Combinatorics·OpenAI Math·Result 171
The hypercube Ramsey conjecture
One of the 372 results in OpenAI's public mathematics catalogue, filed under combinatorics: 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
Resolves the Burr–Erdős hypercube Ramsey conjecture: the two-color Ramsey number of the n-dimensional cube is Θ(2n). Thus every red-blue coloring of a complete graph on a universal constant times the cube's number of vertices contains a monochromatic copy of the cube.
Paper
The hypercube Ramsey number has linear order
We prove that the two-color Ramsey number of the n-dimensional binary cube is at most C2n, where C is an absolute constant. This resolves positively the hypercube Ramsey conjecture of Burr and Erdős.
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
Hypercube Ramsey Conjecture: How Many Dots Force a Cube? · Short · 0:20 · description, sources and transcript →
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- 176The second Kahn–Kalai conjecture with an edge-count boundLean
- 177Bounded-degree coboundary expandersLean
