Differential geometry·OpenAI Math·Result 344
The metric Blaschke 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 metric Blaschke 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 It has not been peer reviewed.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 38 of 84 in Every OpenAI Math Result, Part 3 of 4: Operator Paving, Naimark's Problem and 82 More · starts at 12:56 · watch from there on YouTube →
What OpenAI claims
Proves the metric Blaschke conjecture: every closed connected Riemannian manifold of positive dimension whose injectivity radius equals its diameter is, up to scaling, a standard compact rank-one symmetric space.
Paper
The metric Blaschke theorem
OpenAI's abstract We prove the metric Blaschke conjecture: every connected closed smooth Riemannian manifold of positive dimension whose global injectivity radius equals its diameter is, up to scale, a standard compact rank-one symmetric space.
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 OpenAI posted a preprint on 23 September 2026; it has not been peer reviewed, so treat the result as OpenAI's claim until other mathematicians have checked it.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 metric Blaschke conjecture: every closed connected Riemannian manifold of positive dimension whose injectivity radius equals its diameter is, up to scaling, a standard compact rank-one symmetric space.
- Where is the proof?
- In the paper, The metric Blaschke theorem (PDF).
- Is there a video?
- Yes, on YouTube (29:20, chapter 38).
Also in
- Chapter 8 of 10 in Yau's Uniformization Conjecture, Blaschke Conjecture and 8 More · starts at 2:27 · 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 38 from 12:56 · description, sources and chapters →
Related results in Differential geometry
- 345Infinitely many closed geodesics on Riemannian spheres and closed three-manifoldsVideo
- 346Sharp singular-set bounds for stationary integral varifoldsVideo
- 347Counterexamples to stable-Morse and strong Arnold fixed-point boundsVideoLean
- 348Nonnegative-curvature Einstein classification and an L2 topological gapVideoLean
- 349The Solomon–Yau least-volume conjectureVideo
- 350Yau’s nodal bounds: surfaces and higher dimensionsVideoLean
