Topology·OpenAI Math·Result 304
The Hilbert–Smith conjecture in every dimension
One of the 372 results in OpenAI's public mathematics catalogue, filed under topology: 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.
What OpenAI claims
Every locally compact second-countable Hausdorff group acting faithfully and jointly continuously on a connected finite-dimensional topological manifold is a Lie group. This proves the Hilbert–Smith conjecture in all finite dimensions, for Hausdorff second-countable manifolds without boundary.
Paper
The Hilbert–Smith conjecture in every finite dimension
We prove the Hilbert–Smith conjecture in every finite dimension: every locally compact second-countable Hausdorff group acting faithfully and jointly continuously on a connected Hausdorff second-countable finite-dimensional topological manifold without boundary is a Lie group.
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.
The video
Hilbert-Smith Conjecture: OpenAI Claims a Proof in Every Dimension · Short · 0:21 · description, sources and transcript →
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- 310Quillen's conjecture in rational homology
