I support activism - shame away! But maybe read the rest of this post first.
In my opinion, a couple productive ways for activists to channel their energy would be to:
(1) go on Twitter and criticize bad behavior, call out misleading or misinformed takes, douse hype (Thomas Bloom is great example to follow), etc.
(2) propose, in broad discussion with the mathematics community, realistic and concrete actions to improve the situation.
The sentiment that "everybody hates the AI industry" should certainly be given its fair share of airtime, but it is already quite well known.
Plenty of tech folks have made fools of themselves commenting on mathematics. Conversely, mathematicians may not understand the dynamics of tech labs as well as they think. For example, there seems to be a common misconception that AI companies want to "solve math" as a marketing gimmick to demonstrate superintelligence. This does not match my experience of the frontier labs (OpenAI, Anthropic, Google). It is true that Google employs many people with math backgrounds, who like to try math problems on their products for fun, and initially got overexcited with the results - I acknowledge my own guilt in this - but since then we have exercised considerable restraint behind the scenes.
Lastly, I'd like to advocate for one benefit of the technology. Wizened mathematicians like myself know that "proof indigestion" was a problem even before AI, and almost every paper of appreciable length contains serious mistakes (meaning beyond typos). One of my main research threads in AI is on natural language verification, this is the main way I use AI for my mathematics, and I'm happy that the models have reached the point of helping me catch many errors in my work. Once these idealistic young AI abstainers see how pervasive mistakes are in the literature, they may develop a slightly more accommodating view of the role of the technology. I am happy to provide trial refereeing for those who do not have ChatGPT subscriptions.
Tasmin Chu's latest post contains one possible response to your last suggestion: "What is more worrying: a culture of folklore, or a scientific field that depends on AI companies for peer review and publication?" Chu may be motivated by idealism but her analysis is very precise.
Having contributed more than my fair share of mistakes to the literature without causing mathematics to capsize, I feel it wouldn't be appropriate for me to lose faith in the community's capacity for self-correction. The right kind of mistake can be the most precious source of insight.
Chu also disagrees with Tony's comment on the dynamics of tech labs, in a paragraph that begins "AI companies view research mathematics as an opportunity to advance their own ideological and material interests." I don't think the subjective experience of mathematicians working in the frontier labs is particularly relevant to the question. One should instead look at the messages executives are sending to their investors by way of the media. This tweet about Greg Brockman's interview on finance and business station CNBC (https://x.com/karlmehta/status/2089699041722736769, provided by Gemini) is typical. I copy the tweet because the interview appears to be behind a paywall:
[beginning of tweet]
OpenAI President Greg Brockman says $2,000 of compute solved 10 math problems that had eluded mathematicians for decades:
"Software engineering this year has been totally transformed."
"We're starting to see every aspect of knowledge work really change. But also, we're starting to see scientific discovery."
"We announced a couple of weeks ago that our AI for $2,000 worth of compute was able to solve 10 long-standing math problems that had eluded mathematicians for decades."
"And think about that level of capability applied to biology, applied to material science. It's all starting to happen."
OpenAI published Lean certificates alongside the result, so anyone who doubts the proofs can run them through a proof checker instead of taking the announcement on faith. Formal review is still pending and the $2,000 covers model tokens, not the people who prepared the manuscript. Mathematics is the rare field where that checking layer was already built and waiting.
"I don't think the subjective experience of mathematicians working in the frontier labs is particularly relevant to the question. One should instead look at the messages executives are sending to their investors by way of the media."
Perhaps even more revealing might be a look at the hiring practices of the "Wall Street and Silicon Valley, flush with cash": they do not appear to reveal a firm conviction that human mathematicians will becopme obsolete any time soon:
Regarding the first point, I would not find that response (a mathematical culture of deliberately accepting mistakes) satisfactory. Moreover, it is a false dichotomy; academic institutions could set up open weight models to be queried relatively cheaply, divesting themselves from dependence on AI companies.
Regarding the second point, what's wrong with Brockman's quote? I maintain that they are trying to develop general capabilities, not specifically solve math (OpenAI's reasoning lead Noam Brown discusses this at https://www.youtube.com/watch?v=h4ZguzEMKAU). If in the course of doing so they solve some important math problems, then in my opinion it's their right to announce it. I am quite confident that the number 10 is in fact much higher, and that they choose not to announce the rest under advice of their mathematicians.
Your aversion to mistakes is understandable, and I'm not suggesting that anyone deliberately accept mistakes, rather that one acknowledge that they have always been a driving force in the development of mathematics.
I'm curious about these open weight models: would the academic institutions have to scrape the entirety of published (and unpublished) mathematics for training, and build a data center to handle queries? That doesn't sound like a cheap initial investment, but maybe I'm mistaken about the logistics.
I maintain that OpenAI is trying to develop return on investment, and even if the executives feel that they are trying to develop something else, if OpenAI survives long enough to issue an IPO, they will be legally required to place shareholder interest — in other words return on investment — above all other priorities. This is all that matters to the CNBC audience.
I think we're talking about different kinds of mistakes. It is natural and instructive to make mistakes when thinking about mathematics, but I wouldn't agree that mistakes in the published literature are a driving force in the development of mathematics. Also, all you need to run open weight models is a handful of GPUs (which many universities already have); the data, training, etc. are already taken care of.
Looking forward to a lively discussion in Heidelberg!
What does it mean: "the data, training, etc. are already taken care of"? By whom, and how would it be made available to the universities? I assume it means that the weights are contained in a relatively manageable file, having been developed by a process that at the very least borders on copyright infringement. Training is an open-ended process, however, so the scraping would have to continue.
You could try to set up a journal that has an editorial and quality control process but advertises itself as having very short (a month, maybe even a few weeks) turnaround time. This could go as an experiment, you would surely get plenty of submissions and we would get a real life test of how well current llm's are at spotting significant errors. There would also be a significant incentive for members of the community to find flaws with it. But, if it turns out to have a high success rate and the reviews hold up, you would earn a lot of goodwill in the math community very quickly.
It sounds like this would mean reinforcing dependence of mathematics on the providers of commercial LLMs. In this regard, and apart from how inherently objectionable this would be, I recommend Ed Zitron's latest analysis of how OpenAI may die (https://www.wheresyoured.at/what-happens-if-openai-dies/).
I would like an objective assessment of how good llms are at refereeing right now, rather than relying on anecdotes passed back and forth.
Here is one anecdote: a preprint (not mine) was passed around between journals for four years before somebody ran it by several llms which all found the same serious but fixable mistake. Here is another anecdote: there is an editor at a journal now who uses llms to self-write quick opinions (I think this is bad).
There are subfields of math that have essentially died out because of unresolved refereeing disputes.
The refereeing system as it is now is deeply flawed and not worth trying to preserve. It should be the first thing to try and revamp as soon as the technology to do so becomes available. If it is available now, then we should go for it irrespective of anything we choose to do (or not to) with regards to ai use in math.
Of course, there are things to be concerned about, e.g. whether there are particular types of mistakes that llms will not catch. (I found Shmuel Weinberger's post https://proofsandprompts.com/2026/08/11/what-i-feel-like-when-i-work-with-an-ai/ to be insightful on this. One can imagine that current llm's would optimize for breaking up an argument into lot of little steps where each one has a mistake that looks easily fixable via a standard fix to a human referee, but the long chain is not quite compatible in a subtle way...) If that is the case, we need to find out what those are.
If this is a topic on which some goodwill can be built between the math community and the ai companies, even better.
Weirdly enough (or maybe not), I recently observed that it bothers me a lot more when people don't write in their own voice than when they use an argument suggested by an llm. The later is ''oh, Frank learned some new tricks, this is how he thinks about that argument'' (no shade on any Franks out there), while the former is much more ''Frank is gone, it's just an llm speaking through him''. At this point this is just an emotional response, but I'm surprised by how visceral it is.
P.S.: I initially used Mike for my hypothetical person, but then realized that you might go by that so changed it to Frank...
Shane Kelly's footnote's comment about "large scale advertising campaign" applies word for word to the Washington Post report on last week's meeting at OpenAI, and specifically to its headline: "This may be the first academic profession to see its work taken over by AI." The article is behind a paywall but I can quote the first paragraph:
"In early August, top mathematicians gathered at the offices of ChatGPT maker OpenAI in San Francisco for a summit on an existential question: What will be left for human math experts to do if artificial intelligence soon leaves them all behind?"
"Top mathematicians" should have learned by now that, whatever they say to a journalist, it will be interpreted as commentary on the headline, which is chosen by the editors to convey the message intended for readers. I was interviewed by the journalist but fortunately was not quoted directly; but it does include a link to this post ("News, rumors, gossip") that makes me slightly complicit with this latest exercise in targeted disinformation.
Conveying to a journalist (or a "man-in-the-street/human-online") subtlety, beauty and depth of the research in pure mathematics that chatbots, however fabulous or astral, are yet to achieve (if at all) strikes me as an exceedingly difficult task; I grapple with it -- to an extent-- in the Coda (page 1730):
Thank you for pointing this out! The author is Shane Kelly and the footnote deserves to be quoted in full, because it makes a point I haven't seen elsewhere:
"Mathematicians are currently being instrumentalised in a large scale advertising cam-
paign by AI companies competing for market monopoly. Public grant money is being paid to companies which then receive free advertising from us, often while showing little regard for our research priorities. More seriously, as part of this advertising campaign, some companies are pushing misinformation about the goals of mathematical research. This misinformation has the real potential to influence government funding decisions in a way that funnels money away from scientific goals, and towards private interests.
"This advertising campaign has more serious collateral damage. Mathematics depends on a human research ecosystem which continually generates new problems and sustains the community capable of recognising and pursuing them. Human generated research problems are a scarce and essential part of this mathematical ecosystem. Conceptually incoherent and empirically unsupported rhetoric portraying mathematicians as replaceable threatens a pipeline of early career researchers already in precarious employment conditions. Damaging either undermines the infrastructure on which future mathematical progress depends.
"While the author does want to be transparent about the use of computer assistance in
the preparation of the current manuscript, he does not want to participate in this advertising campaign and contribute to this destruction of the commons. As such, the model and company name will remain absent from this manuscript, but are available upon request."
I think you should be able to find a reading of my slides which is rather critical of Silicon Valley (though I do intend it to be critical of the profession as well). I have no intention of defecting!
I’ve found the reception of my views from the resistance to be pretty thoughtful, by and large. Most disagreements seem to be about the ground truth re: model capabilities, costs, etc., where I think there will be much broader agreement in a few months or years.
I've gotten the sense that there are at least three reasons, coming from 3 somewhat different groups within the labs: (1) PR, of course. (2) Math served as an early source of benchmarks (AIME, for example) and it turned out that methods that led to increased performance on these have generalized to more economically valuable capabilities (e.g. code). I think there's some hope in the labs that this will continue to be true. (3) The labs have hired lots of mathematicians, and those people like to do math and like to use the models to do so.
I think the reason for continued investment is mostly (2) but for what it's worth my sense is that investment in math has never been that large, and may be tapering off; capabilities still seem to be increasing despite this.
This is some mixture of speculation and gossip, so take it with a grain of salt. It's not literally that AIME improvement led to increased coding capabilities, but rather that research done to improve AIME etc. performance generalized to improve coding abilities. I.e. math capabilities are a useful research playground.
Hypothetical question: suppose you are a grad student working for an advisor and writing your first paper. How would you know whether your advisor bounced some thoughts off of ai before giving you advice on the directions of your project? What are you expected to disclose or not disclose in that situation?
Under the proposed regime (even under the Leiden declaration) thanking an advisor (or anyone!) who is known to use ai devalues your work.
In practice, it seems obvious that it will lead to a `don't ask don't tell' situation.
Counter question: assume you are a professor and your work is basically just "prompting" claude to "do a breakthrough" and publish it as "my conversation with Claude Cosmos 9.1 about mathematical or philosophical object X, - timestamp 01122027-UTC005-03:01:23" .
Why wouldn't I just ... talk to Claude Cosmos 9.1 directly? Cut out the middle man you know?
This line of argument is broadly in line with ``It would have been better if Perelman had not proved the 3-dimensional Poincare conjecture and instead we had a large community keep plugging away it for decades''. I wonder how many mathematicians would openly endorse that line of argument. It certainly goes counter to everything I've been taught. The idea that we should preserve a community whose whole ostensible reason for existence is to solve problems by artificially stopping those problems from being solved is should at least be interrogated and we should be very clear with ourselves and also with funding agencies that this is in fact what we are aiming to do. Most of us already know subfields of math that substain themselves simply because there is a community of people invested in keeping the field alive, not because there is progress on problems being made. Do we really want all of math to become like that?
I don't think those responsible for the four developments listed, nor those who plan to draft new Declarations, would agree with this reading of their intentions, but I'll let them speak for themselves when the time comes; or they can respond here. I'll just add that your "whole ostensible reason for existence" is a brutally reductive view of the community of mathematicians. It can even be argued that you have it exactly backwards; "to solve problems" for what or whom, exactly?
In my experience, I always solved problems for myself, because wanted to understand something I hadn't understood yet. And so that I have something to give a talk about, I like doing that. If someone I respect liked the solution or the explanation, engaged with it more or found it surprising, that is a bonus.
Some mathematicians may be genuine solipsists, for whom the existence of a human community of mathematicians is at best a "bonus," but I don't believe the majority of mathematicians view the profession in this way.
Anyway, mathematics doesn't have a single "reason for existence" any more than humanity has a single "reason for existence."
I am well aware that people are varied and some are more social than others. I was just trying to give you an idea of where I personally am coming from in response to your question. I personally like many individual mathematicians and very much enjoy spending time with them, but I also have plenty of complaints (as probably most of us do) about the community as a whole and many problems with it (which I won't list now). I am at least slightly hopeful that in this time of upheaval some of those problems will get swept away and possibly replaced with new ones.
I am also a very literal person. I am concerned about the Leiden declaration as it is written now. It simultaneously disparages ai companies and says that using ai may be immoral, and also that mathematicians should disclose any and all ai use. It doesn't say anything about ``responsible ai disclosure'' not being used against them.
I have already seen plenty of papers on the arxiv by people I know, some not bad and some terrible, disclosing ai use. And, I can't help but wonder whether these disclosures will be used against them in hiring/grant applications and on editorial boards. I have served on a committee involved with hiring postdocs in the past, and nothing about the way that process works allays my concerns. There is a reason why information that may bias a decision is sometimes withheld from a committee. We are all human and being instructed to `ignore this information in our decision' is hard to do in practice.
It seems to me that we are in the process of settling on a new set of rules and norms now, and I am worried that some of these rules will create bad incentives and lead to more problems that they solve.
One example that comes to mind is an advisor using AI to explore a problem and then using the information they learned to guide a student's research. Do students of such an advisor who don't use AI have an unfair advantage over others?
(1) We already have a norm that an author is responsible for everything in their paper, yet now people feel the need to say it out loud.
(2) We already have a norm that if a person can't explain their result in a talk and answer questions, then we don't take their result seriously.
I think these norms have served us sell in the past and they will continue to serve us in this ai infused future. The phenomenon of someone's knowledge being `fragile' is not a recent phenomenon (Feynman complained about it!), though I agree that ai is likely to turbocharge it.
This reply is getting long so let me wrap up. Let me end by saying that my own views on AI are very much unsettled, since as we all know, things are changing very fast. Who knows, maybe I'll end up joining your resistance someday!
But, for now, I see very real and urgent problems that need to be dealt with. I think there is about to be a flood of papers on the arxiv at different levels of ai assistance. This will make it less useful as a way to get publicity for a preprint (whether or not that preprint has any ai in it). In particular, the arxiv's role as a method for graduate students to advertise their work before hiring season may be at risk. Here, I do agree with Tasmin Chu that some sort of limits on the number of submissions may have to be implemented. But, every idea that comes to mind seems exploitable and any rules that are not thought through carefully may make maters worse. It is an interesting problem!
Cheers,
-Grigori
Edit P.S.: I got distracted and forgot to add the reason for my initial post, so let me do that now. The arguments in this post and in the referenced arxiv preprint are all about how to preserve the math community and not about why we should. Someone looking in from the outside will not be persuaded by that. Our reason for preserving the math community has to be a mathematical rather than social one. And if we don't have a compelling mathematical reason, then we have a problem.
P.P.S.: I don't know why ai companies have focused on math as much as they have, but Geordie Williamson's talk at the ICM gave me a possible idea. He said that he didn't realize until recently that finding a counterexample in math is very similar to finding an exploit in hacking. So, there is a very real world application to training AI's to get better at math. This seems to be like a more logical explanation than any sinister plans to destroy the math community.
I agree that some of the gnashing of teeth around AI from some substackers is a bit much. I didn't have an identity crisis when I found out that the Bode plots, and circuit designs (some of which took 10s of pages) or transfer functions I had to produce during my EE undergrad, could be easily produced by computers! In fact, I was expected to hand derive/compute things which were essentially solved problems for a long time. Maybe this is different ... but every other field has been continuously been disrupted for decades. I would blame the AI industry for also sowing panic and discord.
I don't think the main point is to create a welfare program for nerds (although, if you believe the AI industry then this is going to be necessary but not sufficient). The point is to save some essence of the field from extremely well funded companies (really like 2 or 3 of them). Companies', whose benefactors, do not really care about Jacobians or groups etc but cold hard returns.
The AI industry views math as a "way point" on it's quest to capture all the "value in the future light cone" or whatever. Just a benchmark for more investment; and will hollow out the profession for this pursuit.
We can argue if Mathematics should even be a profession anymore. And that is fine! But obviously current mathematicians have an opinion too!
I support activism - shame away! But maybe read the rest of this post first.
In my opinion, a couple productive ways for activists to channel their energy would be to:
(1) go on Twitter and criticize bad behavior, call out misleading or misinformed takes, douse hype (Thomas Bloom is great example to follow), etc.
(2) propose, in broad discussion with the mathematics community, realistic and concrete actions to improve the situation.
The sentiment that "everybody hates the AI industry" should certainly be given its fair share of airtime, but it is already quite well known.
Plenty of tech folks have made fools of themselves commenting on mathematics. Conversely, mathematicians may not understand the dynamics of tech labs as well as they think. For example, there seems to be a common misconception that AI companies want to "solve math" as a marketing gimmick to demonstrate superintelligence. This does not match my experience of the frontier labs (OpenAI, Anthropic, Google). It is true that Google employs many people with math backgrounds, who like to try math problems on their products for fun, and initially got overexcited with the results - I acknowledge my own guilt in this - but since then we have exercised considerable restraint behind the scenes.
Lastly, I'd like to advocate for one benefit of the technology. Wizened mathematicians like myself know that "proof indigestion" was a problem even before AI, and almost every paper of appreciable length contains serious mistakes (meaning beyond typos). One of my main research threads in AI is on natural language verification, this is the main way I use AI for my mathematics, and I'm happy that the models have reached the point of helping me catch many errors in my work. Once these idealistic young AI abstainers see how pervasive mistakes are in the literature, they may develop a slightly more accommodating view of the role of the technology. I am happy to provide trial refereeing for those who do not have ChatGPT subscriptions.
Tasmin Chu's latest post contains one possible response to your last suggestion: "What is more worrying: a culture of folklore, or a scientific field that depends on AI companies for peer review and publication?" Chu may be motivated by idealism but her analysis is very precise.
Having contributed more than my fair share of mistakes to the literature without causing mathematics to capsize, I feel it wouldn't be appropriate for me to lose faith in the community's capacity for self-correction. The right kind of mistake can be the most precious source of insight.
Chu also disagrees with Tony's comment on the dynamics of tech labs, in a paragraph that begins "AI companies view research mathematics as an opportunity to advance their own ideological and material interests." I don't think the subjective experience of mathematicians working in the frontier labs is particularly relevant to the question. One should instead look at the messages executives are sending to their investors by way of the media. This tweet about Greg Brockman's interview on finance and business station CNBC (https://x.com/karlmehta/status/2089699041722736769, provided by Gemini) is typical. I copy the tweet because the interview appears to be behind a paywall:
[beginning of tweet]
OpenAI President Greg Brockman says $2,000 of compute solved 10 math problems that had eluded mathematicians for decades:
"Software engineering this year has been totally transformed."
"We're starting to see every aspect of knowledge work really change. But also, we're starting to see scientific discovery."
"We announced a couple of weeks ago that our AI for $2,000 worth of compute was able to solve 10 long-standing math problems that had eluded mathematicians for decades."
"And think about that level of capability applied to biology, applied to material science. It's all starting to happen."
OpenAI published Lean certificates alongside the result, so anyone who doubts the proofs can run them through a proof checker instead of taking the announcement on faith. Formal review is still pending and the $2,000 covers model tokens, not the people who prepared the manuscript. Mathematics is the rare field where that checking layer was already built and waiting.
[end of tweet]
"I don't think the subjective experience of mathematicians working in the frontier labs is particularly relevant to the question. One should instead look at the messages executives are sending to their investors by way of the media."
Perhaps even more revealing might be a look at the hiring practices of the "Wall Street and Silicon Valley, flush with cash": they do not appear to reveal a firm conviction that human mathematicians will becopme obsolete any time soon:
https://www.wsj.com/tech/ai/the-million-dollar-talent-wars-for-20-something-math-geniuses-5cc5a757
Regarding the first point, I would not find that response (a mathematical culture of deliberately accepting mistakes) satisfactory. Moreover, it is a false dichotomy; academic institutions could set up open weight models to be queried relatively cheaply, divesting themselves from dependence on AI companies.
Regarding the second point, what's wrong with Brockman's quote? I maintain that they are trying to develop general capabilities, not specifically solve math (OpenAI's reasoning lead Noam Brown discusses this at https://www.youtube.com/watch?v=h4ZguzEMKAU). If in the course of doing so they solve some important math problems, then in my opinion it's their right to announce it. I am quite confident that the number 10 is in fact much higher, and that they choose not to announce the rest under advice of their mathematicians.
Your aversion to mistakes is understandable, and I'm not suggesting that anyone deliberately accept mistakes, rather that one acknowledge that they have always been a driving force in the development of mathematics.
I'm curious about these open weight models: would the academic institutions have to scrape the entirety of published (and unpublished) mathematics for training, and build a data center to handle queries? That doesn't sound like a cheap initial investment, but maybe I'm mistaken about the logistics.
I maintain that OpenAI is trying to develop return on investment, and even if the executives feel that they are trying to develop something else, if OpenAI survives long enough to issue an IPO, they will be legally required to place shareholder interest — in other words return on investment — above all other priorities. This is all that matters to the CNBC audience.
I think we're talking about different kinds of mistakes. It is natural and instructive to make mistakes when thinking about mathematics, but I wouldn't agree that mistakes in the published literature are a driving force in the development of mathematics. Also, all you need to run open weight models is a handful of GPUs (which many universities already have); the data, training, etc. are already taken care of.
Looking forward to a lively discussion in Heidelberg!
What does it mean: "the data, training, etc. are already taken care of"? By whom, and how would it be made available to the universities? I assume it means that the weights are contained in a relatively manageable file, having been developed by a process that at the very least borders on copyright infringement. Training is an open-ended process, however, so the scraping would have to continue.
You could try to set up a journal that has an editorial and quality control process but advertises itself as having very short (a month, maybe even a few weeks) turnaround time. This could go as an experiment, you would surely get plenty of submissions and we would get a real life test of how well current llm's are at spotting significant errors. There would also be a significant incentive for members of the community to find flaws with it. But, if it turns out to have a high success rate and the reviews hold up, you would earn a lot of goodwill in the math community very quickly.
It sounds like this would mean reinforcing dependence of mathematics on the providers of commercial LLMs. In this regard, and apart from how inherently objectionable this would be, I recommend Ed Zitron's latest analysis of how OpenAI may die (https://www.wheresyoured.at/what-happens-if-openai-dies/).
I would like an objective assessment of how good llms are at refereeing right now, rather than relying on anecdotes passed back and forth.
Here is one anecdote: a preprint (not mine) was passed around between journals for four years before somebody ran it by several llms which all found the same serious but fixable mistake. Here is another anecdote: there is an editor at a journal now who uses llms to self-write quick opinions (I think this is bad).
There are subfields of math that have essentially died out because of unresolved refereeing disputes.
The refereeing system as it is now is deeply flawed and not worth trying to preserve. It should be the first thing to try and revamp as soon as the technology to do so becomes available. If it is available now, then we should go for it irrespective of anything we choose to do (or not to) with regards to ai use in math.
Of course, there are things to be concerned about, e.g. whether there are particular types of mistakes that llms will not catch. (I found Shmuel Weinberger's post https://proofsandprompts.com/2026/08/11/what-i-feel-like-when-i-work-with-an-ai/ to be insightful on this. One can imagine that current llm's would optimize for breaking up an argument into lot of little steps where each one has a mistake that looks easily fixable via a standard fix to a human referee, but the long chain is not quite compatible in a subtle way...) If that is the case, we need to find out what those are.
If this is a topic on which some goodwill can be built between the math community and the ai companies, even better.
Edit: Here is more anecdotal evidence in a blog post by a theoretical physicist: https://aiforintegrability.substack.com/p/a-proposal-for-ai-assisted-refereeing
Weirdly enough (or maybe not), I recently observed that it bothers me a lot more when people don't write in their own voice than when they use an argument suggested by an llm. The later is ''oh, Frank learned some new tricks, this is how he thinks about that argument'' (no shade on any Franks out there), while the former is much more ''Frank is gone, it's just an llm speaking through him''. At this point this is just an emotional response, but I'm surprised by how visceral it is.
P.S.: I initially used Mike for my hypothetical person, but then realized that you might go by that so changed it to Frank...
I saw this preprint this morning with an interesting footnote 3 on page 3:
https://arxiv.org/pdf/2608.16066
You have an ally there who is willing to be very vocal about this topic.
Shane Kelly's footnote's comment about "large scale advertising campaign" applies word for word to the Washington Post report on last week's meeting at OpenAI, and specifically to its headline: "This may be the first academic profession to see its work taken over by AI." The article is behind a paywall but I can quote the first paragraph:
"In early August, top mathematicians gathered at the offices of ChatGPT maker OpenAI in San Francisco for a summit on an existential question: What will be left for human math experts to do if artificial intelligence soon leaves them all behind?"
"Top mathematicians" should have learned by now that, whatever they say to a journalist, it will be interpreted as commentary on the headline, which is chosen by the editors to convey the message intended for readers. I was interviewed by the journalist but fortunately was not quoted directly; but it does include a link to this post ("News, rumors, gossip") that makes me slightly complicit with this latest exercise in targeted disinformation.
Conveying to a journalist (or a "man-in-the-street/human-online") subtlety, beauty and depth of the research in pure mathematics that chatbots, however fabulous or astral, are yet to achieve (if at all) strikes me as an exceedingly difficult task; I grapple with it -- to an extent-- in the Coda (page 1730):
https://www.ams.org/journals/notices/202011/rnoti-p1716.pdf?adat=December%202020&trk=2191&cat=none&type=.pdf&cover=noti-dec-20-cov.jpg
Thank you for pointing this out! The author is Shane Kelly and the footnote deserves to be quoted in full, because it makes a point I haven't seen elsewhere:
"Mathematicians are currently being instrumentalised in a large scale advertising cam-
paign by AI companies competing for market monopoly. Public grant money is being paid to companies which then receive free advertising from us, often while showing little regard for our research priorities. More seriously, as part of this advertising campaign, some companies are pushing misinformation about the goals of mathematical research. This misinformation has the real potential to influence government funding decisions in a way that funnels money away from scientific goals, and towards private interests.
"This advertising campaign has more serious collateral damage. Mathematics depends on a human research ecosystem which continually generates new problems and sustains the community capable of recognising and pursuing them. Human generated research problems are a scarce and essential part of this mathematical ecosystem. Conceptually incoherent and empirically unsupported rhetoric portraying mathematicians as replaceable threatens a pipeline of early career researchers already in precarious employment conditions. Damaging either undermines the infrastructure on which future mathematical progress depends.
"While the author does want to be transparent about the use of computer assistance in
the preparation of the current manuscript, he does not want to participate in this advertising campaign and contribute to this destruction of the commons. As such, the model and company name will remain absent from this manuscript, but are available upon request."
I think you should be able to find a reading of my slides which is rather critical of Silicon Valley (though I do intend it to be critical of the profession as well). I have no intention of defecting!
I know you and I believe you; but what will the tribunal of the resistance think?
I’ve found the reception of my views from the resistance to be pretty thoughtful, by and large. Most disagreements seem to be about the ground truth re: model capabilities, costs, etc., where I think there will be much broader agreement in a few months or years.
I've gotten the sense that there are at least three reasons, coming from 3 somewhat different groups within the labs: (1) PR, of course. (2) Math served as an early source of benchmarks (AIME, for example) and it turned out that methods that led to increased performance on these have generalized to more economically valuable capabilities (e.g. code). I think there's some hope in the labs that this will continue to be true. (3) The labs have hired lots of mathematicians, and those people like to do math and like to use the models to do so.
I think the reason for continued investment is mostly (2) but for what it's worth my sense is that investment in math has never been that large, and may be tapering off; capabilities still seem to be increasing despite this.
This is some mixture of speculation and gossip, so take it with a grain of salt. It's not literally that AIME improvement led to increased coding capabilities, but rather that research done to improve AIME etc. performance generalized to improve coding abilities. I.e. math capabilities are a useful research playground.
Hypothetical question: suppose you are a grad student working for an advisor and writing your first paper. How would you know whether your advisor bounced some thoughts off of ai before giving you advice on the directions of your project? What are you expected to disclose or not disclose in that situation?
Under the proposed regime (even under the Leiden declaration) thanking an advisor (or anyone!) who is known to use ai devalues your work.
In practice, it seems obvious that it will lead to a `don't ask don't tell' situation.
Counter question: assume you are a professor and your work is basically just "prompting" claude to "do a breakthrough" and publish it as "my conversation with Claude Cosmos 9.1 about mathematical or philosophical object X, - timestamp 01122027-UTC005-03:01:23" .
Why wouldn't I just ... talk to Claude Cosmos 9.1 directly? Cut out the middle man you know?
*edited: for slightly more clarity.
This line of argument is broadly in line with ``It would have been better if Perelman had not proved the 3-dimensional Poincare conjecture and instead we had a large community keep plugging away it for decades''. I wonder how many mathematicians would openly endorse that line of argument. It certainly goes counter to everything I've been taught. The idea that we should preserve a community whose whole ostensible reason for existence is to solve problems by artificially stopping those problems from being solved is should at least be interrogated and we should be very clear with ourselves and also with funding agencies that this is in fact what we are aiming to do. Most of us already know subfields of math that substain themselves simply because there is a community of people invested in keeping the field alive, not because there is progress on problems being made. Do we really want all of math to become like that?
I don't think those responsible for the four developments listed, nor those who plan to draft new Declarations, would agree with this reading of their intentions, but I'll let them speak for themselves when the time comes; or they can respond here. I'll just add that your "whole ostensible reason for existence" is a brutally reductive view of the community of mathematicians. It can even be argued that you have it exactly backwards; "to solve problems" for what or whom, exactly?
In my experience, I always solved problems for myself, because wanted to understand something I hadn't understood yet. And so that I have something to give a talk about, I like doing that. If someone I respect liked the solution or the explanation, engaged with it more or found it surprising, that is a bonus.
I guarantee that if you explained your solution to a chatbot it would give you positive reinforcement.
I'm genuinely confused by what point you are trying to make. What does this have to do with anything I said?
Some mathematicians may be genuine solipsists, for whom the existence of a human community of mathematicians is at best a "bonus," but I don't believe the majority of mathematicians view the profession in this way.
Anyway, mathematics doesn't have a single "reason for existence" any more than humanity has a single "reason for existence."
Let me try to be conciliatory.
I am well aware that people are varied and some are more social than others. I was just trying to give you an idea of where I personally am coming from in response to your question. I personally like many individual mathematicians and very much enjoy spending time with them, but I also have plenty of complaints (as probably most of us do) about the community as a whole and many problems with it (which I won't list now). I am at least slightly hopeful that in this time of upheaval some of those problems will get swept away and possibly replaced with new ones.
I am also a very literal person. I am concerned about the Leiden declaration as it is written now. It simultaneously disparages ai companies and says that using ai may be immoral, and also that mathematicians should disclose any and all ai use. It doesn't say anything about ``responsible ai disclosure'' not being used against them.
I have already seen plenty of papers on the arxiv by people I know, some not bad and some terrible, disclosing ai use. And, I can't help but wonder whether these disclosures will be used against them in hiring/grant applications and on editorial boards. I have served on a committee involved with hiring postdocs in the past, and nothing about the way that process works allays my concerns. There is a reason why information that may bias a decision is sometimes withheld from a committee. We are all human and being instructed to `ignore this information in our decision' is hard to do in practice.
It seems to me that we are in the process of settling on a new set of rules and norms now, and I am worried that some of these rules will create bad incentives and lead to more problems that they solve.
One example that comes to mind is an advisor using AI to explore a problem and then using the information they learned to guide a student's research. Do students of such an advisor who don't use AI have an unfair advantage over others?
(1) We already have a norm that an author is responsible for everything in their paper, yet now people feel the need to say it out loud.
(2) We already have a norm that if a person can't explain their result in a talk and answer questions, then we don't take their result seriously.
I think these norms have served us sell in the past and they will continue to serve us in this ai infused future. The phenomenon of someone's knowledge being `fragile' is not a recent phenomenon (Feynman complained about it!), though I agree that ai is likely to turbocharge it.
This reply is getting long so let me wrap up. Let me end by saying that my own views on AI are very much unsettled, since as we all know, things are changing very fast. Who knows, maybe I'll end up joining your resistance someday!
But, for now, I see very real and urgent problems that need to be dealt with. I think there is about to be a flood of papers on the arxiv at different levels of ai assistance. This will make it less useful as a way to get publicity for a preprint (whether or not that preprint has any ai in it). In particular, the arxiv's role as a method for graduate students to advertise their work before hiring season may be at risk. Here, I do agree with Tasmin Chu that some sort of limits on the number of submissions may have to be implemented. But, every idea that comes to mind seems exploitable and any rules that are not thought through carefully may make maters worse. It is an interesting problem!
Cheers,
-Grigori
Edit P.S.: I got distracted and forgot to add the reason for my initial post, so let me do that now. The arguments in this post and in the referenced arxiv preprint are all about how to preserve the math community and not about why we should. Someone looking in from the outside will not be persuaded by that. Our reason for preserving the math community has to be a mathematical rather than social one. And if we don't have a compelling mathematical reason, then we have a problem.
P.P.S.: I don't know why ai companies have focused on math as much as they have, but Geordie Williamson's talk at the ICM gave me a possible idea. He said that he didn't realize until recently that finding a counterexample in math is very similar to finding an exploit in hacking. So, there is a very real world application to training AI's to get better at math. This seems to be like a more logical explanation than any sinister plans to destroy the math community.
I agree that some of the gnashing of teeth around AI from some substackers is a bit much. I didn't have an identity crisis when I found out that the Bode plots, and circuit designs (some of which took 10s of pages) or transfer functions I had to produce during my EE undergrad, could be easily produced by computers! In fact, I was expected to hand derive/compute things which were essentially solved problems for a long time. Maybe this is different ... but every other field has been continuously been disrupted for decades. I would blame the AI industry for also sowing panic and discord.
I don't think the main point is to create a welfare program for nerds (although, if you believe the AI industry then this is going to be necessary but not sufficient). The point is to save some essence of the field from extremely well funded companies (really like 2 or 3 of them). Companies', whose benefactors, do not really care about Jacobians or groups etc but cold hard returns.
The AI industry views math as a "way point" on it's quest to capture all the "value in the future light cone" or whatever. Just a benchmark for more investment; and will hollow out the profession for this pursuit.
We can argue if Mathematics should even be a profession anymore. And that is fine! But obviously current mathematicians have an opinion too!
Looking from the outside, it does feel like the tide is shifting. I spoke to Terry Tao at ICM (https://www.newscientist.com/article/2583307-why-mathematician-terence-tao-thinks-ai-must-spark-a-rapid-revolution/) and was surprised to hear him very directly say that mathematicians need to organize and take the narrative back from the AI industry. An attitude that inspires more hope than the barrage of press releases out of silicon valley for sure.