An algebraic proof of van der Waerden's theorem (Q916797)

B. van der Waerden's theorem (of 1927) states that, if the natural numbers \({\mathbb{N}}\) are partitioned into finitely many subsets, then one of the subsets contains arbitrarily long arithmetic progressions. The present proof uses algebraic and topological properties of the compact right topological semigroup \(\beta\) \({\mathbb{N}}\), the Stone-Čech compactification of \({\mathbb{N}}\).