Group theory·OpenAI Math·Result 248·Lean formalisation listed
Thompson's group F is nonamenable
One of the 372 results in OpenAI's public mathematics catalogue, filed under group theory: 1 preprint, the latest dated 23 September 2026. This page quotes OpenAI's own summary of the claim, links the paper and abstract, and embeds the animation.
In one line: OpenAI reports a result titled ‘Thompson's group F is nonamenable’ (group theory) in a preprint dated 23 September 2026. It has not been peer reviewed. The channel's animation, Every OpenAI Math Result, Part 2 of 4: PCP for PPAD, Birkhoff Conjecture and 82 More, is on YouTube.
Chapter 65 of 84 in Every OpenAI Math Result, Part 2 of 4: PCP for PPAD, Birkhoff Conjecture and 82 More · starts at 22:12 · watch from there on YouTube →
What OpenAI claims
Proves that Thompson's group F, the group of dyadic piecewise linear homeomorphisms of the interval, is nonamenable, resolving its longstanding amenability problem. (Lean)
Paper
Thompson's group F is nonamenable
OpenAI's abstract We prove that Thompson's group F is nonamenable. This confirms Geoghegan's conjecture and resolves the amenability problem for F.
Status
Preprint. The paper has not been independently reviewed. Treat the result as OpenAI's claim until other mathematicians have checked it. If a video exists, it illustrates the statement; it is not the proof.
Quick answers
- Is it proven?
- Not independently yet. OpenAI posted a preprint on 23 September 2026; it has not been peer reviewed, so treat the result as OpenAI's claim until other mathematicians have checked it.
- What exactly does OpenAI claim?
- Proves that Thompson's group F, the group of dyadic piecewise linear homeomorphisms of the interval, is nonamenable, resolving its longstanding amenability problem. (Lean)
- Where is the proof?
- In the paper, Thompson's group F is nonamenable (PDF).
- Is there a video?
- Yes, on YouTube (29:10, chapter 65).
Also in
- Chapter 3 of 9 in Cannon's Conjecture, Thompson's Group F and 7 More in Group Theory · starts at 0:41 · watch from there on YouTube →
The video
Every OpenAI Math Result, Part 2 of 4: PCP for PPAD, Birkhoff Conjecture and 82 More · Compilation · 29:10 · chapter 65 from 22:12 · description, sources and chapters →
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