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 will embed the animation.
Latest paper
An algebra of infinite little finitistic dimension
The animation for this result has not been released yet. Subscribe on YouTube to catch it.
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
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.
Related results in Algebra
- 199Counterexamples to Auslander–Reiten, Tachikawa and related homological conjecturesLean
- 200Eisenbud–Green–Harris and lex-plus-powers
- 201A counterexample to Kurosh’s division-ring problem
- 202The blockwise Alperin weight conjecture
- 203Donovan's conjecture over fields and complete mixed-characteristic DVRs
- 204Tensor saturation for even spin groups
