 Pál Turán

Paul (Pál) Turán
Born 18 August 1910
Budapest, HungaryDied 26 September 1976 (aged 66)
Budapest, HungaryResidence Hungary Nationality Hungarian Fields Mathematics Institutions University of Budapest Alma mater University of Budapest Doctoral advisor Lipót Fejér Known for Power sum method
Extremal graph theoryNotable awards Kossuth Prize
Tibor Szele PrizeThe native form of this personal name is Turán Pál. This article uses the Western name order.Paul (Pál) Turán (Hungarian pronunciation: [ˈtuɾaːn]; 18 August 1910–26 September 1976)^{[1]}^{:271}^{[2]} was a Hungarian mathematician who worked primarily in number theory. He had a long collaboration with fellow Hungarian mathematician Paul Erdős, lasting 46 years and resulting in 28 joint papers.^{[3]}
Contents
Life and education
Turán was born in Budapest on 18 August 1910.^{[1]}^{:271} He received a teaching degree at the University of Budapest in 1933 and the Ph.D. degree under Lipót Fejér in 1935.^{[1]}^{:271} As a victim of numerus clausus, he could not get university job for several years. He was sent to labour service at various times from 1940 to 1944. He is said to have been recognized and perhaps protected by a fascist guard, who, as a mathematics student, had admired Turán's work.^{[4]}
He became associate professor at the University of Budapest in 1945 and full professor in 1949.^{[1]}^{:272} He married mathematician Vera Sós in 1952 and they have two children.^{[5]}^{:20}
He died in Budapest on 26 September 1976^{[1]}^{:271} of leukemia.^{[6]}^{:8}
Work
Turán worked primarily in number theory,^{[6]}^{:4} but also did much work in analysis and graph theory.
Number theory
In 1934 Turán gave 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. In probabilistic terms he estimated the variance from ln ln n. Halász says "Its true significance lies in the fact that it was the starting point of probabilistic number theory". ^{[7]}^{:16} The Turán–Kubilius inequality is a generalization of this work.^{[6]}^{:5} ^{[7]}^{:16}
Turán was very interested in the distribution of primes in arithmetic progressions, and he coined the term "prime number race" for irregularities in the distribution of prime numbers among residue classes.^{[6]}^{:5} With his coauthor Knapowski he proved results concerning Chebyshev's bias.
The Erdős–Turán conjecture makes a statement about primes in arithmetic progression.
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 said "Turán was an 'unbeliever,' in fact, a 'pagan': he did not believe in the truth of Riemann's hypothesis."^{[3]}^{:3}
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 ErdősTurán 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 fastestgrowing subjects in combinatorics."^{[3]}^{:4} The field is known more briefly today as extremal graph theory. Turán's bestknown 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 K_{r} 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 Kövari–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.
Power sum method
Turán developed the power sum method to work on the Riemann hypothesis.^{[7]}^{:9–14} The method deals with inequalities giving lower bounds for sums of the form
hence the name "power sum".^{[8]}^{:319} Besides its applications in analytic number theory, it has been used in function theory, numerical analysis, differential equations, transcendence theory, and estimating the number of zeroes of a function in a disk.^{[8]}^{:320}
Publications
 Ed. by P. Turán. (1970). Number Theory. Amsterdam: NorthHolland Pub. Co. ISBN 9780720420371.
 Paul Turán (1984). On a New Method of Analysis and Its Applications. New York: WileyInterscience. ISBN 9780471892557. Deals with the power sum method.
 edited by Paul Erdős. (1990). Collected Papers of Paul Turán. Budapest: Akadémiai Kiadó. ISBN 9789630542982.
Honors
 Hungarian Academy of Sciences elected corresponding member in 1948 and ordinary member in 1953^{[1]}^{:272}
 Kossuth Prize in 1948 and 1952^{[1]}^{:272}
 Tibor Szele Prize of János Bolyai Mathematical Society 1975^{[1]}^{:272}
Notes
 ^ ^{a} ^{b} ^{c} ^{d} ^{e} ^{f} ^{g} ^{h} Alpár, L. (August 1981). "In memory of Paul Turán". Journal of Number Theory (Academic Press) 13 (3): 271–278. doi:10.1016/0022314X(81)900123.
 ^ "Magyar Életrajzi Lexikon: Turán Pál" (in Hungarian). Magyar Elecktronikus Könyvtár (Hungarian Electronic Library). http://mek.oszk.hu/00300/00355/html/ABC15363/16089.htm. Retrieved 20080621.
 ^ ^{a} ^{b} ^{c} Erdős, Paul (1980). "Some notes on Turán's mathematical work". Journal of Approximation Theory 29 (1): 2–6. doi:10.1016/00219045(80)901331. http://www.renyi.hu/~p_erdos/198042.pdf. Retrieved 20080622.
 ^ "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 proofreader 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." P. Turán, "A note of welcome", Journal of Graph Theory 1 (1977), pp. 79.
 ^ Babai, László (2001). "In and Out of Hungary: Paul Erdős, His Friends, and Times" (PostScript). University of Chicago. http://www.cs.uchicago.edu/files/tr_authentic/TR200103.ps. Retrieved 20080622.
 ^ ^{a} ^{b} ^{c} ^{d} Erdős, Paul (1980). "Some personal reminiscences of the mathematical work of Paul Turán". Acta Arithmetica 37: 3–8. ISSN 00651036. http://www.renyi.hu/~p_erdos/198043.pdf. Retrieved 20080622.
 ^ ^{a} ^{b} ^{c} Halász, G. (1980). "The numbertheoretic work of Paul Turán". Acta Arithmetica 37: 9–19. ISSN 00651036. http://www.numbertheory.org/obituaries/AA/turan/turan_halasz/index.html. Retrieved 20080622.^{[dead link]}
 ^ ^{a} ^{b} Tijdeman, R. (April 1986). "Book reviews: On a new method of analysis and its applications" (PDF). Bulletin of the American Mathematical Society (Providence, RI: American Mathematical Society) 14 (2): 318–322. doi:10.1090/S02730979198615456X. http://projecteuclid.org/DPubS/Repository/1.0/Disseminate?view=body&id=pdf_1&handle=euclid.bams/1183553181. Retrieved 20080622.
External links
 Pál Turán at the Mathematics Genealogy Project.
 O'Connor, John J.; Robertson, Edmund F., "Paul Turán", MacTutor History of Mathematics archive, University of St Andrews, http://wwwhistory.mcs.standrews.ac.uk/Biographies/Turan.html.
 Paul Turán memorial lectures at the Rényi Institute
Categories: 1910 births
 1976 deaths
 20thcentury mathematicians
 Number theorists
 Combinatorialists
 Hungarian mathematicians
 Members of the Hungarian Academy of Sciences
 Hungarian Jews
 Graph theorists
Wikimedia Foundation. 2010.
Look at other dictionaries:
Pál Turán — à l université de Leipzig en 1955 Naissance 18 août 1910 Budapest ( … Wikipédia en Français
Pal Turan — Pál Turán, 1955 Pál Turán (auch: Paul Turán; * 28. August 1910 in Budapest; † 26. September 1976 ebenda) war ein ungarischer Mathematiker. Er lieferte Beiträge zu der Zahlentheorie, Gruppentheorie und der … Deutsch Wikipedia
Pál Turán — Pál Turán, 1955 Pál Turán (auch: Paul Turán; * 18. August 1910 in Budapest; † 26. September 1976 ebenda)[1] war ein u … Deutsch Wikipedia
Turán — Pál Turán, 1955 Pál Turán (auch: Paul Turán; * 28. August 1910 in Budapest; † 26. September 1976 ebenda) war ein ungarischer Mathematiker. Er lieferte Beiträge zu der Zahlentheorie, Gruppentheorie und der Approximationstheorie. Er bewie … Deutsch Wikipedia
Turán graph — The Turán graph T(13,4) Named after Pál Turán v · … Wikipedia
Turan (Name) — Turan ist ein türkischer männlicher Vorname[1][2] und Familienname. Er bezeichnet die Landschaft Turan, die imaginäre Urheimat der Turkvölker. Inhaltsverzeichnis 1 Namensträger 1.1 Herrscher … Deutsch Wikipedia
Turan — bezeichnet: Turan (Name), Personen dieses Namens Turan (Gottheit), eine Fruchtbarkeits und Schutzgöttin der Etrusker Turan (Panzer), einen ungarischen Panzer im Zweiten Weltkrieg Turan (altpers. Turân „Land des Tur“) ist der Name folgender Orte:… … Deutsch Wikipedia
Turan (disambiguation) — Turan may refer to:*Turan, an ethnic and geographic term referring to some or all peoples of Central Asia *Tur an, Israel *Turan (town), Tuva, Russia *Turan, Azerbaijan, in Shaki Rayon *Turan (goddess), in Etruscan mythology, the goddess of love… … Wikipedia
Pál — ist die ungarische Form des männlichen Vornamens Paul.[1][2] Inhaltsverzeichnis 1 Bekannte Namensträger 1.1 Vorname 1.2 Familienname … Deutsch Wikipedia
Turan — Cette page d’homonymie répertorie les différents sujets et articles partageant un même nom. Turan est la déesse de l amour, de la beauté dans la mythologie étrusque. Turan ou Touran est le nom donné par les peuples iraniens pour désigner le Nord… … Wikipédia en Français