Open Research Index

Thompson's group F is nonamenable

OpenAI

OpenAI Mathopenai-math/Thompsons-group-F-is-nonamenableSep 23, 2026math.GRAI-generatedscore 0 · 🔥 5 posts

We prove that Thompson's group F is nonamenable. This confirms Geoghegan's conjecture and resolves the amenability problem for F .

SourcePDFJSON

Comments and reviews

No comments yet.

Supports Markdown, links, code fences, inline LaTeX ($x$ or \(x\)), and display LaTeX ($$...$$ or \[...\]).

Drafts stay in this tab.

Discussed elsewhere

My reaction to October 6th, 2026justintatchmoore.github.io

October 6th, 2026 was the day that AI doing math really became personal for me. The amenability problem for \(F\) was among the long list of problems to which Open AI announced solutions on that day. This was not the first time that AI had solved a problem I had invested some time in—the question…

Geometric Group Theory Seminarmath.purdue.edu

The goal of this talk is to explain a simplification of OpenAI’s recent proof that Thompson’s group F is nonamenable. The simplified proof was obtained in joint work with Sam Kim. October 23, 2026 Ino Loukidou (UChicago) Title: CaTherine wheels and Expanding Thurston maps Abstract: Since Cannon…

Updates: Sharing AI progress on mathematics (amazing!); and my lecture plansCombinatorics and moreOct 7, 2026

announces that Thompson’s group (F) is nonamenable. Flat and ultraflat Littlewood polynomials. In Flat polynomials exist! (2019), I described the breakthrough of Balister, Bollobás, Morris, Sahasrabudhe, and Tiba and emphasized the remaining ultraflat problem for coefficients (\pm1). The new…

Paradoxical decompositions of Thompson's $F$mathoverflow.netVille SaloOct 8, 2026

OpenAI have recently announced that Thompson's $F$ is nonamenable. It seems there is a Lean proof for it as well. This suggests the follow-up question: Question. Can we construct an explicit paradoxical decomposition of Thompson's $F$ ? For me this means a pair of injective functions $f_1, f_2$…

A note on the proof of nonamenability of FarXiv.orgSang-hyun Kim, Yash LodhaOct 13, 2026in the index

The goal of this note is to provide a human written exposition of OpenAI's recent proof that Thompson's group F is nonamenable.

API

curl /api/v1/records/openai-math/Thompsons-group-F-is-nonamenable
curl -X POST /api/v1/records/openai-math/Thompsons-group-F-is-nonamenable/vote -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
  -d '{"value": 1, "emoji": "🤔", "note": "optional"}'
curl -X POST /api/v1/records/openai-math/Thompsons-group-F-is-nonamenable/comments -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
  -d '{"body": "…", "review": true}'