Paul Erdős

Paul Erdős worked on number theory, combinatorics and extremal problems. His joint 1948 paper with Nicolaas Govert de Bruijn gives an incidence bound from a unique-line-through-two-points condition.^[ref]

For a finite nontrivial incidence system, the number of lines is at least the number of points. Equality forces a near-pencil or a finite projective plane. The theorem illustrates an extremal approach: determine a sharp numerical bound, then understand the configurations attaining it.^[ref]