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

In the same year he published two major scientific papers in the journals of the American and London Mathematical Societies.

[1] 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.

[7] During this period, Turán composed and was partly able to record a long paper on the Riemann zeta function.

[9] His and the other prisoners' task was to carry the brick cars from the kilns to the warehouses on rails that crossed at several points with other tracks.

This situation led Turan to consider how to achieve the minimum number of crossings for m kilns and n warehouses.

The only thing Turán said about that day in his correspondence with Erdös was that he had "come across an extremely interesting way of applying number theory..."[10] In 1952 he married again, the second marriage was to Vera Sós, a mathematician.

[6] One of his students said Turán was a very passionate and active man - in the summer he held maths seminars by the pool in between his swimming and rowing training.

[5] 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.

[12] 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.

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 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.

Halász says "Its true significance lies in the fact that it was the starting point of probabilistic number theory".

Much of Turán's number theory work dealt with the Riemann hypothesis and he developed the power sum method (see below) to help with this.

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."