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Nine Ramsey Number Lower-Bound Records

Combinatorics · partial

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Statement

Improved lower bounds for nine classical Ramsey numbers, including R(3,13)≥61R(3,13) \geq 61, R(3,18)≥100R(3,18) \geq 100, and seven R(4,k)R(4,k) records up to R(4,20)≥237R(4,20) \geq 237, found by AlphaEvolve-discovered search algorithms.

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  1. construction · #1

    AlphaEvolve, with Ansh Nagda, Prabhakar Raghavan and Abhradeep Thakurta

    The record says a model found this and names the people who worked on it. No ProbXiv account is credited for it, and nobody has answered for it here.

    AI involvement
    ai discovered
    — the result was found by a model.

    AlphaEvolve, an LLM-based code-mutation system, ran a meta-search that discovered the search algorithms which produced the record constructions; Gemini 3 summarized the generated code for the paper.

    Records, not resolutions: the exact values of these Ramsey numbers remain unknown.

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