Pál Turán (; 18 August 1910 – 26 September 1976) also known as Paul Turán, was a Hungarian mathematician who worked primarily in extremal combinatorics.

In 1940, because of his Jewish origins, he was arrested by the Nazis and sent to a labour camp in Transylvania, later being transferred several times to other camps. While imprisoned, Turán came up with some of his best theories, which he was able to publish after the war.

Turán had a long collaboration with fellow Hungarian mathematician Paul Erdős, lasting 46 years and resulting in 28 joint papers.

Biography

Early years

Turán was born into a Hungarian Jewish family in Budapest on 18 August 1910. Pál's outstanding mathematical abilities showed early, already in secondary school he was the best student.

At the same period of time, Turán and Paul Erdős were famous answerers in the journal KöMaL. On 1 September 1930, at a mathematical seminar at the University of Budapest, Turan met Erdős. They would collaborate for 46 years and produce 28 scientific papers together.

Turán received a teaching degree at the University of Budapest in 1933. In the same year he published two major scientific papers in the journals of the American and London Mathematical Societies. He got the PhD degree under Lipót Fejér in 1935 at Eötvös Loránd University.

As a Jew, he fell victim to numerus clausus, and could not get a stable job for several years. He made a living as a tutor, preparing applicants and students for exams. It was not until 1938 that he got a job at a rabbinical training school in Budapest as a teacher's assistant, by which time he had already had 16 major scientific publications and an international reputation as one of Hungary's leading mathematicians.

In World War II

In September 1940 Turán was interned in labour service. As he recalled later, his five years in labour camps eventually saved his life: they saved him from ending up in a concentration camp, where 550,000 of the 770,000 Hungarian Jews were murdered during World War II. In 1940 Turán ended up in Transylvania for railway construction. Turán said that one day while working another prisoner addressed him by his surname, saying that he was working extremely clumsily:

:"An officer was standing nearby, watching us work. When he heard my name, he asked the comrade whether I was a mathematician. It turned out, that the officer, Joshef Winkler, was an engineer. In his youth, he had placed in a mathematical competition; in civilian life he was a proof-reader at the print shop where the periodical of the Third Class of the Academy (Mathematical and Natural sciences) was printed. There he had seen some of my manuscripts."

Winkler wanted to help Turán and managed to get him transferred to an easier job. Turán was sent to the sawmill's warehouse, where he had to show the carriers the right-sized timbers. During this period, Turán composed and was partly able to record a long paper on the Riemann zeta function.

Turán was subsequently transferred several times to other camps. As he later recalled, the only way he was able to keep his sanity was through mathematics, solving problems in his head and thinking through problems.

In 1952 he married again, the second marriage was to Vera Sós, a mathematician. They had a son, György, in 1953. The couple published several papers together. by swimming across the Danube.

Turán was a member of the editorial boards of leading mathematical journals, he worked as a visiting professor at many of the top universities in the world. He was a member of the Polish, American and Austrian Mathematical Societies. In 1970, he was invited to serve on the committee of the Fields Prize. Turán also founded and served as the president of the János Bolyai Mathematical Society.

Death

Around 1970 Turán was diagnosed with leukaemia, but the diagnosis was revealed only to his wife Vera Sós, who decided not to tell him about his illness. In 1976 she told Erdős. Sós was sure that Turán was ‘too much in love with life’ and would have fallen into despair at the news of his fatal illness, and would not have been able to work properly. Erdős said that Turán did not lose his spirit even in the Nazi camps and did brilliant work there. Erdős regretted that Turán had been kept unaware of his illness because he had put off certain works and books 'for later', hoping that he would soon feel better, and in the end was never able to finish them. Turán died in Budapest on 26 September 1976 of leukemia, aged 66.

Work

Turán worked primarily in number theory,

Number theory

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 <math>\ln \ln n</math>. In probabilistic terms he estimated the variance from <math>\ln \ln n</math>. 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.

Aside from its applications in analytic number theory, it has been used in complex analysis, numerical analysis, differential equations, transcendental number theory, and estimating the number of zeroes of a function in a disk.

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Honors

  • Hungarian Academy of Sciences elected corresponding member in 1948 and ordinary member in 1953
  • Kossuth Prize in 1948 and 1952
  • Tibor Szele Prize of János Bolyai Mathematical Society 1975

Notes

Sources

  • Paul Turán memorial lectures at the Rényi Institute