Group theory·OpenAI Math·Result 249·Lean formalisation listed
A finitely generated Eilenberg–Ganea counterexample
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 ‘A finitely generated Eilenberg–Ganea counterexample’ (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 It has not been peer reviewed.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 66 of 84 in Every OpenAI Math Result, Part 2 of 4: PCP for PPAD, Birkhoff Conjecture and 82 More · starts at 22:33 · watch from there on YouTube →
What OpenAI claims
Constructs a finitely generated residually finite group with integral cohomological dimension two and geometric dimension three, disproving the Eilenberg–Ganea conjecture. It has no two-dimensional classifying space, even with infinitely many cells. (Lean)
Paper
A finitely generated counterexample to the Eilenberg–Ganea conjecture
OpenAI's abstract We construct a finitely generated residually finite group of integral cohomological dimension two and geometric dimension three, disproving the Eilenberg–Ganea conjecture.
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 OpenAI posted a preprint on 23 September 2026; it has not been peer reviewed, so treat the result as OpenAI's claim until other mathematicians have checked it.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?
- Constructs a finitely generated residually finite group with integral cohomological dimension two and geometric dimension three, disproving the Eilenberg–Ganea conjecture. It has no two-dimensional classifying space, even with infinitely many cells. (Lean)
- Where is the proof?
- In the paper, A finitely generated counterexample to the Eilenberg–Ganea conjecture (PDF).
- Is there a video?
- Yes, on YouTube (29:10, chapter 66).
Also in
- Chapter 4 of 9 in Cannon's Conjecture, Thompson's Group F and 7 More in Group Theory · starts at 1:02 · 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 66 from 22:33 · description, sources and chapters →
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