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I’ve written a guest post on Terry Tao’s blog about the challenges science is facing due to the rise of AI and some thoughts about how we can address them. Many thanks to Terry for hosting me. terrytao.wordpress.com/2026/09/17/a-c…
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Dimitris Koukoulopoulos retweeted
Eighty-six years ago today, at a defining moment in the Second World War, the Greek people stood against fascism.
They chose resistance over surrender, making extraordinary sacrifices in defence of freedom.
On Όχι Day, I join the Greek community in Canada and around the world in honouring the legacy of those who stood up for liberty.
They chose resistance over surrender, making extraordinary sacrifices in defence of freedom.
On Όχι Day, I join the Greek community in Canada and around the world in honouring the legacy of those who stood up for liberty.
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Dimitris Koukoulopoulos retweeted
The formal proof of CFSG may now be among the largest open-source projects ever. Watching agents assemble it is a reminder of the awe-inspiring human achievement behind it. The graph represents some 15,000 pages of intricate arguments developed by mathematicians over decades.
The largest math proof in human history is now computer-verified.
Today, Axiom announces a complete Lean auto-formalization of the Classification of Finite Simple Groups, the "periodic table of symmetry."
About 15,000 pages, built by over 100 mathematicians across generations.
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Dimitris Koukoulopoulos retweeted
The Yang-Mills proof is apparently 1147 pages!
In any case, they should release it immediately in my opinion. They write that they first want to assess the correctness before releasing. But how long would that take for work of that magnitude?
kitp.ucsb.edu/sites/default/…
In any case, they should release it immediately in my opinion. They write that they first want to assess the correctness before releasing. But how long would that take for work of that magnitude?
kitp.ucsb.edu/sites/default/…
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Dimitris Koukoulopoulos retweeted
The recent drop by OpenAI contains a refutation of ETH, a proof of "local smoothing", which implies the full Kakeya conjecture, and a proof of the existence of pure Yang-Mills theory. AGMAI asks for release of the materials connected with the last.
agmai.org/#request-immed…
agmai.org/#request-immed…
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Dimitris Koukoulopoulos retweeted
the inimitable David Harvey wrote about his experience understanding the o(n log n) integer multiplication result: web.maths.unsw.edu.au/~davidharvey/r…
it's absolutely worth a read, both for the technical content and especially for the reflections on math and AI at the start
it's absolutely worth a read, both for the technical content and especially for the reflections on math and AI at the start
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Dimitris Koukoulopoulos retweeted
I expect the big AI labs will soon stop dumping hundreds of papers. They’ve proved their point. The dust will settle and we’ll be left with an amazing tool to assist us with our research. Public access is the key. We need it free. terrytao.wordpress.com/2026/09/17/a-c…
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We need tools for AI-assisted science that are fully secure and aligned with the goals of the scientific community. The only way to guarantee this is to build them ourselves. A "CERN for AI-assisted science" would be a major step in this direction: terrytao.wordpress.com/2026/09/17/a-c…
Mathematicians need to build an LLM infrastructure capable of supporting ambitious research projects in a safe environment, one that guarantees recognition, transparency, and confidentiality, and is compatible with training new generations of mathematicians.
Indeed:
(1) It’s an exciting time to be a mathematician. LLMs can turbocharge our discipline. I can think of two or three ambitious projects that go well beyond conjectures and famous lists of problems, with genuine mathematical depth and significant impact outside mathematics.
But I wouldn’t trust ChatGPT with even the vaguest description of these projects. There are simply no adequate guarantees of confidentiality, transparency, or control over how research ideas are handled on these platforms. And I have no reason to believe Anthropic is any different, by the way.
(2) The way OpenAI has decided to go about Tuesday’s drop — with no meaningful effort to acknowledge the human mathematical contributions underlying the results, no engagement with the established processes of peer review, and no transparency about training datasets, prompts, and procedures — is extraordinarily damaging to the pipeline that produces new mathematicians.
Why would the next generation of talented young people devote their lives to learning and creating mathematics if the future we are offering them consists largely of checking machine-generated proofs?
Eradicating humans from mathematics today, and from STEM tomorrow, would be disastrous for human culture. And I fear that OpenAI’s drop has put mathematics on precisely that path.
Which brings me back to where I started: we need to build LLM infrastructure that is safe for research, mentoring, and peer review, under the control of the mathematical community, and outside the control (and potential predation) of OpenAI and its frenemies.
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Dimitris Koukoulopoulos retweeted
Really nice article. If hard math problems are indeed good "food for the shoggoth" (RL material), there seems no reason for AI companies not to just allow a large group of mathematicians access to internal models, to give more hard questions for the models to solve
I expect the big AI labs will soon stop dumping hundreds of papers. They’ve proved their point. The dust will settle and we’ll be left with an amazing tool to assist us with our research. Public access is the key. We need it free. terrytao.wordpress.com/2026/09/17/a-c…
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I expect the big AI labs will soon stop dumping hundreds of papers. They’ve proved their point. The dust will settle and we’ll be left with an amazing tool to assist us with our research. Public access is the key. We need it free. terrytao.wordpress.com/2026/09/17/a-c…
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Dimitris Koukoulopoulos retweeted
Well worth reading: proofsandprompts.com/2026/10/08/100…
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Dimitris Koukoulopoulos retweeted
@lreyzin We've been given a very powerful tool. We still need to point it to interesting problems and work with it. This is more analogous to the supercollider in physics that confirms theories and intuitions. Our math experiments will need to be interpreted, and lead us to new insights.
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Dimitris Koukoulopoulos retweeted
I realize @AcerFur is being ironic, but the popularity of the idea that AI "merely explores the convex hull" mystifies me. Why wouldn't it be more like the subgroup generated by existing mathematical knowledge? (That's also a metaphor -- I'm not saying there's a group structure.)
mathematicians should start saying "it's within the convex hull" instead of "it's trivial"
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Dimitris Koukoulopoulos retweeted
My dream had always been to prove beautiful theorems as the AI agents unloaded my dishwasher. Well, it went the wrong way... 😂
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Χρειαζόμαστε θεσμικές λύσεις για ελεύθερη πρόσβαση των επιστημόνων σε εργαλεία αιχμής τεχνητής νοημοσύνης. Σε άρθρο μου στην Κ προτείνω τη δημιουργία της κατάλληλης υποδομής - ενός νέου CERN - για τον εκδημοκρατισμό της πρόσβασης στην ΤΝ. kathimerini.gr/world/56448017…
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Το άρθρο πρωτοδημοσιεύτηκε στα αγγλικά στο μπλογκ του Terence Tao terrytao.wordpress.com/2026/09/17/a-c…
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This article’s perspective on the future of humans in math is very closely aligned (!) with my thinking.
Thoughts on math and AI. Are human mathematicians redundant in a world in which AIs are better than humans at proving theorems? The answer may surprise you.
blog.danromik.com/the-feedback-l…
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Dimitris Koukoulopoulos retweeted
I was part of a group that met last week to try to propose recommended changes to the structure of math PhD programs in an age of AI. Our report, together with a collection of related resources, is now available here:
cmsa.fas.harvard.edu/aimathphd_summ…
cmsa.fas.harvard.edu/aimathphd_summ…
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Very powerful address to the UN Security Council by Yoshua Bengio about AI safety.
I was invited to address the @UN Security Council this afternoon to discuss the unprecedented threat posed by uncontrolled frontier AI agents.
Humanity has summoned the courage and wisdom to manage catastrophic risks before. This is one of those moments, far bigger than any r national interest. The choices we make about this technology today will shape generations to come. We must act now.
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Dimitris Koukoulopoulos retweeted
Martin Hairer, one of the other members of AGMAI (the advisory group on mathematics and AI), has written a post on the Proofs and Prompts blog that will I hope clarify what our purpose is. The rest of the blog is highly recommended too.
proofsandprompts.com/2026/09/22/why…
proofsandprompts.com/2026/09/22/why…
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