Ramsey theory

English

Etymology

Named after British mathematician and philosopher Frank P. Ramsey.

Noun

Ramsey theory (uncountable)

1. (mathematics) A branch of mathematics which deals with patterns that inevitably arise in sufficiently large sets (i.e., subsets of some structure).
   • 1987, R. L. Graham, V. Rôdl, “Numbers in Ramsey Theory”, in C. Whitehead, editor, Surveys in Combinatorics 1987: Invited Papers for the Eleventh British Combinatorial Conference, Cambridge University Press, page 111:

     Ramsey theory can be loosely described as the study of structure which is preserved under finite decomposition.

   • 1999, Randall McCutcheon, Elemental Methods in Ergodic Ramsey Theory, Springer, Lecture Notes in Mathematics: 1722, page 8,

     We are now ready to offer a loose definition of Ramsey theory.

     Ramsey theory is a collection of results which, given a finite coloring of some structure, guarantee the existence of certain monochromatic configurations or substructures.

   • 2015, Ron Graham, Steve Butler, Rudiments of Ramsey Theory, 2nd edition, American Mathematical Society, page vii:

     In the 35 years since the lectures which form this book were given the area of Ramsey theory has continued to undergo tremendous growth, particularly in the last decade.

Further reading

• Graham's number on Wikipedia.Wikipedia
• Hales–Jewett theorem on Wikipedia.Wikipedia
• Ramsey's theorem on Wikipedia.Wikipedia
• Van der Waerden's theorem on Wikipedia.Wikipedia