It is reasonable to think that the probability of finding a given property increases with the size of the set being searched. Ramsey theory even asserts that this probability becomes certainty once the search set is large enough. The question that then naturally arises is how to determine the minimal size of the set that guarantees the existence of this property. For instance, you need to choose three people to be certain that two of them are the same sex. But for large sets the problem becomes more complex, and often the best one can do is bracket the value of this minimal size.
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Ramsey theory grew out of eight pages written by Frank Plumpton Ramsey, whose teachers included the mathematician and Nobel laureate in literature Bertrand Russell (1872–1970), the philosopher Ludwig Wittgenstein (1889–1951) and the economist John Maynard Keynes (1883–1946). He might have left a much greater mark on the history of science had he not died of jaundice at the age of 26. Erdős would highlight his paper by working through numerous examples. He would also draw on the probabilistic methods he had introduced earlier in number theory, in particular with the theorem he proved (see the article) with Marc Kac (1914–1984).
