Algebra·OpenAI Math·Result 198·Lean formalisation listed
A counterexample to finitistic-dimension finiteness
One of the 372 results in OpenAI's public mathematics catalogue, filed under algebra: 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 counterexample to finitistic-dimension finiteness (algebra) in a preprint dated 23 September 2026. It has not been peer reviewed. The channel's animation, Finitistic Dimension Conjecture: OpenAI Claims a Counterexample, is on YouTube.
What OpenAI claims
Constructs a finite-dimensional complex algebra whose finite-dimensional modules have unbounded finite projective dimensions. This disproves the little finitistic-dimension conjecture. (Lean)
Paper
An algebra of infinite little finitistic dimension
OpenAI's abstract We construct a finite-dimensional complex algebra whose finite-dimensional modules have unbounded finite projective dimensions. This disproves the little finitistic-dimension 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 OpenAI posted a preprint on 23 September 2026; it has not been peer reviewed, so treat the result as OpenAI's claim until other mathematicians have checked it.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 finite-dimensional complex algebra whose finite-dimensional modules have unbounded finite projective dimensions. This disproves the little finitistic-dimension conjecture. (Lean)
- Where is the proof?
- In the paper, An algebra of infinite little finitistic dimension (PDF).
- Is there a video?
- Yes, on YouTube (0:20).
Also in
- Chapter 36 of 84 in Every OpenAI Math Result, Part 2 of 4: PCP for PPAD, Birkhoff Conjecture and 82 More · starts at 12:08 · watch from there on YouTube →
The video
Finitistic Dimension Conjecture: OpenAI Claims a Counterexample · Short · 0:20 · description, sources and transcript →
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