Every single knowledge worker is going to face this kind of crisis. It will be worse for people who cared deeply about their craft, but the crisis will have the same shape. The way through is to change the way you relate to your work, and to appreciate the fact that you can now produce far more output.

Mathematicians should realize: instead of spending decades on individual theorems, you can now create whole new subfields of mathematics. Of course, you won't be doing the creation directly, in the way the mathematicians of old did; that's just not the name of the game anymore. But you will still be directing the research and involved in the creation.

Grateful for this essay. Made me feel seen.

Someone said:

> No one is stopping you from doing what you enjoy.

But that's wrong. LLMs are creating an environment in which some things are no longer enjoyable.

For example there is less joy to be had in learning a programming language in 2026 than there was in 2016, because there is less utility in it now.

As a mathematics person, I find this at odds with my views. I know the current regime rewards new mathematical discoveries for professional advancement, but that is a job thing, one which can be altered by the powers that be. To me investigating mathematics is fun whether it is new to the world or not. The complaint is similar to lamenting how everywhere has already been visited and there is nothing to be done other than have your own personal experience of a place. I saw the redwoods recently for the first time and I thoroughly enjoyed the experience despite not being the first person to see them. Mathematical discovery is much the same except now we have tools that help us dramatically with the tedious stuff, the researching what others know. In the old days, I would spend a long time figuring something out and only at the end could I figure out where to find it in the literature. Very frustrating. Now, we have machines to guide us to many things and understandings and clarifications. They are guides that help us get to where we want to be and then let us wander as we desire. This is incredible. I am currently using them to develop the computational tools I want to use to explore stuff.

As for squeezing in the time to do mathematics if the paying jobs disappear, there is a good chance we will have a world of plenty very shortly. I have a belief that the Austrian economists are right that there will always be plenty for humans to do and get rewarded for, but I also think that the costs of living will be so low that someone who wants to do mathematics will have plenty of time to do so. I hope this person holds the faith long enough and tries to see how the AI's can help accelerate one's own understanding. I am no fan of AIs generating a bunch of papers that no one reads or cares about, but I could say the same about the immense number of papers made by humans as well. If anything, the AIs make all of that immense knowledge more valuable as it is now knowable and accessible through these tools. There is also the fact that the mathematics job market has been oversaturated for at least 20 years. What our new tools allow is for people to be able to do mathematics outside of having access to a research library and top mathematics department.

> For me, the affective quality of learning mathematics is empathetically tethered to an act of discovery and creation. It is social. We are conversant with another mathematician—perhaps long dead. If we follow the chain of communication we arrive at a mathematician who enjoyed some original discovery. Human mathematics is Talmudic. It is a lively discourse of philosophical and religious richness spanning thousands of years.

This is really beautiful. And no matter what happens, two things have to be true: some form of lively philosophic and religious richness will keep being a core part of our history and will touch every person in some way; and it will change enormously over time (maybe with math continuing to be a small part, maybe not).

There is a part of math that is like that. There's also another part (as Vladimir Arnold provocatively said):

> All mathematics is divided into three parts: cryptography (paid for by CIA, KGB and the like) hydrodynamics (supported by manufacturers of atomic submarines) celestial mechanics (financed by military and other institutions dealing with missiles, such as NASA).

> Cryptography has generated number theory, algebraic geometry over finite fields, algebra, combinatorics and computers.

> Hydrodynamics procreated complex analysis, partial differential equations, Lie groups and algebra theory, cohomology theory and scientific computing.

> Celestial mechanics is the origin of dynamical systems, linear algebra, topology, variational calculus and symplectic geometry.

Those parts can just be delegated to AI the same way they used to be delegated to mathematicians. But Arnold continued:

> The existence of mysterious relations between all these different domains is the most striking and delightful feature of mathematics (having no rational explanation).

When I was in mathematics, reading other people's work was always more rewarding to me than doing my own. I would spend years on a question to get some progress, versus spending a few days or weeks reading a paper to enjoy something new. I understand not everyone is like me but I really welcome the omniscient mathematician machine people are predicting. I can't wait to ask all the questions I care about.

It should be a mandatory part of a technology-related degree to watch "The Man in the White Suit" (1951) https://youtu.be/RC8q1QSkE3M

When a new technology comes along, it diminishes some aspect of the human experience - because whoever had a talent for doing things the older, more difficult way becomes less important.

In that regard, AI is the extreme, because it threatens to make so many of our intellectual talents useless.

One way to differentiate between an art or a craft and a science is that if a genie appeared and offered to trivialize all the discovery work of your career and simply give you the answers today, and you'd say "no", you're probably not doing science.

It is amazing how the scales of time we consider are shrinking even as change is accelerating. We are concerned about individual changes, that will quickly be followed by cascades of more change.

> Something fundamental to the experience of mathematics is being taken.

That is the near term. At least "near term" like we talked about it five years ago. And it won't stop.

AI isn't a tame long term transition - in scale it is bigger than any transition since the first individual cells. In speed it is happening faster than web adoption. No human adoption bottleneck. They are taking the reins of our tools, and don't need human adaption to improve.

Ineffables, and our intellectual primacy are going away, right now, even as we think about it.

I am not making light of it. But not surprised, because how could AI not redefined everything.

But maybe not everything:

20 years from now, 50, 100, there will still be ineffable experiences at the frontiers, by different beings. I believe esoteric curiosity and the intrinsic rewards of discovery will continue. Our propensities to find idiosyncratic interests and pursuits, seek answers and adventures, exist in our psychology because the low median return is decisively outmatched the extremely hight mean returns of unanticipated progress. The benefits of many pursuits will be even greater for them.

It seems unlikely to me, that future beings will become less interesting.

I relate to the author. Anyone who isn't feeling butterflies or stones in their stomach, isn't really processing the moment.

I feel seen and heard.

I'm conflicted in feeling there's now a lot more to do with AI, but also if it ain't me doing most of it, where's the fun in that? Days feel meaningless, and don't know who will pay for what I want to do, after all these years of heavy training.

> “Even if AI can prove theorems and theory-craft more efficiently than humans, and even if these proofs and theories are beautiful and interesting, and even if they are presented with elegance and clarity of thought, mathematicians will still have a place in the appraisal, presentation, understanding and appreciation of this new abundance of pleasing non-human proofs. We can still practice mathematics, learn mathematics, teach mathematics and do mathematics together.”

I am not a mathematician, but this seems like an entirely non-problematic answer to me. Mathematics is ultimately the discovery of relations and their consequences, so of course large language models were eventually going to catch up. But precisely what they do lack is ability to appreciate these relations.

The author says mathematics is a spiritual pursuit.[1] I have asked LLMs about theological topics before and they have also been able to produce perfectly cogent answers (even heavy questions like “how did Aquinas view Pseudo-Dionysius’ negation-laden description of God”). I am not the least bit shaken by this, because it is still on me to evaluate and understand, and appreciate these answers.[2] The author seems to think LLM’s pattern recognition makes redundant human understanding and appreciation, which is a logical leap that doesn’t make sense to me. Maybe the author is conflating utility and purpose? I feel bad, and hope the author takes care of themself, but I really think the author is taking a massive leap here. It is not that deep.

[1] I begrudgingly agree, but with the caveat that tending to a vegetable garden in your backyard is also a spiritual pursuit. Mathematics isn’t some special discipline that elevates you beyond other people, as much as it is useful and interesting.

[2] I of course wouldn’t consult an LLM if I actually wanted to educate myself or reason about these topics. Not only do I want to reason through them myself, but when it comes to issues in philosophy/theology/heavy stuff, you need to take in to account the perspective and experiences of the human writing them. LLMs muddle everyone’s perspective together.

Well for me the twilight had already come when I realized I’d never amount to a decent mathematician. Maybe this is rather a common experience?

LLMs just democratized that process.

Without knowing anything about the specifics of the conjectures that are falling, I wonder if this affair highlights an issue with the quality of the "open conjectures" that are out there.

There are a lot of reasons you might make a conjecture. Perhaps you are motivated by a search for structure: "We suspect that these objects behave like this, therefore we naturally imagine that...". But you might make a conjecture out of empirical evidence: "We checked 1 million examples, time to make a conjecture." While empiricism has its place in mathematics, it might not be the best motivation for a conjecture. As Bishop said, "Do not ask whether a statement is true until you know what it means." If you pose a conjecture based on empirical evidence, perhaps you should be thinking more about why you would imagine your statement be true in the first place.

I know some will think that this rings of goalpost moving, but when I hear about all these counterexamples spelling the end of mathematics as we know it, I just wonder how strong those conjectures really were in the first place. Again, I haven't actually dug into the specifics of any of the results so admittedly I could be totally off base, but I do know that not all conjectures are created equal.

> Mathematicians are, indeed, also paid to teach, peer-review, go to conferences and learn mathematics, but all of that better result in some damn good theorems.

As a mathematician who publishes theorems, I think this is mistaken. New theorems in abstract and pure fields of mathematics never had the economic value of what mathematicians are paid. Even creative works of art can be displayed but mathematical papers are unread by anybody except a tiny number of people who wouldn't want to pay all that much for them if they had to.

The economic value of mathematicians is to teach mathematics. Proving theorems is how we build the credentials we need to be trusted to be allowed to teach it. Teaching young and less young people how to navigate through a mathematical problem is how we make ourselves useful.

LLMs coming up with counter examples to obscure conjectures (albeit old and important to a small number of people) is only a threat in that it removes this ritual of belonging.

Many people are excellent teachers (and very competent mathematicians) without publishing new theorems, and many theorem producers are atrocious teachers.

Perhaps the pecking order may change. Or maybe something else will happen. Maybe society will decide to replace all its teachers with AI, or that mathematics is no longer worth learning. I don't know. But what I know is that nobody saw any of the papers I wrote or the theorems I proved and thought "that's money well spent".

Apologies is this is a simpleton question, but how does this differ than most of the mechanical work previously done by hand, but is now automated?

> "They are forbidden from creating original works to express themselves. However, they are still permitted to comment on writing, interpret it, share their taste. They are still valued for their appraisal, presentation, understanding and appreciation of creative writing. They just can’t write creatively anymore. They can go on as an enthusiastic spectator.

> ... It revealed that the process of prompting novel proofs will be as auraless as ordering doordash. Watch as magic and mystery evaporate. Watch as the sun sets on our heroic age. Is there not something evil in the act of blocking all future generations of mathematicians from the experience of discovery? Forget about accuracy or even attribution. Something fundamental to the experience of mathematics is being taken."

These passages resonated with me, as someone who has been enchanted by writing software for almost 60 years. It crystalizes something that has been nagging at me for many years: I like writing software. Reviewing, testing, spec-ing, designing, etc. are all important, but they are all incidental to the actual creation of software. They are all necessary for me to do if I'm going to write software, but they are peripheral. I didn't latch on to computer programming because I got into flow state reviewing code, or spec-ing it.

And this is happening in one profession after another. For example, fighter pilots. I suspect that a fighter pilot feels about flying jet fighters the same way that I feel about programming. And he or she will soon be exactly as useless: Doing things related to flying, from the sidelines, but not doing the thing him or herself.

AI is stealing all the fun parts.

Have LLMs produced something novel like Cantor's diagonalization procedure once was? Come up with new concepts like set theory once was and axiomatized it? Is there any indication or evidence LLMs can do this? If not, I would wager mathematicians are still going to be a profession in the future. Maybe not as theorem provers in a particular axiomatized system where LLMs can be effective tools but the wider project of synthesis and unification, and the discovery of new modes of mathematical thought will still require mathematicians.

How much of the identity of a mathematician is tied up in being the first to discovery? How much of it is the contest between smart people producing excitement? Maybe someone could chime in on this.

For a mortal like myself, I've never discovered any new mathematics. All I can do is appreciate what I'm taught. But I can still appreciate it. I still watch videos of people solving high school/uni level questions. Why can't you appreciate this new counterexample, just because someone used an LLM to find it?

It's also worth looking at other times technology has changed our world. We invented various engines, so there's not a whole lot of economic value left in being a big strong guy anymore, but plenty of people still exercise because keeping in shape makes them happy.

This is the first I've ever heard math connected to the spiritual. For all my life it has been this rigorous thing grounded in reality in such a way that only people who think a certain way could even approach. Now those people are having this strange "crisis" because AI is being more rigorous than humans I guess. I find it... wild. My, but how the mighty have fallen.

It’s ok to mourn the loss of a frontier and also support the thing driving that loss. The way it looks, the generation of mathematical results will become less and less of a human endeavor. There’s a way that’s sad even if on the whole it is a huge leap for society. This was a great article, and I applaud the author for acknowledging this head on.

A silver lining to think about.. Currently there's a big issue (at least in some countries) that mathematicians must publish from 5 to 7-8 papers within a 5-year window to keep the tenure. So it's a minimum, much more is expected for grants. Yet high quality mathematical papers do take longer to finish (or sometimes to even start), especially if the researcher is working solo, not within a lab. Until today, the answer is to go for applications or for low-hanging fruit. Tomorrow, with the boost of AI help, the researchers may be able to spend more time on their "real problems"

Math is having its DevOps moment. And yet, people who really understand networks are beyond valuable.

In times past having one's photograph taken was a soul-stealing for some.

Some notions:

- finding counter-examples is one of the most exploratory uses of calculation

- there is no evidence, not even in the hands of the inimitable Terence Tao, that Approximate Intelligence (AI) is insightful rather than inferential*

- people who enjoy Mathematics, even amateurs, do so for the beauty

- AI is only good in the hands of those who can provide corrective context

- AI unchecked is a remarkably inefficient noise engine

- Mathematics will provide joy to the curious 'til the heat death of the Universe

- AI is contributing to the heat death of planet Earth

- anthropomorphism, of which I am otherwise not a fan, may yet be a saving grace as without proprioception we may not morph

- we may need to redefine the Turing Tarpit of Perlis

If any of this nonsense really troubles you return again to thermodynamics and revel in the joy of being the local universe's pinnacle of meaty evolution. And go outside and smell the flowers.

* Caveats abound

The endangered art form of human mathematics is one thing. Another thing is that there seems to be little concern for whether a theorem was created using a documented open-weights model or some unknown model in a web chat.

If you want to make the case that the journey of creating the proof is part of doing mathematics, then you should also document that path and make it reproducible, as science should always be.

There were some examples of mathematicians publishing their AI proofs like that in the last days, but by far not all.

> I am suffering a profound spiritual crisis due to these developments.

Another case of Deep Blue.

I actually think it is just the dawn of mathematics. During the last few days I discussed a few questions about abstraction logic [1] with AI that I was wondering about for quite some time (years), but didn't have the time + energy + in-depth expertise, there were like, 4 related questions; it positively solved 3 for me in the way I expected, but couldn't power through before; and for the fourth it proved to me that answering this question would imply solving a known open problem. And I know that it answered all of those questions correctly because I asked it to provide me with Isabelle/HOL proofs for it.

If you are interested in mathematics because it can model things precisely, and you want precise answers about these models, and you want to know how it is all connected (Langlands anyone?), AI is fantastic news. There is plenty of new and interesting and beautiful and elegant mathematics to be had this way, as well.

This is not a time to be scared or frightened. This is a time to be excited as fuck.

There will always be open questions. Now, there will be actually many more of them, because many more people will be asking questions.

[1] http://abstractionlogic.com

Same as programming, I feel like the underlying tension is between math lovers who want new math to be done vs those who want to be the ones to DO the new math.

Both groups love math, but the later group is in a real bind because they have confounded their career with their hobbies/passions.

Welcome to the world of Chess a couple of decades ago...but look at chess now: more popular than ever.

I hope that this doesn't mean that you need write proofs while streaming Twitch. ;)

They are concerned mathematicians are obsolete and seem to be unaware that super intelligence means humans are obsolete.

You need to be thinking about an entirely different form of life for all of humanity, happening in the very near future. Focusing on one specific field that may be earlier in the obsolescence chain is a distraction.

Merit based society based on intelligence or work of nearly any kind is about to cease existence.

For some reason it feels to me that this should make mathematicians feels better. :)

Counterpoint: Benoit Mandelbrot isn't notable for ever proving anything, but highly regarded for having put in years playing around with computers while asking interesting questions about what happens if you abuse the rendering parameters. Same thing with Mitch Feigenbaum uncovering a new constant by drilling down into very simple equations.

The joy and pride of lifting heavy chunks of mathematical infrastructure into place are being made redundant by industrial machinery that any amateur can rent or build for themselves. But it seems to me there's plenty of room to discover new mathematical vistas. The future of mathematical discovery is not cracking hard open problems that everyone in the math community agrees would be an impressive lift, but by bigging into things that nobody else thinks are interesting or important.

Suppose any theorem you set out to prove had already been proved in 100 wonderful ways

No matter how brilliant you are, no matter what intellectual heights you scale, you'll never be Pythagoras or Euclid or any of many famous mathematicians whose insights purchased immortality. Why even live?

To be frank, I occasionally feel this way because I am still absolutely knocked out by very simple things like plane geometry, powers, irrational numbers, exponentiation and logarithms etc. I smile and nod politely about reports of contemporary breakthroughs linking this obscure subfields with another - partly because I haven't put in the years of study to know a great deal about advanced and frontier topics, partly because I'm not smart enough to fully appreciate them, but mostly because they're often about the surprising obverse of some feature in a corner of a utility corridor in the dusty cellar of an annex in the grounds of the Grand Mathematical Temple. Nobody will be able to experience lighting a candle and illuminating the great structures of the main hall for the first time, just like no chemist can ever hope to wake up in the morning and discover a new element and most physicists have abandoned the idea that they will ever be able to do more than tinker around the periphery of the discipline in the hope of extending the precision of measurements by another decimal place.

But the amazement and perplexity about the unreasonable coherence of mathematics (and its equally unreasonable effectiveness in the natural sciences) are what make the field compelling in the first place. The capacity for curiosity and obsession are what yield big discoveries, more so fascination with extending a well-defined knowledge boundary out a little farther. Put another way, pointing out the existence of a problem can be more significant than solving it.

A raw and powerful piece, thanks for sharing.

For years I've wanted to get back into self-studying mathematics, not to make serious contributions but just to appreciate its beauty; but the recent observation that I'll never be able to answer a pure mathematics question that a clanker could not has been off-putting, to say the least.

Unsaid here is that the companies involved have stolen so much (both literally in their plagiarism, and in their breaking of people's spirit), and given back so little. You still need to pay them cold, hard cash for them to help you prove theorems, and meanwhile, mathematicians working at these companies have themselves done little to contextualize and interpret results. That insight has mostly come from outsiders.

> Mathematicians are paid to prove theorems

lol who is paying for this? Mathematicians are generally paid to do other things and get to do this kind of work as a side effect.

Dark night for mathematicians' careers maybe but not for mathematics at all.

OP seems to need to touch some grass, spend time with friends and family, sit by the lake etc. Some sentences in there are quite disturbed.

Regarding math, the new tools are humanity's achievements, they weren't handed down to us from the sky. These tools are spiritual achievements. Just as much as calculators and computers in general. Just as much as the invention of writing and notation. You could also mourn the days when we'd calculate on our fingers only and would orally memorize certain calculation heuristics of geometry handed down the generations.

Regarding jobs, people aren't being paid for having a good time or for having fun and spiritual feelings. When you get paid, someone gives you money. The person or institution giving you the money has to have a reason for doing this. It is very basic logic, but academics don't seem to get this. If your work is pleasing for someone on an artistic or spiritual level, you can find a rich patron, the same way learned scholars did back in the day.

It's not any different from cashiers who get replaced by self-checkout or bank tellers by ATMs. You're not special. It's a job.

And I say this as someone who really appreciates the feeling of gaining insight when cracking a math puzzle or grokking how the definitions fit together and why something is the way it is, why a theorem works, I like mathematical elegance etc. But I don't think that is diminished in the least by being able to consult a smart AI about it.

Pretty sure software developers already had that moment with coding agents. They can't really admit it like this, as it affects their employability now.

> The creation (or even the pursuit) of novel mathematics is one way that humans have historically accessed the ineffable and encountered the divine and mystical.

Would a mathematician please unpack this for me? A theorem is the opposite of ineffable. A conjecture may be ineffable but its pursuit reifies it. I am missing something.

Seems like maybe now we have sufficient tools to actually get on top of string theory. And ultimately it is all about coming up with explanations and formulas and tools that people can use in facing real challenges.

I spent two weeks proving a number theory result myself in lean just to see what I could do. (It’s something about composing polynomials with themselves and what other polynomials you can get that way).

It was a struggle with a lot of dead ends but it is just software engineering. It’s not a world away from getting a Rust program to type check.

The main problem I had with it is that LLMs will happily grind away case checking in Lean until the end of time and it’s up to you to see patterns and find dead ends. For example it wasn’t until I suggested to try translating the problem to a different characteristic that Mythos one shotted the proof (and found a counterexample for a related question I was working on).

My main problem now is _what to do with it_. I am not an academic, don’t know any academics and it’s a minor problem that I picked because I thought it was tractable and turned out to not be in the literature and fairly complicated, and the only reason I spent as much time on it as I did is that I thought I was an hour away from cracking it for about 10 of those days.

(In case anybody is curious about the proof, it’s that you can’t compose a single two variable polynomial over the integers with itself and any number of integer constants via substitution to generate all polynomials, but you can with x^2 - y and 1/2 if you allow rational numbers)

I have two strong reactions to pieces like this:

First, this is about not just a job or career, but someone's identity. And we must have compassion that they are losing something that is fundamental to who they are. To them, it doesn't just feel like they're losing it, it is being taken by these companies that have so often acted in ways we despise

And that is a tragedy! And there are so many tragedies like this that will happen regularly as the technology advances

But my second reaction is one of this great shared experience. I studied math. Many of my friends are mathematicians. And it is now possible for anybody to access mathematical insights or think deeply about strange conjectures and theorems that were previously incomprehensible to anyone who hadn't at least studied mathematics in college

I don't know if 3b1b's Grant Sanderson considers himself a mathematician or science communicator, but I think of him as both. And while I expect he is someone with the mental capacity to find and prove new things in the world, I am grateful for the time he spends instead understanding things at a fundamental level and explaining and celebrating those concepts with his audience.

Not every mathematician can be or wants to be _that_ kind of mathematician. But for the moment, it is enough for me that higher mathematics is more accessible than ever.

And with some trepidation, I predict that the "traditional" job of a mathematician will change (of course it will). And it will change in big obvious ways and also subtle little ones. How will it change, though?

Importantly, math is actually going to be one of the fields where the fundamental things we thought we knew are shaken, because in the next five years we are going to start to see connections between things that were previously considered completely separate.

And so one way the job will change is that anyone who discusses math regularly will need to learn new things.

To me, this is exciting. It's almost like finding a bunch of new dinosaur fossils that fundamentally reshape our understanding. There's going to be a lot of work to do!

Imagine an invention that does a perfect job of brain surgery. And brain surgeons complain.

I am going insane. During the last week or so LLMs have produced a number of counterexamples to significant long-standing conjectures. I will not recount these happenings here, there are many places where you can find the details.

I stopped reading there.

Seriously how are we supposed to evaluate whether these were counterexamples to conjectures that real mathematicians had ever put any amount of effort into or not, if the author won't even link to them?

There are plenty of junk conjectures out there that even the conjucturee never spent time on.

The idea of ordering theorems like doordash is funny, kudos to the author for that :-)

Anyway, your "spiritual journey" doesn't matter. We'll automate mathematics because we can, because it's useful. Don't like it? Well, should have not chosen a capitalist economic system that rewards scientific progress so much.

He sounds as someone really pedantic who never understood what math is about or why it is important.

This is what locking yourself away in an ivory tower gets you. Do things ‘for beauty’ and watch as they are automated and commoditized by the people who depend on them for their continued wellbeing, reduced to a hobby or sport. But the reduction began when you yourself started putting more importance on your enjoyment of the process over the value being provided to your customers.

I'm all for this. I don't think mathematics should be done as a profession. If you can't find free time to do it, it's obviously not that important to you. Open source software works pretty well, doesn't it? Why not math?

I can’t help but confess some sense of satisfaction with the upheaval described in the post. Many proofs and textbooks laden with statements like “without loss of generality”, “immediately”, or “obviously” are followed by anything but. AI now counters that streak of smug by toppling some long held theorems and it’s fun to watch.

AI hasn't done that much compared to humans in research yet. Let us not overestimate its impact.

What it has done in software engineering is kill all human open source spirit. There is hardly any new software out there, people do not talk about interesting things but just how AI "generates value" or similar nonsense. AI has stolen at least three potentially productive years.

The Leiden declaration is fine, but if people who make OpenAI ads like Tao sign it what do we make of it? Professors who are truly concerned should ban AI in universities, talk about IP theft to politicians and so on.

Found a new organization "Mathematicians against AI".