Paul Erdős

Paul Erdős (1913–1996) was a Hungarian mathematician whose prolific collaborations produced influential work in number theory, combinatorics, and graph theory.

Combinatorics: The branch of mathematics concerned with finite or discrete structures and their arrangements. Many of Erdős’s central questions concerned how large or complex discrete structures must be.
Erdős–Ko–Rado theorem: A theorem bounding the size of a family of pairwise-intersecting subsets of a finite set. It exemplifies Erdős’s work on extremal questions about set systems.
Alfréd Rényi: A Hungarian mathematician known for contributions to probability, information theory, and graph theory. Rényi was one of Erdős’s closest collaborators, including on random graph theory.
Erdős problem: An unsolved or solved mathematical question posed by Paul Erdős, often recorded with a monetary prize. His large collection of problems continues to guide research across several mathematical fields.
Number theory: The study of integers and their arithmetic properties. Erdős used elementary and probabilistic methods to establish results about prime numbers and other integers.
Erdős–Stone theorem: A theorem giving the asymptotic edge density needed to force a fixed graph as a subgraph. It became a central asymptotic result in extremal graph theory.
András Hajnal: A Hungarian mathematician whose work includes set theory and combinatorics. Hajnal collaborated with Erdős on influential problems in combinatorics and set theory.
Erdős Prize: A mathematics award presented by the World Federation of Scientists for outstanding contributions to mathematics. The prize bears his name and recognizes work across mathematical disciplines.
Graph theory: The mathematical study of graphs, made of vertices joined by edges. Erdős helped establish graph theory as a central setting for extremal and probabilistic questions.
Erdős–Rényi model: A family of random graph models in which edges are included independently with a specified probability. Erdős and Alfréd Rényi used random graphs to study which graph properties emerge as networks grow.

Linked from 46 pages