up and tell us they'll destroy Earth unless a counterexample to the N-S equations is provided within 24 hours.
- SpicyLemonZest 15d ago
  > I thought Navier-Stokes (and some of the other millenium prize problems) actually had implications for useful technology. This is the core misunderstanding that the open letter is attempting to correct. Developing a better understanding of the Navier-Stokes equations could have a number of implications for useful technology. They're fundamental to fluid dynamics, and turbulence in particular is something that many people feel we could work with more effectively if we better understood how and why it's generated. The Navier-Stokes smoothness problem is an interesting and long-standing benchmark for this understanding; we don't know why it should be so hard to answer, so we hoped that the process of developing a proof to the problem would produce more understanding. (We may still be able to extract this understanding after the fact, if OpenAI's proof is fully human-comprehensible.) Simply knowing that there exists a finite-time blowup is not practically useful. We know that fluids in the real world don't produce random singularities, so the result can't really have much physical meaning. What it illustrates is that the Navier-Stokes equations fail to model physical fluids in some yet to be characterized way.
swid 15d ago
> There is no near term commercial value How much do you think other AI companies would offer to get access to the transcripts of the generation that led to the proof? No doubt OpenAI will include it in their training data somehow and use it to build the next generation. There is already economic value.
ralph84 15d ago
> primarily as a marketing exercise Like the mathematicians working on famous problems in private until they could claim full credit for something interesting wasn't also a marketing exercise for their own careers. The commercial value (or lack thereof) of a proof doesn't depend on whether it was done by a human or a machine.
- paulhebert 14d ago
  These mathematicians dedicated their life to math and were working for a long time to achieve the pinnacle of their careers. OpenAI just burned millions of dollars over a weekend after hearing that someone else was close to solving the problems. Their interest was in their AI system more than the actual math problems. Don’t you see how that’s different?
  - ralph84 14d ago
    I see how it can be devastating to their ego, but no, I don't see a particular difference in a company spending money for clout vs. a person spending time for clout. The underlying motivation is the same.
    - paulhebert 14d ago
      Do you really think people dedicate their life to mathematics for clout? If clout was the goal I don’t think becoming a lifelong mathematics academic would be the first step
      - pickleRick243 14d ago
        for many fairly strong mathematicians, the career calculus is fame and status (mild though it may be) through mathematics or anonymity but financial reward in tech or finance. Yes, clout by becoming a lifelong academic is in fact rational for some and part of their motivation. Of course they really like what they do as well, but earning the respect of the peers they know are also respected by a large swathe of society is very important.

dominotw 15d ago

yeah beacuse no one trust any of their benchmark results now they are scrambling to find a signal thats undeniable

pfdietz 15d ago
I expected this. They prove a millenium result, but it doesn't count because they are bad people. It's this sort of thing that motivates people to burn down the institution you might be trying to defend.
- magicalist 15d ago
  > It's this sort of thing that motivates people to burn down the institution you might be trying to defend. lol, yes, this sort of thing is what many people who voted for Trump were saying, and things are going great for them. > They prove a millenium result, but it doesn't count because they are bad people. OpenAI has only themselves to blame for this, and they know it. They could have handled this so much better. I'd bet there's more meeting time right now going into how to unveil future math results than on meeting about the actual math research.

mosura 15d ago

> What the mathematicians are saying is stop pouring resources that most mathematicians can only dream of accessing into projects that are actively damaging to their field. They face a massive challenge of figuring out how maths can evolve in the face of this new technology, and this is not helping. Is it reasonable for any field to make such demands? If this were doctors objecting to AI becoming good at medical practice would you have the same concerns? While any idea of OpenAI spying on people to pursue their goals is disgusting, the rest of this is par for the course, as Kasparov experienced with IBM in the 90s. Humans still play chess after all.

drivebyhooting 15d ago
Chess is even more mainstream and accessible now!
omnicognate 15d ago
It's not a simple matter of "becoming good at", and yes, I could very well have similar concerns, depending on how it impacts the field. The statement itself mentions that such concerns exist in many other fields. I doubt OpenAI will take such a combative stance and accuse these mathematicians of "demanding" things, as you do. As I said, the purpose of this is marketing and the statement simultaneously undermines the value of that marketing (showing these projects as irresponsible) and gives these companies an even better piece of marketing in its place: "our AI got so good at maths the mathematicians begged us to stop". It's entirely possible they will stop pouring millions into these projects.
- mosura 15d ago
  So let’s say OpenAI cure cancer and put every cancer researcher out of work depriving them of intellectual satisfaction, this would also be a problem? It would certainly impact the field. The fact is these fields are supported by society because of the benefits to everyone else. Once the same results can be achieved in a cheaper and faster way that is what will be done. We should mourn this in the same way we do buggy whip manufacturers. Again people still ride horses.

sobellian 15d ago

That solution (stop pouring resources in to proofs, stay in your lane) works today. How does it work 5, 10, 20 years from now? The software and hardware advances will continue.

causalmodels 15d ago

What do we do about the problems that don't require many millions of dollars in resources? Last weekend I spun up a small agent swarm and pointed it at a field of math I have some affinity towards. Within four hours I had settled three conjectures, one of which is rather famous (for the field, not in general). It cost me about four hundred dollars. I am at a loss about what to do with these results. On one hand I feel like the mathematicians working on these should know about them, but on the other I feel a bit like a barbarian who suddenly finds themselves sacking Rome.

lasersox 15d ago
How do you know the proofs are correct?
- causalmodels 15d ago
  The numerical results are trivial to check. I wrote the analytical results in Lean by hand before asking a former professor to confirm after asking him to keep this private. They're valid.
  - ardme 15d ago
    It's really tough to come to terms with it but making academic contributions in general from the outside (with or without AI tbh) is not often welcome and the whole process feels very gate-kept.
    - FartyMcFarter 15d ago
      If that's the case, that makes me much less sympathetic, even though I can understand how it's very disturbing to see the field suddenly changing like this.
    - gammarator 14d ago
      (academic.) Unfortunately the overwhelming majority of outsiders are missing core knowledge (or are cranks), so the optimal prior from a time management perspective is to ignore them. AI just makes engaging more costly because there’s more volume and it’s harder to get signal on whether they know what they are talking about.

adastra22 15d ago

Humanity is better off for knowing these proofs. This strikes me as academic NIMBYism.

Panoramix 15d ago
Your point is largely addressed in the article, did you try reading it? "In many fields and activities, years of training have traditionally served not only to produce a final answer or product, but also to develop understanding and the ability to formulate new questions and ideas. However, building on a vast body of previous human work, AI systems are becoming increasingly capable of producing the results of such work directly, and these goals cease to align." The point is that these proofs are largely useless without the insights. The value of a proof is largely in the travel, not so much in the destination.
- yieldcrv 15d ago
  Different person here, I read the article and they are all wrong. Hope that helps. Okay, to elaborate, substantively, their point is that the people using these AI models are not doing it for the love of the game, but for marketing. And instead of them - and nobody - spending millions of dollars to solve the problem, successfully, they want every problem of their academic industry to persist because even though they never solve the problem, they synthesize and solve lots of other problems nobody asked for. And get to boost their egos? Yeah, stop that. Actual alignment is on the humans themselves, if they want to remain relevant as academics and mathematicians, they need to learn how to replicate the proofs and the steps that alluded humans for decades and don't worry about the narcissistic elements that slow their industry down.
  - SpicyLemonZest 15d ago
    Their claim is only indirectly related to the motivations of the people using their models. What they're saying is that doing math in this way does not produce the same value as traditional mathematical research, and the people using these AI models aren't concerned about that because their marketing objectives don't depend on whether their results produce mathematical value. If people doing valuable work are made irrelevant by people doing a larger volume of non-valuable work, that's not a positive outcome.

deleted 15d ago

[deleted]

mypalmike 15d ago

I suspect that beyond just marketing, these pursuits yield plenty of useful information about model design that will likely lead to model improvements and optimizations for both mathematics and general reasoning going forward.

soerxpso 15d ago

Are they claiming that the only value in solving these problems was for their field's personal development process? I thought Navier-Stokes (and some of the other millenium prize problems) actually had implications for useful technology. It would be insane to demand that people avoid making progress on technology that can save lives or improve general quality of life, just to protect the sanctity of your karate belt system. Perhaps in lieu of open problems left to solve, mathematicians should be welcome to take up chess or sudoku to keep their minds spry.

Sharlin 15d ago
No, there's most likely zero practical benefit of having found a pathological edge case in which the Navier-Stokes equations do not work. We're most assuredly not talking about "saving lives" here. Unless advanced aliens show up and tell us they'll destroy Earth unless a counterexample to the N-S equations is provided within 24 hours.
SpicyLemonZest 15d ago
> I thought Navier-Stokes (and some of the other millenium prize problems) actually had implications for useful technology. This is the core misunderstanding that the open letter is attempting to correct. Developing a better understanding of the Navier-Stokes equations could have a number of implications for useful technology. They're fundamental to fluid dynamics, and turbulence in particular is something that many people feel we could work with more effectively if we better understood how and why it's generated. The Navier-Stokes smoothness problem is an interesting and long-standing benchmark for this understanding; we don't know why it should be so hard to answer, so we hoped that the process of developing a proof to the problem would produce more understanding. (We may still be able to extract this understanding after the fact, if OpenAI's proof is fully human-comprehensible.) Simply knowing that there exists a finite-time blowup is not practically useful. We know that fluids in the real world don't produce random singularities, so the result can't really have much physical meaning. What it illustrates is that the Navier-Stokes equations fail to model physical fluids in some yet to be characterized way.

swid 15d ago

> There is no near term commercial value How much do you think other AI companies would offer to get access to the transcripts of the generation that led to the proof? No doubt OpenAI will include it in their training data somehow and use it to build the next generation. There is already economic value.

ralph84 15d ago

> primarily as a marketing exercise Like the mathematicians working on famous problems in private until they could claim full credit for something interesting wasn't also a marketing exercise for their own careers. The commercial value (or lack thereof) of a proof doesn't depend on whether it was done by a human or a machine.

paulhebert 14d ago
These mathematicians dedicated their life to math and were working for a long time to achieve the pinnacle of their careers. OpenAI just burned millions of dollars over a weekend after hearing that someone else was close to solving the problems. Their interest was in their AI system more than the actual math problems. Don’t you see how that’s different?
- ralph84 14d ago
  I see how it can be devastating to their ego, but no, I don't see a particular difference in a company spending money for clout vs. a person spending time for clout. The underlying motivation is the same.
  - paulhebert 14d ago
    Do you really think people dedicate their life to mathematics for clout? If clout was the goal I don’t think becoming a lifelong mathematics academic would be the first step
    - pickleRick243 14d ago
      for many fairly strong mathematicians, the career calculus is fame and status (mild though it may be) through mathematics or anonymity but financial reward in tech or finance. Yes, clout by becoming a lifelong academic is in fact rational for some and part of their motivation. Of course they really like what they do as well, but earning the respect of the peers they know are also respected by a large swathe of society is very important.