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# Turán, Pál

(1910–1976), mathematician. As was the case with many of his contemporary mathematicians, Pál Turán (until 1919, Rosenfeld) entered a problem-solving contest sponsored by the Hungarian monthly journal *Középiskolai Matematikai Lapok* (Mathematical and Physical Journal for Secondary Schools). By the point at which the finest problem solvers entered the universities, they were already familiar with each other’s mathematical interests and strengths. At Pázmány Péter University, Turán was the student of Lipót Fejér, who came from a similar background. Turán received his Ph.D. in 1935.

Many of the students who had come from Jewish middle-class backgrounds formed lifelong friendships and collaborated professionally, deeply influenced by bonds forged during regular meetings at the statue of “Anonymous” in the city park and by excursions to the Buda Hills, and to Zugliget and its surroundings. Their camaraderie was enforced by the social and political discrimination many of them faced. That is how the friendship and fruitful professional collaboration of the aristocratically disposed Turán and Pál Erdős (1913–1996) began. From 1934, they wrote 30 articles jointly.

Starting in 1937, Turán taught at the high school of the National Rabbinical Seminary and lectured in the framework of the free university sponsored by OMIKE (Országos Magyar Izraelita Közművelődési Egyesület; Central Israelite Educational-Cultural Society in Hungary). During World War II, he was in the forced labor service and later hid in Budapest. In 1946, he began teaching at the University of Budapest (becoming a full professor two years later). Elected as an associate member of the Hungarian Academy of Sciences in 1948, he became a regular member in 1953. In 1949 and again in 1952 he received the Kossuth Prize.

Between 1963 and 1966, Turán served as president of the János Bolyai Mathematical Society. He was on the editorial board of several international mathematical periodicals *(Acta Arithmetica, Journal of Number Theory, Archiv für Mathematik)* and from 1949 was editor in chief of *Matematikai Lapok.* From 1949 until 1975 (when he became terminally ill) he was the director of the Department of Algebra and Number Theory at the University of Budapest. In 1968 he became a member of the Mathematical Institute of the Hungarian Academy of Sciences, heading the Department of Complex Function Theory. He was also a guest professor at many European and North American universities.

Turán was one of the most important mathematicians of twentieth-century Hungary. The number of his publications, written alone or with a coauthor, exceeds 245, and his research led him to remarkable finds in almost every branch of mathematics. His most important discovery is the power sum method that bears his name. His graph theorem initiated extremal graph theory. Turán also played a crucial role in the birth of probabilistic number theory, and the development of comparative prime number theory is also connected to his name. He was a leading figure in approximation and interpolation theory, the theory of uniform distribution, in complex function theory, and in statistical group theory.

Although Turán was not religious, he never denied being Jewish—not even during the Stalinist period—and this was a source of conflict between him and rival mathematicians, even during the regime of János Kádár. In the late 1940s, Turán participated actively in the life of the Jewish community; his course of life was typical of the careers of Jewish intellectuals and academics during the Communist regime. His main works appeared in the three-volume *Collected Papers of Pál Turán,* edited by Erdős in 1990.

## Suggested Reading

György Alexits, “Turán Pál,” *Magyar Tudomány* 22.3 (1977): 238–240; Alfréd Rényi, “Turán Pál matematikai munkássága,” *Matematikai Lapok* 11.4 (1960): 229–259.

## Author

## Translation

Translated from Hungarian by Veronika Szabó