Ramsey theorem

What was discovered

In every sufficiently large structure, order necessarily appears (for example, among six people there are always three who all know one another or three mutual strangers). The origin of Ramsey theory and extremal combinatorics.

Ramsey proved it as a lemma for a case of the Entscheidungsproblem and died at the age of 26.

What it led to

• extremal combinatorics
• Szemerédi's theorem
• the mathematics of Erdős
• the Green-Tao theorem

Built on

• Graph theory: seven bridges of Königsberg1736
• first-order logic (decision problem)

📄 Original publication

Links