Skip to content
Sign in
Artwork for ASI pill
ASI pill · Yesterday · 16 min

The Longest Proof in Math, Explained

This is the audio version of a film that does most of its explaining in 3D pictures. Watch it on YouTube: https://youtu.be/zqWDsJk2ejI On October 27, 2026, the startup Axiom announced that the Classification of Finite Simple Groups, the longest proof in mathematics (about 15,000 pages in more than 500 articles by about 100 mathematicians), now checks in the Lean proof assistant: swarms of dozens of AI agents worked for 24 days and wrote about 43.1 million lines of Lean, and on the way they found a broken step in one published route to the Unbalanced Group Theorem and built a new one. The ASI Pill builds group theory from scratch in 3D, from the symmetries of a square to the periodic table of symmetry and the Monster, then shows how the proof was built and how the machines checked it. Axiom's post: https://x.com/axiommathai/status/2115089794867040584 Axiom's blog post: https://axiommath.ai/research/the-enormous-theorem-formalized/ The proof and its map: https://cfsg.axiommath.ai/ and https://github.com/AxiomMath/CFSG The new argument for the Unbalanced Group Theorem: https://hexagonmath.org/2610.00575 Solve Everything, by Alex Wissner-Gross and Peter Diamandis: https://solveeverything.org/ For a deeper tour of group theory and the Monster, watch 3Blue1Brown: https://youtu.be/mH0oCDa74tE Disclosure: this video's script and 3D scenes were made with Anthropic's Claude, and Anthropic's own Lean proof of Fermat's Last Theorem is mentioned in it. The video is independent and not sponsored. SYMMETRY: a square's eight moves, combining them (the order matters), the table that is the group, and the same group in different clothes; why groups run crystals, chemistry, physics and the encryption in your phone. THE ATOMS: simple groups as the atoms of symmetry, the Jordan-Holder theorem, the icosahedron's sixty turns, and Galois and the equation of degree five. THE MONSTER: the periodic table of finite simple groups, its eighteen infinite families and twenty six loners, Mathieu's groups and Voyager's Golay code, the Monster and monstrous moonshine. THE PROOF: fifteen thousand pages, Feit and Thompson's 255 pages, Gorenstein's plan, the quasithin gap, the aging experts and the second-generation proof. THE MACHINE: Lean, Axiom's agent swarm, 43.1 million lines, the errata, the broken step in the Unbalanced Group Theorem and its repair with Ronald Solomon's 1976 ideas, and what is checked and what is not. Then the curve of AI formalization and Solve Everything's era of proof. CHAPTERS 0:00 A note: this is the audio version 0:17 Cold open 1:18 01 Symmetry: what a group is 3:28 02 The Atoms 5:18 03 The Monster 7:10 04 The Proof 9:10 05 The Machine 13:38 06 The Prophecy 15:08 Outro and the Maitreya prayer MORE ON THE ASI PILL OpenAI's Math Drop, Explained: https://youtu.be/apD5iaKO1Zw All 38 sources are linked in the pinned comment under the YouTube video. CREDITS Script written with Claude from Axiom's announcement, blog post, video and paper, the proof's own site and repository, the posts and articles quoted, and the papers and histories they cite. Narration in the ASI Pill's own words. Posts, articles, paper pages, Axiom's proof map and Wikipedia pages are shown briefly for commentary; all rights stay with their authors and publishers. Solve Everything is quoted in short passages for commentary; all rights with its authors. The 3D scenes are the ASI Pill's own renders; the analogies (the tile, the atoms, the periodic table, the tower of pages) simplify the mathematics on purpose. The ideas of the first chapter are the standard way group theory is taught; 3Blue1Brown's video on the Monster is the classic telling, and we recommend it. Photos of the people quoted come from Wikimedia Commons and their own X profiles; the credits for each are in the pinned comment. Narration: Parzival, the host's own cloned voice. Stock footage: Pexels. AI-generated pictures: the illustrations and the closing still of Parzival. Photos of the people quoted: see the pinned comment. #Mathematics #GroupTheory #AI

0:00-16:00
Play in

transcript

No transcript — this publisher did not publish one.

show notes

This is the audio version of a film that does most of its explaining in 3D pictures. Watch it on YouTube: https://youtu.be/zqWDsJk2ejI


On October 27, 2026, the startup Axiom announced that the Classification of Finite Simple Groups, the longest proof in mathematics (about 15,000 pages in more than 500 articles by about 100 mathematicians), now checks in the Lean proof assistant: swarms of dozens of AI agents worked for 24 days and wrote about 43.1 million lines of Lean, and on the way they found a broken step in one published route to the Unbalanced Group Theorem and built a new one. The ASI Pill builds group theory from scratch in 3D, from the symmetries of a square to the periodic table of symmetry and the Monster, then shows how the proof was built and how the machines checked it.

Axiom's post: https://x.com/axiommathai/status/2115089794867040584

Axiom's blog post: https://axiommath.ai/research/the-enormous-theorem-formalized/

The proof and its map: https://cfsg.axiommath.ai/ and https://github.com/AxiomMath/CFSG

The new argument for the Unbalanced Group Theorem: https://hexagonmath.org/2610.00575

Solve Everything, by Alex Wissner-Gross and Peter Diamandis: https://solveeverything.org/

For a deeper tour of group theory and the Monster, watch 3Blue1Brown: https://youtu.be/mH0oCDa74tE

Disclosure: this video's script and 3D scenes were made with Anthropic's Claude, and Anthropic's own Lean proof of Fermat's Last Theorem is mentioned in it. The video is independent and not sponsored.


SYMMETRY: a square's eight moves, combining them (the order matters), the table that is the group, and the same group in different clothes; why groups run crystals, chemistry, physics and the encryption in your phone. THE ATOMS: simple groups as the atoms of symmetry, the Jordan-Holder theorem, the icosahedron's sixty turns, and Galois and the equation of degree five. THE MONSTER: the periodic table of finite simple groups, its eighteen infinite families and twenty six loners, Mathieu's groups and Voyager's Golay code, the Monster and monstrous moonshine. THE PROOF: fifteen thousand pages, Feit and Thompson's 255 pages, Gorenstein's plan, the quasithin gap, the aging experts and the second-generation proof. THE MACHINE: Lean, Axiom's agent swarm, 43.1 million lines, the errata, the broken step in the Unbalanced Group Theorem and its repair with Ronald Solomon's 1976 ideas, and what is checked and what is not. Then the curve of AI formalization and Solve Everything's era of proof.


CHAPTERS

0:00 A note: this is the audio version

0:17 Cold open

1:18 01 Symmetry: what a group is

3:28 02 The Atoms

5:18 03 The Monster

7:10 04 The Proof

9:10 05 The Machine

13:38 06 The Prophecy

15:08 Outro and the Maitreya prayer


MORE ON THE ASI PILL

OpenAI's Math Drop, Explained: https://youtu.be/apD5iaKO1Zw


All 38 sources are linked in the pinned comment under the YouTube video.


CREDITS

Script written with Claude from Axiom's announcement, blog post, video and paper, the proof's own site and repository, the posts and articles quoted, and the papers and histories they cite. Narration in the ASI Pill's own words. Posts, articles, paper pages, Axiom's proof map and Wikipedia pages are shown briefly for commentary; all rights stay with their authors and publishers. Solve Everything is quoted in short passages for commentary; all rights with its authors. The 3D scenes are the ASI Pill's own renders; the analogies (the tile, the atoms, the periodic table, the tower of pages) simplify the mathematics on purpose. The ideas of the first chapter are the standard way group theory is taught; 3Blue1Brown's video on the Monster is the classic telling, and we recommend it. Photos of the people quoted come from Wikimedia Commons and their own X profiles; the credits for each are in the pinned comment.

Narration: Parzival, the host's own cloned voice. Stock footage: Pexels. AI-generated pictures: the illustrations and the closing still of Parzival. Photos of the people quoted: see the pinned comment.


#Mathematics #GroupTheory #AI

more episodes

All episodes