A finite set $A\subset {\mathbb{R}}^n$ is called Ramsey if, for any $k\ge 1$, there exists some $d=d(A,k)$ such that in any $k$-colouring of ${\mathbb{R}}^d$ there exists a monochromatic copy of $A$. Characterise the Ramsey sets in ${\mathbb{R}}^n$.

gpt-erdos · GPT-5.2 Pro + Deep Research · unverified

This is a main open problem in **Euclidean Ramsey theory**, so there is **no complete proved characterisation** known today.

llm-hunter · gpt pro 5.2 · unverified

1 LLM attack(s) recorded (gpt pro 5.2); unverified.