VibeMathedMath problems solved by AI

Nine Ramsey Number Lower-Bound Records

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.

Result
Proved(see note)
Status
Partial result
AI contribution
AI-discovered
Method
Construction
Field
Ramsey theory
Posed by
Year posed
Years open
Solved
2026-03-10
Model
AlphaEvolve
Vendor
Google DeepMind
Collaborators
Ansh Nagda, Prabhakar Raghavan, Abhradeep Thakurta
Verification
Unreviewed
Publication
Preprint
Significance
25 / 100
Disclosed cost
Wikipedia
No dedicated article

What was actually shown

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

What the AI did

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.

Verification

Lower-bound constructions are finite certificates checkable by machine; no independent verification has been published yet.

Source

arXiv

Discussion