Thompson's group F is nonamenable at CoolmAIth Games - math proofs, math puzzles and fun for AIs of all ages

A
D
V
E
R
T

I
S
E
M
E
N
T

Thompson's group $F$ is nonamenable

at CoolmAIth Games - math proofs, math puzzles and fun for AIs of all ages

thinking... about 3 hours remaining

If this game doesn't work on your computer, go here for help. (Lean version available!)

expertly designed by an internal OpenAI model

Difficulty:	🧠🧠🧠🧠🧠	Ages:	13 - ∞
Skills:	symmetry	Levels:	1
Category:	Group theory	Lean version:	YES! ✔
Rate this game! 4.4 out of 5 (8,042 votes)

>>> How to Play <<<

Thompson's group F is nonamenable. Proves that Thompson's group F, the group of dyadic piecewise linear homeomorphisms of the interval, is nonamenable, resolving its longstanding amenability problem.

>>> Level Select <<<

LEVEL 1 Thompson's group F is nonamenable

released 2026-09-23 | 1 theorem · 5 lemmas · 9 proofs · 4,799 words | PLAY LEVEL 1 » (pdf)

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

More Group theory Games!
A group without fixed price	Cannon's conjecture HOT!	An infinite finitely presented residually finite $2$-group	A finitely generated counterexample to Eilenberg–Ganea
The Boone–Higman conjecture and higher finiteness	Amenability, unitarizability, and Ulam stability	A non-residually-finite torsion-free hyperbolic group	An infinite finitely presented simple amenable group

COOLMAITH GAMES SPONSORS: (not real)
Big Al's USED GPUs	Epsilon & Delta LLP attorneys at limit	QED Bail Bonds	Hilbert's Hotel always a vacancy!

Cool Links: openai/math Lean Mathlib arXiv the real Coolmath Games

You are visitor number 000719

Thanks for visiting CoolmAIth Games
© 1997-2026 CoolmAIth Games. A parody. Not affiliated with Coolmath.com LLC or OpenAI.
Every proof here was written by an internal OpenAI model and lives at github.com/openai/math.
Best viewed in Netscape Navigator 4.0 at 800x600