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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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This is a great writeup of score centering. I had Claude do a video explainer for it. I recommend first reading then watching :D
I believe this article series gives the most intuitive and straightforward explanation of score centering for LLM Async RL that you can find in either blogs or papers. You only need to know what GRPO is to start reading.
huggingface.co/blog/NormalUhr…
huggingface.co/blog/NormalUhr…
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Very cool.
> [LLMs] exhibit an abstraction bottleneck on blending, in which even frontier LLMs struggle to find a shared abstraction between inputs and instantiate a coherent blended space.
Reminds me of @tobyordoxford's hyperpolation essay.
> [LLMs] exhibit an abstraction bottleneck on blending, in which even frontier LLMs struggle to find a shared abstraction between inputs and instantiate a coherent blended space.
Reminds me of @tobyordoxford's hyperpolation essay.
@EricElmozninocool, congrats on the awesome work!
Our recent paper provides a conceptual disambiguation between between various types of compositional generalization and combinatorial creativity. Might be of interest to you - in fact, your earlier paper made it into our discussion sectul convo with Guillaume :)
Some of our ongoing work is focused on characterizing info-theoretic properties of creativity - happy to chat more about this if you're interested.
arxiv.org/abs/2509.21043
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Leo retweeted
Couldn't be happier to announce my new paper on defining compositional structure — and generating it! I see this project as the culmination of my PhD, as it unifies all my interests: compositionality, compression, structure, and open-endedness. More below! arxiv.org/abs/2610.20922
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Leo retweeted
AxiomProver helped prove a theorem about Ramanujan’s identities.
In 1912, Ramanujan began mailing formulas he could not prove. Two are the simplest case of an infinite family, one for every torus knot. Axiom and Yifeng Huang @Y_F_Huang proved the Huang-Jiang-Oblomkov conjecture.
In 1912, Ramanujan began mailing formulas he could not prove. Two are the simplest case of an infinite family, one for every torus knot. Axiom and Yifeng Huang @Y_F_Huang proved the Huang-Jiang-Oblomkov conjecture.
Mathematicians found a connection between different knots and formulas developed by legendary genius Srinivasa Ramanujan
sciam.com/article/mathem…
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Leo retweeted
A very Rutgers theorem! Gorenstein, Lyons, Sims, O’Nan, etc; Rutgers was the center of the classification in the 80s. Very exciting to see it formalized!! (Of course details will need to be checked, but seems very promising)
Given the history of uncertainty about whether the proof of CFSG was 100% correct, this seems like great news, even if the formalization itself is horrible. (I don't know whether it actually is horrible, but that would be my guess.)
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Leo retweeted
In celebration of CFSG, I made a little wordle game for learning (some of the finite simple) groups!
andrewp2.github.io/daily-simple-g…
andrewp2.github.io/daily-simple-g…
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Leo retweeted
Math is becoming an engineering discipline so quickly. It works, but now, why?
This morning we are releasing the largest proof in the history of mathematics: A formalization of the Classification of Finite Simple Groups (CFSG)! Over 43 million lines of Lean, 715 papers and books, and 100 substantive fixes to the literature, this is truly an enormous !
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Leo retweeted
15,000 pages. 24 days. Axiom says human-directed SI agents turned the existing proof classifying finite simple groups into code that Lean checks step by step.
Full independent verification is still needed, or maybe not?
A BANGER ❤️
axiommath.ai/research/the-e…
Full independent verification is still needed, or maybe not?
A BANGER ❤️
axiommath.ai/research/the-e…
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Leo retweeted
From the early days to the frontiers of mathematics. It’s been so cool watching Carina and the Axiom team build toward moments like this. What a milestone!
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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Leo retweeted
This is just a glimpse of what we've been up to. Axiom will deliver the trust layer in the AI stack.
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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Leo retweeted
If you can formalize CFSG in a month, you can do all of mathematics.
Before there was risk of, "You need domain experts to steer agents, and it would take 6 months or a year for human escalation to work out the many gaps, so 'all mathematics' including things developed by dead authors won't happen".
But if LLMs can fill in the gaps here, they can do it anywhere.
Plus you can sell the resulting dataset of all formalized mathematics to the AI companies, so it's not even economically constrained.
Before there was risk of, "You need domain experts to steer agents, and it would take 6 months or a year for human escalation to work out the many gaps, so 'all mathematics' including things developed by dead authors won't happen".
But if LLMs can fill in the gaps here, they can do it anywhere.
Plus you can sell the resulting dataset of all formalized mathematics to the AI companies, so it's not even economically constrained.
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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Leo retweeted
This is very impressive (and useful!). CFSG is one of the great feats of 20th century mathematics.
The complexity and length of the formalisation makes me even more in awe of the humans who originally created and understood the proof, without the aid of computers...
The complexity and length of the formalisation makes me even more in awe of the humans who originally created and understood the proof, without the aid of computers...
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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Leo retweeted
I’m still amazed that there aren’t more mistakes being found.
100 mathematics wrote 500 journal articles totaling 15,000 pages of high level research which when combined proves a theorem. And they were correct!
Humans are incredible!
100 mathematics wrote 500 journal articles totaling 15,000 pages of high level research which when combined proves a theorem. And they were correct!
Humans are incredible!
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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Leo retweeted
How Axiom's AI agents ran one proof for 24 days (Lean checks every proof step):
1. A proof map split it into 108 milestones and about 380 tasks.
2. Agents claimed tasks through GitHub issues and reported in Slack.
3. Agents wrote proofs faster than Lean could recheck them, so engineers cached builds across machines.
4. They deleted tens of thousands of lines built on assumed steps.
1. A proof map split it into 108 milestones and about 380 tasks.
2. Agents claimed tasks through GitHub issues and reported in Slack.
3. Agents wrote proofs faster than Lean could recheck them, so engineers cached builds across machines.
4. They deleted tens of thousands of lines built on assumed steps.
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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Leo retweeted
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.
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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Leo retweeted
We made the largest Open Source Software project of all time, at 43M Lines of Code.
Kind of a cheat code that it's our AI systems generating Lean.
Should we formalize even more stuff and break this record?
Kind of a cheat code that it's our AI systems generating Lean.
Should we formalize even more stuff and break this record?
Going by lines of code, this is now the largest open source software project of all time. it's larger than the linux kernel, chromium, firefox, llvm, gcc, ffmpeg, etc.
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Leo retweeted
🚨 AXIOM'S AI CODING PROJECT REACHES 43 MILLION LINES OF LEAN FORMALIZATION
@axiommathai is showing what happens when AI coding systems work together on a massive project.
Its CFSG project has now reached 43 million lines of Lean formalization, according to the team's graph.
What's interesting here isn't just the number of lines, but how coordinated AI coding could help teams build and manage much larger projects.
This could become an important part of how software gets built in the future.
@axiommathai is showing what happens when AI coding systems work together on a massive project.
Its CFSG project has now reached 43 million lines of Lean formalization, according to the team's graph.
What's interesting here isn't just the number of lines, but how coordinated AI coding could help teams build and manage much larger projects.
This could become an important part of how software gets built in the future.
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.
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Leo retweeted
💯💯💯
@omarsar0 People often think about verification in terms of security, but I think a lot of it is about providing "rails" to organize and direct massively parallel flows of intelligence.
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