I really struggle to understand this discussion. Mathematics isn't a way to keep a specific kind of intellectual happy by providing fun, meaningless puzzles to solve in isolation. It's the bedrock of all other science. The goal is to find solutions and to advance the field - but we seem to be treating it like some sort of occupational therapy for bored geniuses.

As we solve lower level problems, we can unlock real world math solutions. Stellerator Design, Quantum error correction, Predictive superconductivity, Inverse protein and enzyme design - the list goes on. Many solutions AI can find can bring us closer to these - so let's fire up whatever datacenter we can find and get us to these outcomes.

> To me, someone who chooses a worthwhile problem, obtains a proof completely using AI, understands it thoroughly, and uses it to develop interesting further questions or directions has made a substantial mathematical contribution. I would give that person substantial credit even if they supplied no new ingredient in the original proof.

Yup. This is what Terence Tao has been saying about digestion of results for several months now. Mathematics has become a field where results themselves matter less, the social aspect of attracting others to understand your results and explore new problems has become more important.

In a sense it is a little bit like software engineering, where writing code can sometimes be delegated to AI, and is arguably less important than understanding what the customer really wants from this software.

Isn't it the passage of mathematics from the age of craftsmanship to the age of industrial making ?

My recent take on AI is that people haven't adapted to the new huge potential of the tool, and don't dream big enough (yet).

It's like seeing a car engine for the first time, lamenting about the future of horses, and not realizing it'll also help us fly.

Why do nearly all the articles exploring the development of AI applied to math assume that capabilities won’t extend beyond theorem proving?

> other skills will matter more: choosing which terrain is worth exploring, steering fleets of airplanes, and explaining what they find to the rest of the world.

These all seem totally achievable by LLM agents, or at least, I don’t see an obvious reason why it wouldn’t be. 3blue1brown’s recent discussion on this subject was a bit better, but he spent the plurality of main body of the video assuming this scenario, devoting less time to the other possibilities. To me, it seems dangerous to build a math career on the foundation that AI won’t be able to explain math well in a few years, let alone a few months (which seems entirely plausible given the recent math progress).

There's a long collection of comments by mathematicians at [1]. A large number of workers in the field are rather discouraged. The main quality complaint is that the proofs are ugly, long, and incomprehensible. One mathematician comments that the first proofs of new major results are often like that. Elegance comes later. The main social complaint is that the social foundations of mathematics just changed, in a big way. The main practical complaint is "what do I do now", especially from PhD students who just lost their thesis topic. They sound like the Uber drivers fighting Waymo.

One comment was "A common piece of wisdom is that mathematicians only have a few tricks in their bag – which they skillfully apply again and again." Feynman made that point in his autobiography. For various reasons, he had a different set of mathematical tools than others in his field, and that helped him to solve problems that stumped others.

A big AI model has access to all known tools. AIs have more breadth than any human. Some of these breakthrough proofs seem to come from applying techniques from areas different from what people in the field tend to use. I'm not qualified to comment on math at that level, but the comments by mathematicians seem to hint in that direction. That may indicate why throwing vast amounts of compute at these problems works - an AI can try everything.

[1] https://proofsandprompts.com/2026/10/08/100-reactions-to-100...

It’s amazing for me to see math research going from craft to technology.

CS had this moment decades ago, sans some theoretical parts that are joining the bandwagon now.

I did a bit of math research in grad school collaborating with my math postdoc roommate. I found the aversion to any computation making its way into the craft to be odd decades ago.

Well, now the proof’s in the AI generated pudding.

I wonder what LLM's would achieve (if anything at all) if no mathematicians had used it to format their articles, etc (remember, no data is being used to train models! Of course).

Given the capabilities of OpenAI's unreleased model, I think the model helps mathematicians more than it hurts them. Some of the open problems that were solved were "It would be nice to know that", but many of the others represented ways in which we had been stuck for many years. There had been very little progress on analytic number theory, particularly the Riemann hypothesis or its variants. (One result, "no Landau-Siegal zeroes", even had a 10-page elementary proof that everyone missed for a century.) Complexity theory had seemingly more open questions than results. Progress could meaningfully accelerate now that we have a quick test of which of our ideas are good, and which are bad.

The wildcard is that we have no idea what the model after that will be capable of, or the model after that.

It’s strange to me seeing multiple talk about how Terry’s viewpoint has evolved or not as a response to this post. He didn’t write this.

> But even if it had solved every problem in the Langlands program, to imagine that would have “solved number theory” would be as naive as saying that the construction of the periodic table solved chemistry.

Of course if you solve any existing problem, new ones appear. That's not the point. The point is that AI will be able to advance on any problem better than any human.

> To me, someone who chooses a worthwhile problem, obtains a proof completely using AI, understands it thoroughly, and uses it to develop interesting further questions or directions has made a substantial mathematical contribution. I would give that person substantial credit even if they supplied no new ingredient in the original proof. Choosing worthwhile problems may end up mattering more than producing proofs.

That is the correct take, but I can understand that given how current funding system (esp grants) work the incentive are stacked against doing that.

It's worth mentioning that many of these papers haven't been fully reviewed and confirmed as being correct. Several had to be retracted upon closer inspection. Too many people are assuming that passing lean checks for some of the papers means that all of them will hold up under scrutiny. It remains an open question if humans or any available system are capable of peer review for some of the more complicated proofs.

This is just a side point, but:

> We have much more control over how we hire mathematicians, publish papers, and train students than over the behavior of trillion-dollar companies, and that is where our efforts would be better spent.

We should also make sure that there are no trillion-dollar companies. The existence of large and powerful companies is a problem, whether or not the field of mathematics is in crisis. All these companies should be shattered so that they cannot do things until after society as a whole is sure they're okay with those things.

I wonder if this happened to math first because the goal is so clear (proving a statement, etc.). Math is just going through it first, and I think other fields will get their turn soon too. If so, I'm not sure if things like a PhD are even needed. Someone in a bachelor's program who just learns the basics and how to use AI tools might be better.

It has changed from elegance and human understanding to brute force. But that trend was started a while ago, before AI became really useful.

From TFA:

"I’m ready to board the plane, because I want to see what’s there. At the same time, I would add that people who previously have been walking around on earth with their eyes closed are not going to recognize anything however high they fly; I still believe that many of the skills that mathematicians have now will not only be transferable but vital to the new world order."

That sounds a bit disconnected and rude.

Please can we add the name of the guest authors in the titles of these posts?

It sounds like Maths Co. will be only hiring forward deployed mathematicians from now on.

I mean he's basically admitting that math academia is outdated.

If we don't interview candidates based on results, what is it? Politics. It already was. I had a JEMS paper in grad school and got zero postdoc offers. Many other cases.

The real shift is that math will become a hobbyists game. Make money other ways and then spend your money on humans and tokens to solve your problems.

Terry's stance has shifted gradually. This reminds me of Garry Kasporov's response and stance a few decades ago agains deep blue (and deeper blue). I think in a closed system/game (or "field"), this kind of AI superiority is inevitable. However, I do agree with Terry that we need the right form of transition if we want to continue holding the rein or at least playing a part in the subject.

Useful reference to "Colossus - the Forbin Project".[1] Watch starting at 00:30:00, and see this scenario predicted in detail, half a century ago.

[1] https://archive.org/details/colossus-the-forbin-project-1970...

“Note there is also a difference between knowing mathematics deeply and explaining it fluently; they are related but different skills. Ideally I want both, but it is the first that I ultimately value more highly.”

Once again perpetuating the cardinal sin of lionizing mathematics heroes. Which to be fair is just THE culture of higher mathematics.

What good is a minuscule elite Cabal of savants? If these deep insights are inaccessible to 99.999% of the population, then they are no better than the manuscripts written by AI. We already have those.

The whole situation in mathematics reminds me of two years ago when models started coding well and all the developers were really sad. Now we use it as a tool and, as a whole, are able to make much more.

> someone who chooses a worthwhile problem, obtains a proof completely using AI, understands it thoroughly, and uses it to develop interesting further questions or directions has made a substantial mathematical contribution

among all the discourse, it seems mathematicians are vaguely converging on this higher layer of abstraction being where the human value in math is now. It seems across domains (such as in software too), people speak of “judgement”, “taste” and other fuzzy concepts around defining problems rather than solving them. The lowest level of abstraction where humans win is asking the questions, rather than merely answering them.

As math is so verifiable, the “transition” seems most poignant and quick there. Watching these big name mathematicians discuss this unfolding revolution in real time is fascinating.

I theorize that number of problems AI is possible of solving is limited. My theory rests on an assumption that all human knowledge is a result of lived experience. AI as a statistical machine doesn't know lived experience, therefore it can't solve problems that a living person interacting with reality could solve. Therefore human brain > AI, or so long AI is unconscious anyway.

Sure it can solve math problems by just following the implication arrows. But those are just low hanging fruits, i.e problems that humans were too lazy to deal with.

> gulf between ... novel proofs and ... understanding

Machine proofs are useful machine understanding. You don't read the proofs, that's holding it wrong. You point another agent at the proof and prompt "use these ideas to prove this lemma that's useful to me". And it works, agents are faster given access to the proofs than without.

> But even if it had solved every problem in the Langlands program, to imagine that would have “solved number theory” would be as naive as saying that the construction of the periodic table solved chemistry.

This analogy is pants on head stupid. They're talking as though the only thing AI will ever solve is the Langlands program, not as though we have discovered a generic tool.

It's like saying "they drove the car one mile -- and every mile driven leads to more roads that we can trot along, why are you so worried about the future of horses?"

What is the current thought on AI creating new emergent forms of mathematics? Even the most stunning results like the proof of the quasi-RH are a clever combination of known mathematics. Humans have created (discovered?) stunning new ideas (e.g. complex numbers) that have opened wide new horizons -- do we think AI will be capable of creting / discovering novel new things like this?

There’s an elegance to how the Feds just got out of funding this stuff and within a year all proofs were solved by the private sector

I know, unrelated truths and coincidental timelines, part of me giggles nonetheless since the whole belief system behind the market relies on infinite coincidences

> Much of the reaction seems to reflect a feeling that the subject that they love is under attack, and is being “hollowed out”.

Sums up the reaction from a lot of developers too.

Mathematicians can just say no to this technology.

1. Make mathematics a closed community, only people who join this community can read and work on its stuff. I imagine a VPN that contains all maths knowledge that only members can view, similar to how big tech handle their codebases. It needs to be hard to copy and paste that stuff into the open internet and doing so should involve serious punishments like jail time, similar to posting say proprietary Google code on the internet.

2. Anyone caught using AI is excommunicated from the society, his access to the VPN permanently revoked, and his work is never interacted with again.

3. There will be a bit of a disruptive period as maths moves from open to closed model. During that time AI will keep solving more problems, but as long as mathematicians stop contributing more open problems, at some point AI will stop (either because it has solved all open problems, or it can’t make progress anymore because scaling is no longer economical).

I think Association for Human Mathematics should do this, I think they will be surprised by how much funding the public is willing to allocate to this (public hates AI), because fundamentally humans like thinking about and doing maths, and do not mind dedicating a bit of the surplus produced from society to let others do this, similar to arts. Just because I can prompt a better melody from Suno, doesn’t mean humans will stop wanting to make music.

Of course other mathematical associations can and should form, which fully embrace AI. But if the VPNs secure, these associations will not be competing as they won’t even have shared consensus of what problems to solve. They both will still need to compete to get public funding, which is fine, I think AI math will have a harder time justifying their funding since anyone can prompt a robot.

Wake me up when AI solves Collatz.

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Three years ago people were laughing at LLM arithmetic mistakes. Today the Simons Foundation is starting up a fund to keep professional mathematicians from suiciding:

https://www.simonsfoundation.org/news/simons-foundation-laun...

Anyone still pretending this is normal technology is completely delusional. We're in the beginning of a singularity takeoff.

Have the pro-AI people finally found a new mathematician? Otherwise it is always the same 10 people on Tao's blog citing each other.

This guest author runs a seminar to lure people into AI:

https://math.uchicago.edu/~fcale/AI.html