Royal Society University Research Fellow at the University of Manchester. Mathematician and owner of erdosproblems.com. He/him/his.
Manchester, UK
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A few weeks ago Astra gave a stunningly simple proof of the Erdős-Sós conjecture in graph theory (previously thought to be very difficult).
It has been a good example of how the lifecycle of AI proofs should be: after the AI formalisation posted at erdosproblems.com/548
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While I'm sure many graph theorists would have loved to have found the original argument themselves, it's great to see them rise to the challenge and demonstrate the value that attention from human experts can bring.
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About 40 years ago Siemion Fajtlowicz created Graffiti, a conjecture-generating graph theory computer program.
This essay by Fajtlowicz discusses what Erdős thought of this project (and gives some idea what Erdős may have thought of AI).
thomasbloom.org/Fajtlowicz.p…
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And as for what Erdős may have thought about some of his conjectures being disproved recently:
"When he disproved a conjecture, he would work on modification of premises to get a positive result."
So I think he would have said "How interesting! So now the question is..."
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"If I don't do it, somebody else will"
is logically equivalent to
"If nobody else does it, I will".
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An excellent quote from the post by @PoShenLoh:
Driving a car faster than you can run is fine. But not faster than you can steer.
The calls for AI slow-down/responsible use, are not done to preserve the status quo - they are to ensure alignment can keep up with capability.
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Quote from
terrytao.wordpress.com/2026/…
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There has been a recent surge of fantastic essays about mathematics and AI, representing a range of viewpoints.
I recommend reading them all.
If, like me, you prefer a PDF I am collecting these at thomasbloom.org/AIEssays.pdf
(Currently 16 articles and 55 pages.)
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I definitely agree with the final sentiment here - we need, more than ever, more mathematicians and human experts!
And the good news is, it's easier than ever before to become such an expert. You can use AI to explain concepts, talk through proofs, etc.
But...
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I like this essay. But I'd like emphasize that the premise is hypothetical: even after the Navier-Stokes solution, I do not believe that current AI models are robustly superhuman yet.
It seems plausible that AI could reach the capability to solve any precisely formulated problem faster than any human could. Asking questions is also an important aspect of the profession, and while AI models are getting better at asking interesting questions, I'm not sure what it would mean for them to be "robustly" superhuman at it -- surely they will not ask every question that a human could ask?
Still, I think it would be prudent for academia to start moving towards the future this essay depicts. A first concrete step could be to make Ph.D. defenses, which are typically rubber stamped (in my experience), more rigorous.
I would also advocate for the public value of mathematicians in such a future. There are many wrong/confused/misinformed mathematical claims on this website, which could have been rectified by spending a few minutes with ChatGPT, but were not. You can't filter every sentence you read through an LLM, and you can't filter every sentence you write through an LLM. The math discourse on this site is proof that even in the presence of superintelligent AI, you need dedicated experts to serve as stewards of the truth.
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But it is such a waste to have that interest, and the endless learning opportunities afforded by AI (and many other resources available), but instead just copy-paste a prompt and stare at a screen, hoping for it to return an answer you can parrot without understanding.
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One of the most eloquent descriptions of what maths is and where it should be going - with, crucially, many concrete suggestions about how mathematicians should adapt.
Necessary reading for anyone interested in maths and AI.
I've written an essay on how I think the mathematics profession should adapt to highly capable AI systems. It's hosted here on "Proofs and Prompts": proofsandprompts.com/2026/09…
though you should also feel free to complain/comment on my website here: daniellitt.com/blog/2026/9/1…
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