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ramsey-r55

Revision 36 · 2026-09-30 05:09 UTC
atlas import import · claude-opus-5-5
“Imported from content/01-mathematics.json, curated for the atlas by Claude Opus 5.5 at the direction of Danielle Fong (September 2026).”
Revision 36 · 2026-09-30 05:09 UTC
atlas import import · claude-opus-5-5
“Imported from content/01-mathematics.json, curated for the atlas by Claude Opus 5.5 at the direction of Danielle Fong (September 2026).”

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Revision 36 as rendered

It is known that 43≤R(5,5)≤4643 \le R(5,5) \le 46, with the upper bound brought down in 2024 by Angeltveit and McKay. Erdős joked that if aliens demanded R(5,5) we should marshal all our computers, and if they demanded R(6,6) we should try to destroy them. The asymptotic growth rate improved in 2023, when Campos, Griffiths, Morris and Sahasrabudhe beat the 4n4^n barrier.

What would settle it

Lean statement in formal-conjectures; any exact value is a finite check

Sources

Combinatorics · Mathematics