> 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.

You're making up a narrative about another person. You have no clue what's happening to him, without talking to him.

I’m just going to say this 100 times I guess. Terence Tao has had a very consistent narrative on AI in math for a very long time, at least since 2023. He’s always described it as a surprisingly good tool and has advocated that mathematicians adopt the technology without becoming totally reliant on it. He’s also always argued that mathematics is fundamentally about human understanding. There’s no change in his messaging recently on the basic narratives.

It is not right to project one’s grief onto others and then characterize all their actions through this lens! (This post is attributed to other people and doesn’t sound like his voice by the way, which highlights the problem with doing so.) And it’s especially wrong to pose what looks like a therapy diagnosis on a stranger in public as a non-expert.

> AI will run and trample anything that stays in front of it.

Right now that entirely depends on the whims of a few people. We can try to make it not be that but I don't have much hope in that area. See climate change

> As a software engineer, I myself have only recently recovered from it

Can I ask you how you came here? Right now I am getting closer to "purpose death" as you call it. Software engineering is one of the few things I am good at and the only thing that I can rely on to put food on my table. Even if I end up being someone who gives minor suggestions to the AI, it always feels like C level execs can't wait to get rid of me

> 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

> this will be a universal feeling for every human for the rest of existence

As someone that has accepted a very long time ago that nihilism is the only self-consistent philosophy, I've made peace with the fact that humanity has no purpose and therefore disagree with your conclusion. I haven't been driven to absurdism, either.

Instead, I derive purpose and self-worth from within.

Most people don’t reach self-actualization and never have. This has nothing to do with AI.

With regards to technology specifically, new tech has been making high-investment skills useless for the last 500+ years. The printing press, the loom, etc. This is not anything new.

Some of these AI doomers really need to read more than AI Substacks and Twitter feeds. I suggest a book about the history of technology.

It is perfectly reasonable to suggest that we make an effort to direct a technology in certain directions. It is not reasonable to throw all rational thought out the window and operate as if real world AI is synonymous with science fiction.

The authors of this piece are Silvia De Toffoli and Eamon Duede. It is hosted at Terence Tao's blog, but he did not write it.

I read

> 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.

I don't think that "death" is the perfect word here - it typically describes a permanent state. FWIW, what you describe ("temporary state of complete loss of personal purpose") is called "Sinnkrise" in German (crisis of meaning/purpose).

(And because not everybody might know: the comment references Kübler-Ross' five stages of grief (when confronted with a tragic outlook)¹: denial → anger → bargaining → depression → acceptance)

¹) https://en.wikipedia.org/wiki/Five_stages_of_grief

Top comment on this post taking "reply to the title" to the next level.

> I’d say Terrance has recently left the denial phase, …

There’s a byline at the top of the article that lists the authors of this blog post, neither of which are Terry Tao.

> [This is a guest post by Silvia De Toffoli and Eamon Duede. This blog post was initially written in a different file format and converted using AI. — T.]

> I truly think because of the pace of innovation this will be a universal feeling for every human for the rest of existence.

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.

I, on the other hand, don't want to be a permanent serf to whoever manages to merge their brain with ASI first and think it's high time we begin decommissioning datacenters through direct action.

> I’d say Terrance has recently left the denial phase, the anger phase

What are these comments? Tao, in particular, has been pro AI since years ago...

I would argue that purpose death is a normal step towards enlightenment and it was only the fierce, unrelenting, all consuming drive of capitalism in the western world over the last 4 or 5 generations that have pushed everyone to define themselves (nearly) solely in terms of their work.

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.

I invite you to consider that your doomer views on AI trampling everything in front of it humanize the technology and give it an agency that is in fact in the hands of its creators. It’s very convenient for them to make people think they have no control over their creation. It’s like Facebook claiming they’re not a publisher but on steroids

> This kind of argument is always dangerous, because it essentially resorts to moving goalposts. "Oh, AI can now do X? Sure it is amazing, but it can't do Y yet, so we're totally safe!"

It's not about moving goalposts. What you're not understanding is that, even if for you is crystal clear that AI will be 100x smarter tomorrow, those in charge cannot simply bet all on that. Right now AI cannot really replace the core sauce of mathematicians (all the "understanting" and "asking the real questions" stuff), so it'd be unwise for, say, countries to start making decisions as if AI is capable of that.

Technology advances, but extrapolating the value of human labour to 0 is equally invalid.

> Math, on the other hand, was paid for because people and states believed progress in math might lead to meaningful improvements in other branches of science, and, in turn, in our lives. If this is better served by AI, should we keep paying for the same number of tenure positions?

That is a pretty huge "if". The ultimate purpose of mathematics and really all scientific inquiry is human understanding of the natural world. It's not at all clear whether large language models can replace that any more than calculators can replace human mastery of arithmetic. Is society ready for engineers to design bridges and airplanes without understanding the underlying mathematics by simply handing off the entire process to a black box "AI architect"? Are people ready to ingest drugs "vibe-designed" by human drones pushing buttons on an "AI drug discovery" machine and just going "meh, seems about right!"

It might also be useful to take a step back from the hype that the frontier labs are obviously incentivised to incite. Before speculating about how "AI math" capabilities might supplant cutting-edge research in mathematics and other sciences, take a look at OpenAI's own job postings (https://openai.com/careers/search/?). Why doesn't OpenAI demonstrate its world-beating AI capabilities by automating more routine roles like "Account Associate", "Systems Architect" or "Android Engineer"?

Why would my tax dollars go to fund someone's journey on what's essentially a hobby at this point?

It might feel that way, but I'll ask again: where's the payoff? Where's all the amazing software that everyone is now supposedly shipping 10x faster than before?

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.

Maybe, but what remains of the human professional mathematics will be unrecognizable (at least for those without tenure I guess). All of our credit assignment systems are breaking and access to computational/financial resources is becoming way more important. Math has been one of the most open academic fields but everyone is becoming afraid of sharing their ideas. Personally, my job has slowly been moving from open-ended brainstorming to prompting/digesting LLM output (or LLM output transmitted by grad students). And the students are so demoralized! Also, the academic funding structures which have supported math departments are looking less and less stable - I imagine many of them will shrink.

I think it's possible that it will play out that way, and that it's just too soon to see it. Tao was very optimistic about AI up until a few months ago, and I think what's changed is that an AI generated proof isn't that informative unless it is understandable by humans. So far experts are finding the solution to Navier-Stokes incomprehensible, so we only learn one thing (it's false), instead of the hundreds of things we learn from reading a proof we can understand.

Maybe this is a one-off, or maybe in a few weeks we'll figure out how to get AI to explain the proof in terms we can understand. Then math research will accelerate. But maybe it's not a one-off, and by this time next year we will have an oracle that just answers all of our questions, but in such a way that we don't even know what questions to ask anymore. Then AI will just mop up the existing and the subject will end.

It points to a possible alignment: math helps humans to _discover_. So can AI.

You're right though; the economic and emotional impact of OpenAI's executives are much more obvious today. In comparison, the actual implications of Navier-Stokes blow-ups on the epistemological landscape will take at least two years to become obvious to any intelligence, if ever.

I'm optimistic that the Joe in the street will soon be able to make earth shattering discoveries with the help of AI, at least once a week, when universal basic tokens come to pass. Then the nihilists will also keep their existential or otherwise depression to their AI therapists. Hopefully then the puritan billionaires can only helplessly compare the profligate blooming of a thousand new avenues to unrestrained moral depravity

It's a clever pun, but it implies maths is ended, which is the exact opposite of what the article says. Given how many people responded to strawman misinterpretations of the Fields medallists' statement yesterday I don't expect that to have a positive effect on the discussion.

You even notice that with the recent opus and fable models by Anthropic.

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.

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.

If you look at the Leiden Declaration https://leidendeclaration.ai/ then you notice two weird IMO facts:

- 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

A useful term here is “instrumental reason.” The Ethics of Authenticity is a good read on the topic:

https://jaredhenderson.substack.com/p/the-modern-malaise?r=5...

You can remove pretty much everything in the modern world, from cars to computers etc.. and humans would still continue with their lives. Such and argument is only anti-progress.

Why draw the line at the industrial age? Humans subsisted for millenia before the ready preparation of fire.

We also use technology to care for the people in medicine and it requires pretty advanced science and engineering. Doesn't that shred your argument?

> I thought the reason we were encouraging people to go into STEM, and providing clever people with large salaries, was that mathematical results were of practical value to the wider human race. In which case, it’s surely very good news that AI can get those results.

The impact of mathematics on other disciplines goes much further than specific results. Just as important, if not even more so, are the language and ways of thinking that typically come out of the process of establishing those results. Results without the accompanying conceptual understanding are about as useful as a mere oracle for math theorems.

Another point that seems to be frequently missed or mischaracterized is that mathematicians are not opposed to computational tools as a matter of principle and in fact do use them when they help their research. The current controversy is not about a hypothetical future where mathematicians have easy access to open-source, open-weight, auditable natural-language assistants to help them internalize a new result or search for counterexamples. It's primarily about the recent behavior of certain for-profit companies suddenly trying to disrupt mathematics by caricaturing it in the public eye as a game they can "solve" or "beat" for headlines and valuation.

I agree at the high level. STEM bringing general benefit and greater understanding of the world is the main reason. This is true whether or not humans or an AGI is driving the progress.

> Disproof of the Jacobian conjecture by example

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.

You can also brute force the existence of a proof...

It is true that the biggest splashes have been from counterexamples and such, but I have seen many smaller examples of proving positive results in my own field.

Perhaps not superhuman yet but sufficient to completely upend the status quo. And I'm supposed to believe that this won't change in a year? or two?

Exactly, people are jumping at the shadow on the wall- LLMs have achieved remarkable things regarding their limitations, but those limitations show no signs of yielding

For the moment, AI is not capable of advancing mathematics _in the sense_ you're describing. AI is very bad at designing stuff, asking questions, etc. Maybe in the future you'll be able to ask the AI "cure cancer" and it'll do it, but for now we're very far away from that (this doesn't mean the current achievements aren't impressive).

The authors discuss the dual roles of proofs, and the new need to differentiate them better, clearly in the article.

business endeavors that cared only about the process, and would gladly avoid the [...] process

you mean they care about the product...

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! In my mind, this makes it unfit to deserve any credit at all -- it cannot give credit to others, so it deserves no credit itself. It took the last tiny step, but certainly not any of the important ones.

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.

Conversely, I think mathematics should retain this aspect of “number-poetry”. Consider a mathematical pursuit that lacks number-poetry but retains other features such as attribution, calculation, and puzzle-solving: I think of competitions like the largest prime number or the furthest digit of pi. Do these not feel in some sense trivial, more suited to IFLS Facebook posts than arxiv preprints?

I don't think that's particularly true. The whole point of the Millennium Prize problems as the article states was not on absolute difficulty of the problems but on the high chance of a proof producing fruitful results leading to new concepts and theories. Any pursuit of capital T truth will of course aim for better and more clarifying abstractions and is not a subjective turn by any means.

> This subjective attitude turns mathematics into nothing more than number-poetry.

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.

Grigori Perelman rejected the Fields Medal and the Clay prize among other things for what he considered unjust decisions and lack of ethics and proper attribution to other mathematicians. I find it surprising that he hasn't been mentioned yet, given it involves another Clay prize (ironically another lack of attribution, I guess). There is a long tradition of mental problems among great mathematicians, but maybe this was not the case, or maybe in a Lovecraftian way the observation of deep truths has a terrible toll.