This Math 1.0 followed by Math 2.0 framing is wrong. Mathematics did not start a few decades ago when problem solving became the norm. And it will not end now when problem solving turns out to be "easy".
Mathematics will revert to it's main practice, which is to study.
There are lots of weird panic reactions by some prominent problem solvers. See for example the ridiculous cease and desist like statement of AHM shared at Tao blog.
Put this Math 1-2.0 with that AHM statement together and you'll realize that this is a power struggle and that you see only one side of it.
Mathematicians have very diverse opinions about this. I, for example, am for as much as possible automatic harvesting of all these "low hanging" fruits. Should be disclosed as soon as possible, free of any bottleneck, and citable. The mathematics community may do whatever its various members desire to do with these results. Let them decide individually what to do with them. This AI tool is here to stay.
But what if the fundaments of all these, in the human produced literature, actually contain hidden circularities and holes which make very hard the progress?
IMO for the moment the greatest value from these AI tools is that we can start an audit and hopefully proceed on a saner foundation, after we use the tools and think about it.
This is different than too many AI generated proofs or panic reactions from the academic system with its stupid incentives.
This is something I like joking around about, with regard to how LLMs are 'decent' [debatable but taken as a premise] software engineers. For a long time people have said DNA/RNA/etc is the programming of life.
If it is indeed HIGHLY analogous to programming, we would then expect LLMs/future systems to be HIGHLY proficient at accurate ex-vivo gene [or enzyme/protein] modification/construction
It is akin to programming but more complicated. In this case, you can run the same code on different systems and get different results, and this is in fact an advantage of the language as a whole. Same DNA throughout your entire body yet you have distinct cellular identities thanks to this ability.
But the hard part is really nothing is annotated or defined. We have annotated and defined some things but its tricky work and so much left to describe. Its like you have entered a house and have no idea what each room is for, or what the light switches do, or even what even is a light switch, or a room for that matter. Maybe you identify a repeated plastic switch through the building that seems to be nearby doorways, you call this the light switch. What does it do exactly? Have to flip it and hope you can detect what changed. Hopefully when you flip it the whole house doesn't just die in the womb, but actually limps along in some way where you can say "this switch controls the garage developing as an attached structure or detached in the back yard" Even more fun when the switch is just one piece of the circuit of a dozen plus switches that all have to flip a certain way in a certain order over a certain time for some function.
You will probably find this paper by Hessameddin Akhlaghpour very interesting: [An RNA-based theory of natural universal computation](https://pubmed.ncbi.nlm.nih.gov/34979104/).
I have bookmarked the links to read later but until then I would ask in what sense? To my knowledge the known physics currently is all within the realms of a Turing machine, which is equivalent to lambda calculus.
You can play with it. Equivalence with Turing machines is not the point of interest
Sorry about this "not A but B", now is one of those situations where is needed.
Is not:
- cellular automata,
- Turing machines
implemented chemically.
The goal, first of UPIM, then chemlambda or chemSKI, is simply to:
- find chemical complexes,
- or to make them
(though I suspect that we shall discover them in our cells)
so that they enter in random chemical reactions which are akin the graph rewriting inspired by lambda calculus or SKI combinators or Interaction Combinators.
The thesis is that this chemical translation still can do "anything" despite the lack of control of reactions or the combinatorial explosion of possible reaction networks.
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 will revert to it's main practice, which is to study.
There are lots of weird panic reactions by some prominent problem solvers. See for example the ridiculous cease and desist like statement of AHM shared at Tao blog.
Put this Math 1-2.0 with that AHM statement together and you'll realize that this is a power struggle and that you see only one side of it.
Mathematicians have very diverse opinions about this. I, for example, am for as much as possible automatic harvesting of all these "low hanging" fruits. Should be disclosed as soon as possible, free of any bottleneck, and citable. The mathematics community may do whatever its various members desire to do with these results. Let them decide individually what to do with them. This AI tool is here to stay.