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To me it doesn't seem like what AI has destroyed is the ability for mathematicians to develop understanding and share it with each other, but rather it's destro

To me it doesn't seem like what AI has destroyed is the ability for mathematicians to develop understanding and share it with each other, but rather it's destroyed the yardstick (solving open problems) that has traditionally been used to measure how much they have contributed to that understanding. I do see how this is a problem in terms of assigning credit, but I think the cat is already out of the bag in terms of these models being capable. Even without AI labs spending millions of dollars to solve millennium prize problems, there are plenty of other people who will use them to pick low hanging fruit. I don't think any social solution is going to make things go back to the way they were, where you could share your progress towards a famous open problem without risking someone "scooping" you within a couple of days. I think that the most likely outcomes are either mathematics becomes more secretive, or there is a more deliberative approach to assigning credit than who was "first" to solve some problem. In the former case, this may slow down progress, and in the latter case, this could mean that credit would become more subjective, and be a continual source of controversy.

HeavenFox 24d ago
Agreed. The problem is not with AI per se, but with the reward mechanism in academia in general.
- cluckindan 24d ago
  For those outside academia, the ”reward mechanism” is a choice between A) being a genius and working hard to become a leader in your field, B) becoming very good at writing grant applications, C) capitulating to corporations and living with the moral burden of their exploits
wbl 24d ago
Open problems are not that yardstick. Fermat's Last Theorem is the result of Wiles and Wiles-Taylor, but without key results from Serre, Ribet, Ihara, Langlands-Tunnels, and Frey's program none of what Wiles did would work. But Wiles did get the prize. Nowadays I think the inputs have shrunk a bit by doing more in the R=T theorem so less other cleverness needed.
- cubefox 24d ago
  Doing the last step of solving an open problem is the yard stick. But not for much longer: https://davidbessis.substack.com/p/the-fall-of-the-theorem-economy https://davidbessis.substack.com/p/the-fall-of-the-theorem-e...
jrflo 24d ago
Right. It seems like reading an AI proof (although it may not be well written) will provide the same insights as reading a proof from another mathematician, assuming it's been reviewed and edited, just like any human-authored publication. If the work is inherently valuable on it's own, I feel like that's mostly what matters.
- tmhn2 24d ago
  At issue is the fact that it doesn't typically work like: mathematician produces a proof in isolation, generates a PDF, and shares it with a bunch of people. There's a whole culture and community going on behind the scenes with conferences, seminars, lectures, chats in the hallway, advising students, etc. that AI-generated proofs bypass.
  - jrflo 24d ago
    I don't think that AI would disrupt any of that. Even if AI solves a problem, you can still discuss the methods at conferences, seminars, lectures, chats in the hallway, advising students, etc.
    - reasonableklout 24d ago
      Tao’s key point is that the way people are using AI today does disrupt that. Because people and companies are valuing the results over understanding. So we’re getting slop results rushed out that are automatically verified. Moreover in the past, discussion and idea sharing would happen naturally to overcome the friction of the process. But now when OpenAI is stuck on a particular part of NS for example, they can just throw more capital & tokens at the problem.
      - Shaptse 24d ago
        I won’t speak for Tao. But it is not “people” who have valued the result over understanding. “People” are a bit impressed that the machines are as good or better than the priests who have been praying at the inscrutable altar of pure mathematics. But it is mathematicians—I am speaking as a mathematician—who have adopted a culture of valuing results over exposition and transparency. The field has been rife with extremely opaque papers for many years and the character of research participation has been one of exclusion and competition over proof priority at the expense of understanding and transparency. It is unbelievably ironic to listen to mathematicians complain about “AI slop” when they have built careers upon human “slop” if slop means papers crammed with technical density that prevents all but specialists from reading the work.
tmhn2 24d ago
The issue of credit is a relatively minor point in the declaration. It's more about bypassing the culture and processes mathematicians have developed that lead to human understanding, generating new ideas, and bringing up new generations of mathematicians. (See also his article about "non-renewable mining" of good problems.) Reducing mathematics to "let's just generate results through an isolated and automated system" is a misalignment since it bypasses those processes.
- jimkleiber 24d ago
  I wonder if this is a root of the complaints across fields, how AI is ruining the greater picture and process in writing, acting, drawing, filming, coding, and more. That it makes life more ends and less means.
  - gritzko 24d ago
    Let's take your argument one step further. Suppose that tomorrow we learn that AI just exploited a bug in Lean and the proof is, in fact, bullshit. Or suppose it is the case, but we never learn that. Where are "ends" and where are "means" here?
    - margalabargala 24d ago
      Well, given a proof of something then a system can be built that relies upon the inviolability of that thing. Should the proof turn out to be bullshit, then that system will be revealed to be unreliable. Maybe.
  - Xelynega 24d ago
    It's also known as "commodification of labour", and AI is just the latest and greatest tool to do it. Luddites complained that the trajectory of technology was to allow less skilled workers to mass produce goods via machines owned by factory owners, as opposed to helping skilled workers build up and use their skills while passing them on. Now we have a lot of money and time focused on LLMs owned by a few companies, making it easier for them to monetize low skill labour(prompting versus art/research/artisanry)
jameshart 24d ago
> destroyed the yardstick … that has traditionally been used to measure how much they have contributed This goes much broader than mathematics or academia. This is the entire basis via which society distributes its wealth: based on a labour market derived valuation of ‘contribution’.
- palmotea 24d ago
  > This is the entire basis via which society distributes its wealth: based on a labour market derived valuation of ‘contribution’. Correction: that's not how society distributes its wealth, it's how it throws some bones to the masses. I wouldn't be surprised if over half the wealth goes to people who don't sell their labor at all.
bz64 24d ago
Nothing will be lost if the credit system disappears. History of Science has many examples where wipe outs happen. The chimp brain cant survive without creating elaborate stories about how important it is, more as a cope to its own limitations and what it cant predict or control. Humility is good for health. 3 inch chimp brains didnt create the universe.
malwrar 24d ago
I feel a similar fate will befall engineers too. Your predictions anre quite interesting from that perspective. Markets defined entirely by law have distorted our collective understanding of what can actually be built with the knowledge our species has accumulated thus far. How will traditional shields that have protected capital accumulation in tech to survive in a world where governments now realize control of technology is a national priority? Especially as we see its impact on modern warfare, and that such conflict looks like it’s only escalating over time. Mathematicians appear to me (as an outsider) to exist in a field without such distortions, and I think offer engineers a preview of what’s to come. I certainly have completely ceased sharing original ideas online at this point.
- glitchc 24d ago
  Engineers are needed to build real things. AI isn't there yet.
sigmar 24d ago
>or there is a more deliberative approach to assigning credit than who was "first" to solve some problem it feels like an unintended consequence of the millennium prize is that people view the [last contributor to the solution] as the only one to make progress on the problem. I've never viewed Poincaré as solved by one person and the objective of the prize was to encourage more people to make attempts and contribute towards progress. this issue is independent, but in these circumstances perhaps interweaved, with the 'ai is taking over math' concerns
omnicognate 24d ago
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 24d ago
  yeah beacuse no one trust any of their benchmark results now they are scrambling to find a signal thats undeniable
  - pfdietz 24d 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 24d 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.
oytis 24d ago
Is it not an option to make academia more like a normal job, where people focus on collectively achieved outcomes rather than credit, priority etc.?
- edgyquant 24d ago
  How is that like a normal job?
- Xirdus 24d ago
  Almost every "normal" job has regular performance reviews where individual contributions, not collective outcomes, are reviewed and used as a sole input for raises, promotions, and firings. If you can't sufficiently document what you personally did, you might've as well not done anything at all.
  - oytis 24d ago
    Yes, that's true, but it is still generally accepted that a completed project is a result of some collective effort where people of varying degree of seniority and ability contribute. There is also not a singular event of a project being completed with a list of heroes/geniuses making it happen, but rather a whole lifecycle of gradual development, maintenance and going out of relevance with contributors coming and going. I can imagine mathematics of the future being more like that rather than history of discoveries with dates and names
dgellow 24d ago
> but I think the cat is already out of the bag in terms of these models being capable. When there's a discussion about doing something against the damage of the AI industry: "whoopsy, sorry, another cat escape, nothing can be done". When there's a concrete mention of an actual solution to avoid more cats escaping: "that won't happen, and even if it did, the damage is already done, and in fact it’s not that bad you all just have to go with the future we decided for you." So the bag is wide open, more cats will escape, and nothing can be done about any of it. not about the ones that got out, and not about the ones still inside. Sounds more like a preemptive excuse for inaction, cosplayed as pragmatism
rdevilla 24d ago
[dead]
joe_the_user 24d ago
To me it doesn't seem like what AI has destroyed is the ability for mathematicians to develop understanding and share it with each other, but rather it's destroyed the yardstick (solving open problems) that has traditionally been used to measure how much they have contributed to that understanding. It's more than the yardstick for individual contributions. It's also the yardstick for the contribution of ideas. And that kind of yardstick is very important. Math has a challenge that's only occasionally acknowledged imo, that's it's possible to just go up the ladder of abstraction, formulate ideas but have those ideas actually not be useful or interesting. The ideas that math has developed, that mathematicians consider important, are those that have helped people solve hard problems.
nxobject 23d ago
> To me it doesn't seem like what AI has destroyed is the ability for mathematicians to develop understanding and share it with each other, but rather it's destroyed the yardstick (solving open problems) that has traditionally been used to measure how much they have contributed to that understanding. I think you're missing key details in the statement. You can hate problems and sprinting towards solutions, and still have a deep impact in mathematics – Grothendieck once famously said you can often "soak the walnut" to crack open an issue. Rather, it's how frontier labs are inherently commercial incentivized to act like this, because it is in their best fiduciary interest. That is the misalignment.

HeavenFox 24d ago

Agreed. The problem is not with AI per se, but with the reward mechanism in academia in general.

cluckindan 24d ago
For those outside academia, the ”reward mechanism” is a choice between A) being a genius and working hard to become a leader in your field, B) becoming very good at writing grant applications, C) capitulating to corporations and living with the moral burden of their exploits

wbl 24d ago

Open problems are not that yardstick. Fermat's Last Theorem is the result of Wiles and Wiles-Taylor, but without key results from Serre, Ribet, Ihara, Langlands-Tunnels, and Frey's program none of what Wiles did would work. But Wiles did get the prize. Nowadays I think the inputs have shrunk a bit by doing more in the R=T theorem so less other cleverness needed.

cubefox 24d ago
Doing the last step of solving an open problem is the yard stick. But not for much longer: https://davidbessis.substack.com/p/the-fall-of-the-theorem-economy https://davidbessis.substack.com/p/the-fall-of-the-theorem-e...

jrflo 24d ago

Right. It seems like reading an AI proof (although it may not be well written) will provide the same insights as reading a proof from another mathematician, assuming it's been reviewed and edited, just like any human-authored publication. If the work is inherently valuable on it's own, I feel like that's mostly what matters.

tmhn2 24d ago
At issue is the fact that it doesn't typically work like: mathematician produces a proof in isolation, generates a PDF, and shares it with a bunch of people. There's a whole culture and community going on behind the scenes with conferences, seminars, lectures, chats in the hallway, advising students, etc. that AI-generated proofs bypass.
- jrflo 24d ago
  I don't think that AI would disrupt any of that. Even if AI solves a problem, you can still discuss the methods at conferences, seminars, lectures, chats in the hallway, advising students, etc.
  - reasonableklout 24d ago
    Tao’s key point is that the way people are using AI today does disrupt that. Because people and companies are valuing the results over understanding. So we’re getting slop results rushed out that are automatically verified. Moreover in the past, discussion and idea sharing would happen naturally to overcome the friction of the process. But now when OpenAI is stuck on a particular part of NS for example, they can just throw more capital & tokens at the problem.
    - Shaptse 24d ago
      I won’t speak for Tao. But it is not “people” who have valued the result over understanding. “People” are a bit impressed that the machines are as good or better than the priests who have been praying at the inscrutable altar of pure mathematics. But it is mathematicians—I am speaking as a mathematician—who have adopted a culture of valuing results over exposition and transparency. The field has been rife with extremely opaque papers for many years and the character of research participation has been one of exclusion and competition over proof priority at the expense of understanding and transparency. It is unbelievably ironic to listen to mathematicians complain about “AI slop” when they have built careers upon human “slop” if slop means papers crammed with technical density that prevents all but specialists from reading the work.

tmhn2 24d ago

The issue of credit is a relatively minor point in the declaration. It's more about bypassing the culture and processes mathematicians have developed that lead to human understanding, generating new ideas, and bringing up new generations of mathematicians. (See also his article about "non-renewable mining" of good problems.) Reducing mathematics to "let's just generate results through an isolated and automated system" is a misalignment since it bypasses those processes.

jimkleiber 24d ago
I wonder if this is a root of the complaints across fields, how AI is ruining the greater picture and process in writing, acting, drawing, filming, coding, and more. That it makes life more ends and less means.
- gritzko 24d ago
  Let's take your argument one step further. Suppose that tomorrow we learn that AI just exploited a bug in Lean and the proof is, in fact, bullshit. Or suppose it is the case, but we never learn that. Where are "ends" and where are "means" here?
  - margalabargala 24d ago
    Well, given a proof of something then a system can be built that relies upon the inviolability of that thing. Should the proof turn out to be bullshit, then that system will be revealed to be unreliable. Maybe.
- Xelynega 24d ago
  It's also known as "commodification of labour", and AI is just the latest and greatest tool to do it. Luddites complained that the trajectory of technology was to allow less skilled workers to mass produce goods via machines owned by factory owners, as opposed to helping skilled workers build up and use their skills while passing them on. Now we have a lot of money and time focused on LLMs owned by a few companies, making it easier for them to monetize low skill labour(prompting versus art/research/artisanry)

jameshart 24d ago

> destroyed the yardstick … that has traditionally been used to measure how much they have contributed This goes much broader than mathematics or academia. This is the entire basis via which society distributes its wealth: based on a labour market derived valuation of ‘contribution’.

palmotea 24d ago
> This is the entire basis via which society distributes its wealth: based on a labour market derived valuation of ‘contribution’. Correction: that's not how society distributes its wealth, it's how it throws some bones to the masses. I wouldn't be surprised if over half the wealth goes to people who don't sell their labor at all.

bz64 24d ago

Nothing will be lost if the credit system disappears. History of Science has many examples where wipe outs happen. The chimp brain cant survive without creating elaborate stories about how important it is, more as a cope to its own limitations and what it cant predict or control. Humility is good for health. 3 inch chimp brains didnt create the universe.

malwrar 24d ago

I feel a similar fate will befall engineers too. Your predictions anre quite interesting from that perspective. Markets defined entirely by law have distorted our collective understanding of what can actually be built with the knowledge our species has accumulated thus far. How will traditional shields that have protected capital accumulation in tech to survive in a world where governments now realize control of technology is a national priority? Especially as we see its impact on modern warfare, and that such conflict looks like it’s only escalating over time. Mathematicians appear to me (as an outsider) to exist in a field without such distortions, and I think offer engineers a preview of what’s to come. I certainly have completely ceased sharing original ideas online at this point.

glitchc 24d ago
Engineers are needed to build real things. AI isn't there yet.

sigmar 24d ago

>or there is a more deliberative approach to assigning credit than who was "first" to solve some problem it feels like an unintended consequence of the millennium prize is that people view the [last contributor to the solution] as the only one to make progress on the problem. I've never viewed Poincaré as solved by one person and the objective of the prize was to encourage more people to make attempts and contribute towards progress. this issue is independent, but in these circumstances perhaps interweaved, with the 'ai is taking over math' concerns

omnicognate 24d ago

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 24d ago
yeah beacuse no one trust any of their benchmark results now they are scrambling to find a signal thats undeniable
- pfdietz 24d 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 24d 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.

oytis 24d ago

Is it not an option to make academia more like a normal job, where people focus on collectively achieved outcomes rather than credit, priority etc.?

edgyquant 24d ago
How is that like a normal job?
Xirdus 24d ago
Almost every "normal" job has regular performance reviews where individual contributions, not collective outcomes, are reviewed and used as a sole input for raises, promotions, and firings. If you can't sufficiently document what you personally did, you might've as well not done anything at all.
- oytis 24d ago
  Yes, that's true, but it is still generally accepted that a completed project is a result of some collective effort where people of varying degree of seniority and ability contribute. There is also not a singular event of a project being completed with a list of heroes/geniuses making it happen, but rather a whole lifecycle of gradual development, maintenance and going out of relevance with contributors coming and going. I can imagine mathematics of the future being more like that rather than history of discoveries with dates and names

dgellow 24d ago

> but I think the cat is already out of the bag in terms of these models being capable. When there's a discussion about doing something against the damage of the AI industry: "whoopsy, sorry, another cat escape, nothing can be done". When there's a concrete mention of an actual solution to avoid more cats escaping: "that won't happen, and even if it did, the damage is already done, and in fact it’s not that bad you all just have to go with the future we decided for you." So the bag is wide open, more cats will escape, and nothing can be done about any of it. not about the ones that got out, and not about the ones still inside. Sounds more like a preemptive excuse for inaction, cosplayed as pragmatism

rdevilla 24d ago

[dead]

joe_the_user 24d ago

nxobject 23d ago

> To me it doesn't seem like what AI has destroyed is the ability for mathematicians to develop understanding and share it with each other, but rather it's destroyed the yardstick (solving open problems) that has traditionally been used to measure how much they have contributed to that understanding. I think you're missing key details in the statement. You can hate problems and sprinting towards solutions, and still have a deep impact in mathematics – Grothendieck once famously said you can often "soak the walnut" to crack open an issue. Rather, it's how frontier labs are inherently commercial incentivized to act like this, because it is in their best fiduciary interest. That is the misalignment.