# Ramsey theory

> 5 AI-made results on Ramsey theory, each explained in plain English. Ramsey theory asks how large a structure must be before some orderly pattern is…

Canonical: https://closedform.nishachay.tech/topic/ramsey-theory/
Last updated: 2026-10-14

Ramsey theory asks how large a structure must be before some orderly pattern is forced to appear inside it.

5 AI-made results on Ramsey theory, from 6 papers in the OpenAI math collection, each explained in plain English. 4 have a formal Lean proof listed; 1 is claimed in a paper and not yet machine-checked. The oldest question here dates back to 1935: [Sharp logarithmic exponents for off-diagonal Ramsey numbers](https://closedform.nishachay.tech/e/openai-math-2026-170/).

## Results (5)

- [Superexponential van der Waerden numbers](https://closedform.nishachay.tech/e/openai-math-2026-160/) - Entry 160 · Proves van der Waerden numbers grow faster than any exponential, answering a question of Erdős for two colors. (Formal proof listed)
- [Sharp logarithmic exponents for off-diagonal Ramsey numbers](https://closedform.nishachay.tech/e/openai-math-2026-170/) - Entry 170 · For every fixed s ≥ 5, the Ramsey number r(s,t) now has its exact power of log t, up to a vanishing error. (Formal proof listed)
- [The hypercube Ramsey conjecture](https://closedform.nishachay.tech/e/openai-math-2026-171/) - Entry 171 · Two-coloring the links among a constant times 2ⁿ points always gives a one-color n-dimensional cube, the paper claims. (Claimed, not checked)
- [Classification of finite Euclidean Ramsey configurations](https://closedform.nishachay.tech/e/openai-math-2026-172/) - Entry 172 · An exact algebraic test tells which finite point sets must appear in one color in any coloring of space. (Formal proof listed)
- [Cycle–clique Ramsey numbers](https://closedform.nishachay.tech/e/openai-math-2026-189/) - Entry 189 · Exact Ramsey numbers for a cycle versus a clique: R(C_m, K_n) = (m − 1)(n − 1) + 1 when m ≥ n ≥ 3. (Formal proof listed)

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