Differential geometry·OpenAI Math·Result 349
The Solomon–Yau least-volume conjecture
One of the 372 results in OpenAI's public mathematics catalogue, filed under differential geometry: 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 proof of the Solomon–Yau least-volume conjecture (differential geometry) in a preprint dated 23 September 2026. It has not been peer reviewed. The channel's animation, Every OpenAI Math Result, Part 3 of 4: Operator Paving, Naimark's Problem and 82 More, is on YouTube.
Chapter 42 of 84 in Every OpenAI Math Result, Part 3 of 4: Operator Paving, Naimark's Problem and 82 More · starts at 14:20 · watch from there on YouTube →
What OpenAI claims
Proves the Solomon–Yau least-volume conjecture for minimal hypersurfaces of round spheres. For every m ≥ 2, a closed connected minimal immersion into the unit sphere Sm+1 with non-totally-geodesic image has volume at least that of the smallest minimal Clifford product, counting covering multiplicity.
Paper
The Solomon–Yau least-volume theorem
OpenAI's abstract We prove the Solomon–Yau least-volume conjecture for minimal hypersurfaces of unit round spheres: in every dimension m ≥ 2, a closed connected minimal immersion with non-totally-geodesic image has volume at least the smallest m-dimensional minimal Clifford product. Volume is measured on the domain, so covering multiplicities are included.
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 OpenAI posted a preprint on 23 September 2026; it has not been peer reviewed, so treat the result as OpenAI's claim until other mathematicians have checked it.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?
- Proves the Solomon–Yau least-volume conjecture for minimal hypersurfaces of round spheres. For every m ≥ 2, a closed connected minimal immersion into the unit sphere Sm+1 with non-totally-geodesic image has volume at least that of the smallest minimal Clifford product, counting covering multiplicity.
- Where is the proof?
- In the paper, The Solomon–Yau least-volume theorem (PDF).
- Is there a video?
- Yes, on YouTube (29:20, chapter 42).
Also in
- Chapter 2 of 9 in Calabi Flow, Affine Bernstein Problem and 7 More in Differential Geometry · starts at 0:22 · watch from there on YouTube →
The video
Every OpenAI Math Result, Part 3 of 4: Operator Paving, Naimark's Problem and 82 More · Compilation · 29:20 · chapter 42 from 14:20 · description, sources and chapters →
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