I would push for an audit of the whole mathematical corpus (all articles etc ingested by the present AI) as soon as possible. Since there are of the order of 10^7 articles, compared with the progression of results announced, this might be possible in less than a year.
All these results exploit the existing corpus. With enough time and maybe several orders more attention, we humans would discover these results.
So instead of producing heaps of new proofs (but be welcome to do this IMO), make an audit, OpenAI or Anthropic or anybody who listens.
The title communicates a different idea than the body of the text. I'd rather give a quote from the body, which is very reasonable:
"We believe the recent developments have profound implications for mathematics but the systems are likely to be comparably strong in other technical domains, including cyber security, autonomous weapons, biological and chemical agent development and the spread of misinformation.
I have previously compared the arrival of these new AI tools to the moment Galileo picked up a telescope for the first time and was able to see things in our solar system that we’d never seen before. It is an exciting and transformative moment to be doing science. But it is also a very dangerous period and we need to be careful about our use of language when describing these dangers."
So the "problematic" part is not about mathematics, really.
Thanks. IMO the most fun is in the CAPTCHA, which turns on its head the Turing test.
But it goes even further than their greCAPTCHA and it solves their consumed time problem.
Indeed, in their proposal they have a human bottleneck, but in the june 2026 proposal is suggested that one could use an AI to generate the results without the knowledge of the submitted article.
If the AI can generate a pretty close result, with the article fed gradually as a prompt, then reject.
And even further, that it might be not even a need to publish anymore.
Just use the article for training and make a public database with some numbers about the successful researcher, where we see an influence score (how many times an idea from an accepted article are used by other accepted articles), a publication score (how many articles the author had).
I wonder if the reality will be more or less surprising, my bet is on "more".
Sorry to be uncool and try and explain away the joke, but. I'm reading three parts to this.. one is the risk to the job of researches, by the impacts of the systems that they have typically used until now, by being flooded with texts that look like research articles, but are produced by llms.. another is a critique of that system in the first place, in the interaction of both for profit publishing, and research funding based on measuring of publishing in those for-profit journals..
and then there is also a concern about theft of work, and plagiarism, by AI providers, ingesting pre-published work, and training on it, and additionally those providers maybe acting as gate-keepers or .. imposing their own normative values or being opaque and not impartial in how they operate..
Did I parse that correctly?
Yes. The main idea visible through this pile of problems is that human ingenuity (of the management) will find a way to use anything for more money (publishers) or more prestige (academic researchers).
The mathematicians who complain now had no worries about the way the generous idea of open access turned into the gold open access, where the author pays for publication.
These people have no problems with the phd students who are forced to publish or perish and even if they survive there is no future for them.
Now the problem is IMO that for the first time the interest of the publishers and academics are not aligned.
Publishers want more articles to sell back to the academics.
Academics are pushed by the system to publish more.
But all the work is done by academics who write and review the articles.
And also a huge inflation of articles devalue the publication unit.
So a CAPTCHA idea is only natural, even if the kind of a malefic idea a manager could have.
The last days we are served these high goals about understanding, "digestion" and so on.
But if you look at the practice of present mathematics, in the last 20 years it is all about publishing solutions to problems.
There are famous problems to be solved, there is a hierachy of conjectures to be solved. A quick search here on HN gives pearls like "Theory building papers are dime a dozen and don't get published in high tier journals unless they solve a problem".
And all of a sudden it turns out that problem solving can be automatized.
So then what will problem solvers do? Well, from now on they will "digest" problems solved by AI.
In a way or another they will find a way to stay on top.
That's the goal, at least, but mathematics as a living practice does not have much to do with these games of power.
“You are right. There is nothing in yesterday’s mathematics that you can prove with
exterior algebra that could not also be proved without it. Exterior algebra is not
meant to prove old facts, it is meant to disclose a new world. Disclosing new worlds
is as worthwile a mathematical enterprise as proving old conjectures.”
Gian-Carlo Rota in “Indiscrete Thoughts”
Yes. AI is a useful tool and we are going to adapt and use it.
The phd student will be forced to publish 10 breaktrough articles, the university department which does not offer "free" access to AI (for its members) will see the its ratings going down, when compared with the other universities.
It will be "use AI or perish" for academic management so on the side of academic management the ones with vision will thrive and the ones without will perish.
But what about the publishers? In the last decades the academic research was made into a feeder for publishers. The main goal of a researcher is to write articles, which are later sold back to other researchers.
This economic system is under big stres now, because for a while at least the academic management and publishers will have contradictory goals.
And that is why this scare which is induced by those who profit the most from the present system.
Arxiv is a good blueprint for what we should build on. Terry Tao gave a recent talk about how "canonicalization" is the key bottleneck. The limitation of Arxiv is that is non-canonical, non-peer reviewed. However, there is no reason that journals should have a monopoly on peer review (it should be noted that peer reviewers aren't even directly compensated for it, granted it is supposedly "priced in" to academic salaries.)
Yes. See ICLR for example, which is a peer-reviewed conference, on the OpenReview platform, with no publisher involved, the papers are just hosted on the OpenReview website. It's a similar situation with ICML. NeurIPS also doesn't involve any traditional publisher. Because why would they? There is an online platform to do the reviews, discussions, uploading the camera-ready etc. There is no real role for IEEE or ACM or Elsevier or Springer in this any more. Machine learning as a field has shown that it's perfectly doable, over many years now.
This will not happen. The fear comes from the real problem: publication as a measure.
The mathematics itself will only benefit from the discovery of cross links from the human created literature. Think about these LLM as infinitely patient and very long attention experts in what was already done.
So on one side, for a few years at least, it will become normal to publish tens of articles. The article inflation is what scares the present system.
On the other side, after a while, when all the existing mathematical corpus will be mined and most of buried connections will be explored, we shall have a much more better foundation for future mathematics.
It is very naive or misleading to think about mathematics as if it were chess or go.
In few year these (future) tools will be in standard use.
Most mathematicians do compete for funding, based essentially on how many articles they can publish and where. Publication strongly favors problem solving. Universities are ranked on the same criteria.
What we see is a panic reaction to the fact that problem solving is "easy", which affects the future of the management of mathematics, not of mathematics itself.
Mathematicians are not luddites afraid of AI, is the academic publishing industry mixed with management interests speaking here.
- that it was stirred by the International Mathematical Union Committee on Publishing
- that is a mixture of the older San Francisco Declaration on Research Assessment DORA https://sfdora.org/read/ and recent fear of commercial AI competition
The academic system developed in the last ~50 years will crumble. On the broad scale of human intellectual history, this was a blip and not even the most productive phase. But it provided mass office employment and so this is all much more about the general knowledge work job replacement issue than anything specific to math. All desk/computer/office jobs will face the same fate. Math is just easier to verify. But engineering design, architecture, lower levels of lawyers and accountants where the selling point isn't charm and connections, they will all have this moment soon.
The is no "the mathematicians". Some mathematicians, very influent ones, are mad at AI, for social reasons, because it shows problem solving is "easy".
Mathematics is fine and will be fine in the future.
Mathematics called and says she's fine. She's curious about how is that possible.
Misaligned are the present academic merit system hand in hand with financial interests of academic publishing industry.
The system will be exploited and there will be an inflation of problem solving articles produced with AI. Nobodies will be more productive than 10 Fields medal recipients, each year.
So of course that the ones at the top of this system are scared.
This is a social problem of the present system, not a problem of mathematics.
Mathematicians will do mathematics and politicians will do politics, what's new?
Second, I think very relevant that the original meaning of "encyclopedia" is "recurrent education".
So I arrived to think that the present and future forms of AI in mathematics and sciences should be seen as modern day encyclopedic efforts.
Once we pass over the flurry of solving famous open problems (and wouldn't you like to know?) the next natural step is an audit of the ehole corpus of mathematics and sciences accumulated until now.
And then pass further on a saner basis and damn about problem solvers and unhappy publishers and management.
I struggled a little bit reading this. but I think your point is valid. if we are actually advancing the field then we should just be unconditionally happy. ignoring the attribution issue, there is a real concern that the process of math has been somewhat undermined. so we have a giant lean proof that shows that there is a solution to an important problem. but we didn't find the solution, and we didn't get it expressed in such a way that it helps develop the common language of mathematics, and thus isn't a very useful building block for later work (like the actual solution).
the math people seem to really keep an eye on what's important, so I'm sure this isn't going to lead to fields medalists hanging around in dive bars all afternoon stretching out cheap pitchers of beer. but this is kind of a slop problem.
> I struggled a little bit reading this. but I think your point is valid. if we are actually advancing the field then we should just be unconditionally happy.
If advancement comes at the expense of having fewer (or no) humans left in the field, then no.
They're eating the seed-corn, and you're cheering them on. Don't be so short-sighted. There's a reason farmers keep seed corn, and it's because they'd like to eat again next year.
We're singing and cheering our way into an intellectual famine.
Concrete example: Navier-Stokes. I don't make any claims about the truth of the announcement of the proof. But for the sake of the argument le't just suppose we know now that there is a smooth solution with smooth boundary and initial data which blows out in finite time.
Navier-Stokes is the simplest among evolution problems for continuum media, because it has maximal material symmetry (that's the mathematical meaning of a fluid).
If this is solved then go to a harder one, Coulomb friction. As a real life phenomenon, friction is very interesting to explore and mathematically is much harder than NS.
So it is not like we will ever be left without things to think about.
Oh, you want another? The present AIs are things made of mathematics. I would like to understand as a mathematician how and why they can beat human problem solvers?
Is that because mathematics is in some precise, interesting sense, more "computable" than it seems?
I would push for an audit of the whole mathematical corpus (all articles etc ingested by the present AI) as soon as possible. Since there are of the order of 10^7 articles, compared with the progression of results announced, this might be possible in less than a year.
All these results exploit the existing corpus. With enough time and maybe several orders more attention, we humans would discover these results.
So instead of producing heaps of new proofs (but be welcome to do this IMO), make an audit, OpenAI or Anthropic or anybody who listens.
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