Ramsey Number R(5,5)

R(s,t) is the least n such that every red/blue edge-colouring of \(K_n\) contains a red \(K_s\) or blue \(K_t\). Determine R(5,5). Current bounds: 43 ≤ R(5,5) ≤ 48.

Erdős's parable: if aliens demand R(5,5) or Earth is destroyed, humanity should compute; if they demand R(6,6), we should attempt destruction-level counterattack. Progress is glacial: R(4,5) = 25 fell to exhaustive computer search reported in 2024; R(5,5)'s window has narrowed by only a handful across ninety years. Every point shaved requires petabyte-scale graph generation and symmetry breaking — and the answer may forever exceed practical computability, which is rather the point of Ramsey theory.