An automated proof that R(B_8,B_10)=37

Abstract

We present a short proof that the book Ramsey number $R(B_8,B_{10})$ equals 37. The lower bound $R(B_8,B_{10}) \ge 37$ is already available in the literature, so it is enough to rule out a 37-vertex graph containing neither a copy of $B_8$ nor a copy of $B_{10}$ in its complement. The problem as well as the proof were found with AutoMath, an AI-assisted mathematical discovery workflow developed by the first author. A Lean formalization of the upper-bound argument is available in the accompanying repository.