chapter  20
20 Pages

Ramsey Theory

Frank Plumpton Ramsey (1903-1930) was a British mathematician who had many interests, including English literature, philosophy, economics and politics. Ramsey [194] wrote a collection of 18 papers called The Foundations of Mathematics, and Other Logical Essays, in which he intended to improve upon Principia Mathematica by Bertrand Russell and Alfred North Whitehead. These papers ranged in dates from 1923 to 1929 and were edited after his death. The result for which he is best known occurred in a paper, presented to the London Mathematical Society and published in 1930 (the year he died). This paper was titled “On a problem of formal logic” [193] and his famous result occurred only as a minor lemma that he used to solve a problem in logic but this result led to an area in Extremal Graph Theory that became known as Ramsey Theory.

One version of Ramsey’s famous theorem is stated next.