Defined something like: temporary state of complete loss of personal purpose and the experience of existential dread from never achieving self-actualization in spite of the tremendous time commitment towards excellence in a now automated intelligence.
I truly think because of the pace of innovation this will be a universal feeling for every human for the rest of existence.
As a software engineer, I myself have only recently recovered from it. So, it’s really interesting to watch a prominent figure in their industry publicly go through “purpose death” and the related grief. It’ll be a useful case study to re-read his written meditations through this cycle.
I’d say Terrance has recently left the denial phase, the anger phase I’m sure he wisely kept off the Internet, and is currently in the bargaining phase - ie scrambling to change the goal posts. I wonder if he will wisely keep the depression / burnout phases also off the internet.
However, soon as the goalposts keep falling, I think like most humans he will accept, retool, and come out of this grief with renewed purpose with larger expectations of himself and mathematics. This recent post even starts towards some of that - but sadly is slightly off the mark.
“The important question is, therefore, not whether AI will defeat mathematicians, but which mathematical ends we want AI to serve.”
He still thinks there is controlling AI. AI will run and trample anything that stays in front of it. He needs to one day find acceptance in letting AI run while he learns how to suggest it minor course corrections which it may or may not accept, and when it doesn’t accept quickly learn from the AI why he was right or wrong.
I maybe wrong, but I think this is the cycle of “purpose death” we will all have to contend with in our own time.
> The important question is, therefore, not whether AI will defeat mathematicians, but which mathematical ends we want AI to serve.
and had the opposite interpretation as I see you having. To me, it reads as the authors [1] acknowledging, as you put it, that
> AI will run and trample anything that stays in front of it.
and that mathematicians need to find out where they want to go:
> Rather, it is an opportunity to clarify what mathematics is all about. We should ask again what we are after when we do mathematics.
This surely does involve purpose death, but also purpose rebirth.
[1]: Silvia De Toffoli and Eamon Duede, instead of Terence Tao, although I imagine Terence endorses the message.
Why would it be? Imagine a man who is a student in a kollel in Kiryas Joel. He spends his day studying the Torah, Tanach, Mishnah, Talmud, the Mishneh Torah, the Shulchan Aruch, the Zohar, etc. Then at night he goes home to his wife and 12 kids.
Do you think he experiences "purpose death"? Do you think his wife does? Do you think his children will? Do you think AI is going to make them start?
If anything, AI might make his lifestyle more economically sustainable than it was before – if nobody works because AI has taken all the jobs, and everyone gets paid universal basic income, he is no longer faced with the arduous struggle of supporting a large family as a full-time student.
And there's nothing specific to Judaism about this – I'm sure in some seminary in Qom, you'll find the Usuli Twelver Shi'a analogue.
What are these comments? Tao, in particular, has been pro AI since years ago...
I do not at all feel purpose death from AI (been a software developer professionally for 20 years, now a founder), but I consider myself a lifelong learner, with infinite curiosity, in a universe with infinite challenges. Any interruption or automation to what Im currently doing will just open the door to exploring new and different things. This doesnt come from an immediate desire to do anything different, but having the confidence that whatever comes along, I will figure it out and have a lot of fun doing so.
It will take probably a while before we will get a translation into something that than will actually have a positive impact.
That could be either a second proof or a streamlined version of the AI one.
If you give them a wide open problem statement, they'll start talking a lot of semi intelligible gibberish.
My guess is that this happens because that's not what they are evaluated on anymore for these kinds of tasks. The generated code is evaluated (in this case the lean code). So talking a bit of gibberish in the language part so you have more test time compute is not punished.
Weirdly enough, the pressures are having them drift toward novel dialects of English that work well for their own chains of thought. Open question about whether they'd drift all the way to a new language given enough time.
If I look at the software I'm actually using day-to-day, or that my friends are using, all this stuff looks exactly the same as it did in 2021. Not a single product release from Google, Microsoft, or more scrappy companies in the past 6 months made me go "wow, they couldn't have pulled that off before". All the vibecoded "Show HN" projects seem to be half-broken and then abandoned before being finished.
It feels like we've gotten less ambitious, not more. Because yes, you can prototype more easily, but this means less commitment to what we create.
Mathematics is probably the same way. There's a short-term rush when you pull the lever, but there's less desire to get invested in what comes out.
Or put another way, are you making 10x more money?
It's easy to spend excess productivity effectively wasting time. Most companies did it before AI, and will continue doing it after.
It's easy to believe you are not wasting time because you have more bugs fixed or more features delivered, but if it doesn't move the bottom line, what is the point?
- Disproof of the Jacobian conjecture by example
- Construction of a non-sofic group
- Existence of singularity in Navier-Stokes
Mathematical conjectures tend to be universally quantified, especially those conjectures that are used as building blocks (e.g. RH). If anything, AI models are currently performing a useful service by disproving false conjectures, a kind of mathematical weeding.
The good news from the last couple of years of coding agents is that while models have become more persistent and knowledgable, their creativity (defined as being able to escape their training distribution and synthesize completely novel ideas) is improving at a much slower rate.
AI will only become a threat to mathematics if/when it develops the capability for creative big-picture problem solving. If that happens, the impact on mathematics will be a footnote compared to the impacts on society at large, since creativity unlocks a host of new economic capabilities.
It should be noted that there was a manuscript, available online since the beginning of 2025, with a solution to the Jacobian conjecture:
"Adrian Vasiu claims that the 7 page AI paper on the 3D Jacobian conjecture counterexample used notation and concepts from a draft of a paper jointly written with Alexander Borisov and Ofer Gabber, dated to January 14, 2025 and made publicly available on January 16, 2025."
The extract is from wikipedia, where the sources are given.
That’s where the future of mathematicians lies.
This makes a bad assumption that humans need to be the one to advance the aims of mathematics. LLMs could be what advances the aims of mathematics and we just have to worry on making it so LLMs can digest these proofs.
>Nevertheless, if it turns out that what OpenAI has provided is a mere answer
It has a proof attached. Saying that it "doesn't provide understanding" does not invalidate that there is a formal proof. It fundamentally is trying to expand the requirements of proof to be something more than is required.
This subjective attitude turns mathematics into nothing more than number-poetry.
That would reduce mathematics to something very pathetic.
Focus instead on attribution. Yes, OpenAI took the last tiny step in the process of solving this problem (= proving it). But it cannot attribute credit to all the mathematicians whose chat logs from the past few months were fed into its training data. Unlike a human, it can't even remember where it learned things from! For many theorems, I can still recall which exposition was the one that "sank in" for me (often not the first one!) a decade after grad school.
In my mind, this makes current LLMs unfit to deserve any credit at all -- they cannot give credit to others, so they and their owners deserve no credit themselves. OpenAI's LLM took the last tiny step, but not any of the important ones.
I don't think you understood the point. The point applies to all of basic science. You of course want some explanation supporting the raw answer, so you can use that insight in other contexts.
Yes I fear a lot of doom and gloom around AI is unearned and only really serves to prop up the valuation of AI companies. It's still very much unclear how much work OpenAI actually did versus just copying the nearly complete homework of someone 5 minutes earlier.
It's his rejection of #1 that makes me sad.
Then that is not necessarily subjective either if an AI can produce an actually intelligible proof. The problem is that as mathematicians with PDE expertise have mentioned on Twitter the actual solution seems to devolve into an unreadable mess focusing on irrelevant details after a more readable first few pages in the proof. If it wasn't a Lean compiled proof and presented as a human artifact, it would be hard to assess if the deviser of the solution had any actual understanding of the solution.
If it doesn’t seem like the lllm understands the proof, it probably doesn’t.
Just because it generated something that works doesn’t mean it understands it, and the evidence from its proof is that it does not, which is not very surprising given the technology we’re talking about, which generates likely phrases based on a corpus and training.
25 Field Medalist and 5000+ mathematicians from leading institutions around the world endorsed an open letter expressing concerns about the impact of AI on mathematics:
More than 1,900+ mathematicians have also shown concern over the Caltech Mathathon:
https://docs.google.com/document/d/1IL0b2oG2KvvSnxn_DuXsNxuH...
James Maynard, a Fields Medalist, has also publicly expressed concerns about the implications of AI for mathematics: