{"id":"openai-math/Thompsons-group-F-is-nonamenable","pdf":"https://github.com/openai/math/blob/main/preprints/Thompsons-group-F-is-nonamenable-September-23-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Thompsons-group-F-is-nonamenable-September-23-2026","tags":["group-theory","amenability","thompson-group"],"score":0,"title":"Thompson's group F is nonamenable","domain":"Group theory","family":"248","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.GR","summary":"We prove that Thompson's group F is nonamenable. This confirms Geoghegan's conjecture and resolves the amenability problem for F .","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":5,"published":"2026-09-23","reactions":{},"discussion":[{"url":"https://justintatchmoore.github.io/homepage/10-6-2026.html","kind":"web","site":"justintatchmoore.github.io","text":"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…","added":"2026-10-24","title":"My reaction to October 6th, 2026"},{"url":"https://www.math.purdue.edu/calendar/seminars/ggt/#:~:text=The%20goal%20of%20this%20talk%20is%20to%20explain%20a%20simplification%20of%20OpenAI%E2%80%99s%20recent%20proof%20that%20Thompson%E2%80%99s%20group%20F%20is%20nonamenable","kind":"web","site":"math.purdue.edu","text":"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…","added":"2026-10-24","title":"Geometric Group Theory Seminar"},{"url":"https://gilkalai.wordpress.com/2026/10/07/updates-sharing-ai-progress-on-mathematics-amazing-and-my-lecture-plans/#:~:text=announces%20that%20Thompson","date":"2026-10-07","kind":"web","site":"Combinatorics and more","text":"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…","added":"2026-10-24","title":"Updates: Sharing AI progress on mathematics (amazing!); and my lecture plans"},{"url":"https://mathoverflow.net/questions/515834/paradoxical-decompositions-of-thompsons-f","date":"2026-10-08","kind":"web","site":"mathoverflow.net","text":"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 $f_1, f_2$…","added":"2026-10-24","title":"Paradoxical decompositions of Thompson's $F$","author":"Ville Salo"},{"url":"https://arxiv.org/abs/2610.18360","date":"2026-10-13","kind":"web","site":"arXiv.org","text":"The goal of this note is to provide a human written exposition of OpenAI's recent proof that Thompson's group F is nonamenable.","added":"2026-10-24","title":"A note on the proof of nonamenability of F","author":"Sang-hyun Kim, Yash Lodha","record":"arxiv/2610.18360"}],"formalized":true,"family_title":"Thompson's group F is nonamenable"}