Gallai’s Theorem: A Detailed Exposition of Witt’s Proof

Abstract

Gallai’s theorem states that if the Euclidean plane is colored with finitely many colors then every finite configuration of points admits a monochromatic homothetic copy. This paper presents a detailed exposition of a proof originally published by Ernst Witt in 1952 and subsequently expanded by Alexander Soifer. Additional intermediate steps are supplied throughout, yielding a self-contained and easily verified proof. The argument is formulated recursively through finite configurations associated with a double induction and thereby makes explicit the finite structures underlying the theorem.