Pál Turán
Pál Turán | |
---|---|
Born | |
Died | 26 September 1976 | (aged 66)
Nationality | Hungarian |
Alma mater | Eötvös Loránd University |
Known for | Extremal graph theory Turán graph Turán number Turán's brick factory problem Turán sieve Turán's inequalities Turán's lemma Turán's method Turán's theorem Turán–Kubilius inequality Erdős–Turán conjecture Erdős–Turán inequality Erdős–Turán conjecture on additive bases Erdős–Turán construction Erdős–Turán–Koksma inequality Kővári–Sós–Turán theorem |
Awards | ICM Speaker (1970) Kossuth Prize (1948, 1952) |
Scientific career | |
Fields | Mathematics |
Institutions | Eötvös Loránd University |
Doctoral advisor | Lipót Fejér |
Doctoral students | László Babai János Pintz Peter Szüsz |
Pál Turán (Hungarian:
In 1940, because of his
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
At the same period of time, Turán and Pál Erdős were famous answerers in the journal
Turán received a teaching degree at the
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.[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.[5][4]
He married Edit (Klein) Kóbor in 1939; they had one son, Róbert.[6]
In World War II
In September 1940 Turán was interned in
- "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."[7]
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.[7] During this period, Turán composed and was partly able to record a long paper on the Riemann zeta function.[5][8]
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.[4]
In July 1944 Turán worked on a brick factory near Budapest.[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. At these crossings the trolleys would "bounce" and some of the bricks would fall out, causing a lot of problems for the workers. This situation led Turan to consider how to achieve the minimum number of crossings for m kilns and n warehouses. It was only after the war, in 1952, that he was able to work seriously on this problem.[7]
Turán was liberated in 1944, after which he was able to return to work at the rabbinical school in Budapest.[4]
After WWII
Turán became associate professor at the
In 1952 he married again, the second marriage was to
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. In 1960 he celebrated his 50th birthday and the birth of his third son, Tamás,[b] by swimming across the Danube.[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. He was a member of the
Death
Around 1970 Turán was diagnosed with
Work
Turán worked primarily in number theory,[13]: 4 but also did much work in analysis and graph theory.[14]
Number theory
In 1934, Turán used the
Turán was very interested in the distribution of primes in arithmetic progressions, and he coined the term "prime number race" for irregularities in the
Analysis
Much of Turán's work in analysis was tied to his number theory work. Outside of this he proved Turán's inequalities relating the values of the Legendre polynomials for different indices, and, together with Paul Erdős, the Erdős–Turán equidistribution inequality.
Graph theory
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
Power sum method
Turán developed the power sum method to work on the Riemann hypothesis.[15]: 9–14 The method deals with inequalities giving lower bounds for sums of the form
- hence the name "power sum".[16]: 319
Aside from its applications in
Publications
- Ed. by P. Turán. (1970). Number Theory. Amsterdam: North-Holland Pub. Co. ISBN 978-0-7204-2037-1.
- Paul Turán (1984). On a New Method of Analysis and Its Applications. New York: Wiley-Interscience. ISBN 978-0-471-89255-7. Deals with the power sum method.[17]
- Paul Erdős, ed. (1990). Collected Papers of Paul Turán. Budapest: Akadémiai Kiadó. ISBN 978-963-05-4298-2.[18]
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
- ^ Later professor of mathematics at University of Illinois Chicago
- ^ Tamás Turán became a philosopher and scholar of the Hebrew language.[11]
- ^ a b c d Alpár 1981, p. 271.
- ^ "Magyar Életrajzi Lexikon: Turán Pál" (in Hungarian). Magyar Elektronikus Könyvtár (Hungarian Electronic Library). Retrieved 21 June 2008.
- ^ Erdős 1998, p. 2.
- ^ a b c d "Paul Turán" (in Russian). School of Mathematics and Statistics, University of St Andrews, Scotland. Retrieved 2022-04-26.
- ^ a b c d Szüsz 1980, p. 11.
- ^ a b Babai, László (2001). "In and Out of Hungary: Paul Erdős, His Friends, and Times". University of Chicago. Archived from the original (PostScript) on 2007-02-07. Retrieved 22 June 2008.
- ^ a b c Turán 1977, p. 7.
- ^ P. Turán, «A note of welcome», Journal of Graph Theory 1 (1977), pp. 7-9.
- ^ Turán 1977, p. 8.
- ^ "Mathematical Graffiti #1 – Pál Turán e la Siberia… evitata" (in Italian). MaddMaths. Retrieved 2022-04-26.
- ^ Tamas Turan. Hungarian Academy of Sciences, Center for Jewish Studies of the Institute for Minority Studies
- ^ Alpár 1981, p. 271-271.
- ^ ISSN 0065-1036. Retrieved 22 June 2008.
- ^ See the death notice, publication list, and appreciations by József Szabados (analysis and approximation theory), by Pál Erdős and Mihály Szalay (number theory), and by Miklós Simonovits (graphy theory) in Matematikai Lapok 25 (1974) pages 211-250 (http://real-j.mtak.hu/9373/1/MTA_MatematikaiLapok_1974.pdf); although mostly Hungarian, much of the mathematics is easily understood and many of the citations are to English articles. Retrieved 10 April 2022.
- ^ ISSN 0065-1036.
- ^ . Retrieved 22 June 2008.
- .
- .
Sources
- Hersch, Reuben (1993). "A Visit to Hungarian Mathematics". The Mathematical Intelligencer. 15 (2): 13–26. S2CID 122827181.
- Szüsz, P. (1980). "P. Turán: Reminiscences of his student". Journal of Approximation Theory. 29 (1): 11–12. .
- Turán, Paul (1977). "A note of welcome". Journal of Graph Theory. 1: 7–9. .
- Erdős, Paul (1998). "Some Notes on Turan's Mathematical Work" (PDF). Journal of Approximation Theory. 29 (1): 2–5. .
- Alpár, L. (1981). "In memory of Paul Turán". Journal of Number Theory. Academic Press. 13 (3): 271–. .
External links
- Media related to Pál Turán at Wikimedia Commons
- O'Connor, John J.; Robertson, Edmund F., "Paul Turán", MacTutor History of Mathematics Archive, University of St Andrews
- Paul Turán memorial lectures at the Rényi Institute