English

Van der Waerden's theorem on arithmetic progressions -- a survey of some historical and modern developments

Combinatorics 2026-03-30 v1 Dynamical Systems Number Theory

Abstract

Van der Waerden's theorem, published in Nieuw. Arch. Wisk. 15 (1927), acted as a catalyst for major further developments in Ramsey theory. In this survey, we delve into the legacy of this mathematical gem, tracing its historical origin, exploring its wide-ranging connections across research areas, and highlighting some of the important results it has inspired.

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Cite

@article{arxiv.2603.25922,
  title  = {Van der Waerden's theorem on arithmetic progressions -- a survey of some historical and modern developments},
  author = {Vitaly Bergelson and Florian K. Richter},
  journal= {arXiv preprint arXiv:2603.25922},
  year   = {2026}
}

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49 pages