van der Waerden's theorem

Meanings

1. In Ramsey theory, a theorem stating that, for any given positive integers r and k, there is some number N such that if the integers {1, 2, ..., N} are colored, each with one of r different colors, then there are at least k integers in arithmetic progression whose elements are of the same color.

Etymology

Named after the Dutch mathematician B. L. van der Waerden.