Pál Turán

Turán died in Budapest on 26 September 1976 of leukemia, aged 66.

Turán became associate professor at the University of Budapest in 1945 and full professor in 1949. Turán married twice. He married Edit (Klein) Kóbor in 1939; they had one son, Róbert. His second marriage was to Vera Sós, a mathematician, in 1952; they had two children, György and Tamás.

As a Jew, he fell victim to numerus clausus, and could not get a university job for several years. He was sent to labour service at various times from 1940-44. He is said to have been recognized and perhaps protected by a fascist guard, who, as a mathematics student, had admired Turán's work.

Erdős wrote of Turán, "In 1940–1941 he created the area of extremal problems in graph theory which is now one of the fastest-growing subjects in combinatorics." The field is known more briefly today as extremal graph theory. Turán's best-known result in this area is Turán's graph theorem, that gives an upper bound on the number of edges in a graph that does not contain the complete graph Kr as a subgraph. He invented the Turán graph, a generalization of the complete bipartite graph, to prove his theorem. He is also known for the Kővári–Sós–Turán theorem bounding the number of edges that can exist in a bipartite graph with certain forbidden subgraphs, and for raising Turán's brick factory problem, namely of determining the crossing number of a complete bipartite graph.

In 1934, Turán used the Turán sieve to give a new and very simple proof of a 1917 result of G. H. Hardy and Ramanujan on the normal order of the number of distinct prime divisors of a number n, namely that it is very close to ln ⁡ ln ⁡ n {\displaystyle \ln \ln n} . In probabilistic terms he estimated the variance from ln ⁡ ln ⁡ n {\displaystyle \ln \ln n} . Halász says "Its true significance lies in the fact that it was the starting point of probabilistic number theory". The Turán–Kubilius inequality is a generalization of this work.

Pál Turán (Hungarian: [ˈpaːl ˈturaːn]; 18 August 1910 – 26 September 1976) also known as Paul Turán, was a Hungarian mathematician who worked primarily in extremal combinatorics. He had a long collaboration with fellow Hungarian mathematician Paul Erdős, lasting 46 years and resulting in 28 joint papers.

Turán was born into a Jewish family in Budapest on 18 August 1910.At the same period of time, Turán and Erdős were famous answerers in the journal KöMaL. He received a teaching degree at the University of Budapest in 1933 and the PhD degree under Lipót Fejér in 1935 at Eötvös Loránd University.