Editing Gábor Szegő

{{Short description|Hungarian mathematician (1895–1985)}}
{{Infobox scientist
| name              = Gábor Szegő
| image             = Gabor Szego, 1925.jpg
| image_size        = 
| alt               = 
| caption           = Szegő in 1925
| birth_date        = {{Birth date|1895|01|20|df=y}}
| birth_place       = [[Kunhegyes]], [[Austria-Hungary]] (now [[Hungary]])
| death_date        = {{Death date and age|1985|08|07|1895|01|20|df=y}}
| death_place       = [[Palo Alto, California]], [[U.S.]]
| nationality       = 
| fields            = [[Mathematics]]
| workplaces        = [[University of Königsberg]]<br />[[Washington University in St. Louis]]<br />[[Stanford University]]
| alma_mater        = [[University of Vienna]]
| doctoral_advisor  = [[Wilhelm Wirtinger]]<br />[[Philipp Furtwängler]]
| doctoral_students = [[Paul C. Rosenbloom|Paul Rosenbloom]]<br/>[[Joseph Ullman]]
| known_for         = [[Fekete–Szegő inequality]]<br/>[[Pólya–Szegő inequality]]<br/>[[Grace–Walsh–Szegő coincidence theorem]]<br/>[[Rogers–Szegő polynomials]]<br/>[[Szegő kernel]]<br/>[[Szegő limit theorems]]<br/>[[Szegő polynomial]]<br />[[Blaschke product#Szegő theorem|Szegő theorem]]<br />[[Orthogonal polynomials on the unit circle|Szegő recurrence]]
| awards            = 
| thesis_title      = Ein Grenzwertsatz über die Toeplitz Determinanten einer reellen Funktion
| thesis_year       = 1918
}}

'''Gábor Szegő''' ({{IPA|hu|ˈɡaːbor ˈsɛɡøː|lang}}) (January 20, 1895 &ndash; August 7, 1985) was a Hungarian-American mathematician. He was one of the foremost [[Mathematical analysis|mathematical analysts]] of his generation and made fundamental contributions to the theory of [[orthogonal polynomials]] and [[Toeplitz matrix|Toeplitz matrices]] building on the work of his contemporary [[Otto Toeplitz]].

==Life==
[[File:George Polya and Gabor Szego in Berlin.jpg|thumb|Szegő with [[George Pólya]] in Berlin, delivering the manuscript of ''[[Problems and Theorems in Analysis]]'' to [[Springer Science+Business Media|Springer]].]]

Szegő was born in [[Kunhegyes]], [[Austria-Hungary]] (today [[Hungary]]), into a [[Jew]]ish family as the son of Adolf Szegő and Hermina Neuman.<ref name="kunhegy">[http://www.kunhegyes.hu/kunhegyes/hires/szego.htm Biography on the homepage of Kunhegyes] (in Hungarian)</ref> He married the chemist Anna Elisabeth Neményi in 1919, with whom he had two children.

In 1912 he started studies in [[mathematical physics]] at the [[University of Budapest]], with summer visits to the [[University of Berlin]] and the [[University of Göttingen]], where he attended lectures by [[Ferdinand Georg Frobenius|Frobenius]] and [[David Hilbert|Hilbert]], amongst others. In Budapest he was taught mainly by [[Lipót Fejér|Fejér]], [[:hu:Beke Manó|Beke]], [[József Kürschák|Kürschák]] and Bauer<ref>{{cite web| url = http://www.renyi.hu/~dezso/panorama/kantor.pdf| title = Biographies - Alfréd Rényi Institute of Mathematics (bios of Bauer Mihály and Beke Manó)}}</ref> and made the acquaintance of his future collaborators [[George Pólya]] and [[Michael Fekete]]. His studies were interrupted in 1915 by [[World War I]], in which he served in the infantry, artillery and air corps.
In 1918 while stationed in Vienna, he was awarded a [[doctorate]] by the [[University of Vienna]] for his work on [[Toeplitz matrix|Toeplitz determinants]].<ref>{{MathGenealogy |id=8363}}</ref><ref>[http://histsoc.stanford.edu/pdfmem/SzegoG.pdf Official memorial citation] {{webarchive|url=https://web.archive.org/web/20090325231306/http://histsoc.stanford.edu/pdfmem/SzegoG.pdf |date=2009-03-25 }}, [[Stanford University]].</ref> He received his [[Privat-Dozent]] from the University of Berlin in 1921, where he stayed until being appointed as successor to [[Konrad Knopp|Knopp]] at the [[University of Königsberg]] in 1926.  Intolerable working conditions during the [[Nazi regime]] resulted in a temporary position at the [[Washington University in St. Louis]], [[Missouri]] in 1936, before his appointment as chairman of the mathematics department at [[Stanford University]] in 1938, where he helped build up the department until his retirement in 1966.  He died in [[Palo Alto, California]]. His doctoral students include [[Paul C. Rosenbloom|Paul Rosenbloom]] and [[Joseph L. Ullman|Joseph Ullman]]. The Gábor Szegö Prize, Szegő Gábor Primary School, and Szegő Gábor Matematikaverseny (a mathematics competition in his former school) are all named in his honor.

==Works==
Szegő's most important work was in [[analysis (mathematics)|analysis]]. He was one of the foremost analysts of his generation and made fundamental contributions to the theory of [[Toeplitz matrix|Toeplitz matrices]] and [[orthogonal polynomials]]. He wrote over 130 papers in several languages. Each of his four books, several written in collaboration with others, has become a classic in its field. The monograph ''[[Orthogonal polynomials]]'', published in 1939, contains much of his research and has had a profound influence in many areas of [[applied mathematics]], including [[theoretical physics]], [[stochastic process]]es and [[numerical analysis]].

==Tutoring von Neumann==
At the age of 15, the young [[John von Neumann]], recognised as a mathematical prodigy, was sent to study advanced calculus under Szegő. On their first meeting, Szegő was so astounded by von Neumann's mathematical talent and speed that, as recalled by his wife, he came back home with tears in his eyes.<ref>Impagliazzo, John; [[James Glimm|Glimm, James]]; [[Isadore Singer|Singer, Isadore Manuel]] [https://books.google.com/books?id=XBK-r0gS0YMC&pg=PA15 ''The Legacy of John von Neumann''], American Mathematical Society, 1990, p. 5, {{ISBN|0-8218-4219-6}}.</ref>  Szegő subsequently visited the von Neumann house twice a week to tutor the child prodigy. Some of von Neumann's instant solutions to the problems in calculus posed by Szegő, sketched out on his father's stationery, are now on display at the von Neumann archive at Budapest.<ref>''John Von Neumann: The Scientific Genius Who Pioneered the Modern Computer'', by Norman Macrae, American Mathematical Soc., 2000, page 70</ref>

==Honours==
[[File:Gabor Szego (cropped).jpg|thumb|Bust of Gábor Szegő in his hometown of Kunhegyes]]
Amongst the many honours received during his lifetime were:

* [[Julius König|Julius König Prize]] of the Hungarian Mathematical Society (1928)
* Member of the [[Königsberg]]er Gelehrten Gesellschaft (1928)
* Corresponding member of the [[Austrian Academy of Sciences]] in Vienna (1960)
* Honorary member of the [[Hungarian Academy of Sciences]] (1965)

==Bibliography==
*{{citation|title=The collected Papers of Gábor Szegő, 3 Vols (ed. [[Richard Askey]])|year=1982|publisher=Birkhäuser|isbn=3-7643-3063-5}}
*{{citation|first1=George|last1=Pólya|author-link=George Pólya|first2=Gábor|last2=Szegő|title=[[Problems and Theorems in Analysis|Problems and Theorems in Analysis, 2 Vols]]|publisher=Springer-Verlag|orig-year=1925|year=1972}}
*{{citation|first=Gábor|last=Szegő|title=Asymptotische Entwicklungen der Jacobischen Polynome|publisher=Niemeyer|year=1933}}<ref>{{cite journal|author=Shohat, J.|author-link=James Alexander Shohat|title=Szegő on Jacobi Polynomials|journal=Bull. Amer. Math. Soc.|year=1935|volume=41|issue=3|pages=165–169|url=http://projecteuclid.org/euclid.bams/1183498071|doi = 10.1090/S0002-9904-1935-06050-1|doi-access=free}}</ref>
*{{citation|first=Gábor|last=Szegő|title=Orthogonal Polynomials|publisher=American Mathematical Society|year=1939}};<ref>{{cite journal|author=Shohat, J.|title=Review: Gabor Szegő: ''Orthogonal Polynomials''|journal=Bull. Amer. Math. Soc.|year=1940|volume=46|issue=7|pages=583–587|url=http://projecteuclid.org/euclid.bams/1183502776|doi=10.1090/s0002-9904-1940-07231-3|doi-access=free}}</ref> 2nd edn. 1955
*{{citation|first1=George|last1=Pólya|first2=Gábor|last2=Szegő|title=Isoperimetric problems in mathematical physics|series=Annals of Mathematics Studies|volume=27|publisher=Princeton University Press|year=1951|url=https://books.google.com/books?id=HWc8gFW2XXgC|isbn=0691079889}}
*{{citation|first1=Gábor|last1=Szegő|first2=Ulf|last2=Grenander|author-link2=Ulf Grenander|title=Toeplitz forms and their applications|publisher=Chelsea|year=1958}}<ref>{{cite journal|author=Spitzer, F.|author-link=Frank Spitzer|title=Review: Ulf Grenander and Gabor Szegő, ''Toeplitz forms and their applications''|journal=Bull. Amer. Math. Soc.|year=1959|volume=65|issue=2|pages=97–101|url=http://projecteuclid.org/euclid.bams/1183523047|doi=10.1090/s0002-9904-1959-10296-2|doi-access=free}}</ref>

==Selected articles==
*{{cite journal|title=Beiträge zur Theorie der Toeplitzschen Formen|journal=Math. Z.|year=1920|volume=6|issue=3–4|pages=167–202|doi=10.1007/bf01199955|last1=Szegő|first1=G.|s2cid=118147030 |url=https://zenodo.org/record/1447413}}
*{{cite journal|title=Beiträge zur Theorie der Toeplitzschen Formen, II|journal=Math. Z.|year=1921|volume=9|issue=3–4|pages=167–190|doi=10.1007/bf01279027|last1=Szegő|first1=G.|s2cid=125157848 |url=https://zenodo.org/record/1447419}}
*{{cite journal|title=A problem concerning orthogonal polynomials|journal=Trans. Amer. Math. Soc.|year=1935|volume=37|pages=196–206|mr=1501782|doi=10.1090/s0002-9947-1935-1501782-2|last1=Szegő|first1=G.|doi-access=free}}
**{{cite journal|title=Correction|journal=Trans. Amer. Math. Soc.|volume=39|issue=3|pages=500|mr=1501861|doi= 10.2307/1989765|jstor=1989765|last1=Szego|first1=Gabriel|year=1936}}
*{{cite journal|title=Inequalities for the zeros of Legendre polynomials and related functions|journal=Trans. Amer. Math. Soc.|year=1936|volume=39|pages=1–17|mr=1501831|doi=10.1090/s0002-9947-1936-1501831-2|last1=Szegő|first1=Gabriel|doi-access=free}}
*{{cite journal|title=On some Hermitian forms associated with two given curves of the complex plane|journal=Trans. Amer. Math. Soc.|year=1936|volume=40|issue=3|pages=450–461|mr=1501884|doi=10.1090/s0002-9947-1936-1501884-1|last1=Szegő|first1=Gabriel|doi-access=free}}
*{{cite journal|title=On the gradient of solid harmonic polynomials|journal=Trans. Amer. Math. Soc.|year=1940|volume=47|pages=51–65|mr=0000847|doi=10.1090/s0002-9947-1940-0000847-6|last1=Szegő|first1=G.|doi-access=free}}
*with [[Albert Charles Schaeffer|A. C. Schaeffer]]: {{cite journal|title=Inequalities for harmonic polynomials in two and three dimensions|journal=Trans. Amer. Math. Soc.|year=1941|volume=50|issue=2|pages=187–225|mr=0005164|doi=10.1090/s0002-9947-1941-0005164-7|last1=Schaeffer|first1=A. C.|last2=Szegő|first2=G.|doi-access=free}}
*{{cite journal|title=On the oscillations of differential transforms. I|journal=Trans. Amer. Math. Soc.|year=1942|volume=52|issue=3|pages=450–462|mr=0007170|doi=10.1090/s0002-9947-1942-0007170-6|last1=Szegő|first1=G.|doi-access=free}}
*{{cite journal|title=On the oscillations of differential transforms. IV. Jacobi polynomials|journal=Trans. Amer. Math. Soc.|year=1943|volume=53|issue=3|pages=463–468|mr=0008100|doi=10.1090/s0002-9947-1943-0008100-4|last1=Szegő|first1=G.|doi-access=free}}
*with Max Schiffer: {{cite journal|title=Virtual mass and polarization|journal=Trans. Amer. Math. Soc.|year=1949|volume=67|pages=130–205|mr=0033922|doi=10.1090/s0002-9947-1949-0033922-9|last1=Schiffer|first1=M.|last2=Szegő|first2=G.|doi-access=free}}
*{{cite journal|title=On certain special sets of orthogonal polynomials|journal=Proc. Amer. Math. Soc.|year=1950|volume=1|issue=6|pages=731–737|mr=0042546|doi=10.1090/s0002-9939-1950-0042546-2|last1=Szegő|first1=G.|doi-access=free}}
*with Albert Edrei: {{cite journal|title=A note on the reciprocal of a Fourier series|journal=Proc. Amer. Math. Soc.|year=1953|volume=4|issue=2|pages=323–329|mr=0053267|doi=10.1090/s0002-9939-1953-0053267-7|last1=Edrei|first1=A.|last2=Szegő|first2=G.|doi-access=free}}

==References==
{{Reflist}}

==External links==
*{{MacTutor Biography|id=Szego}}
*{{cite journal|author=Askey, Richard|title= Gábor Szegő - One hundred years (Topic #25)|journal=Op-Sf Net|date=17 May 1995 |url=http://math.nist.gov/opsf/personal/szego.html}}
* [https://people.math.osu.edu/nevai.1/AT/SZEGO/nevai=nevai1996=askey_nevai=szego.pdf Gábor Szegő: 1895-1985], by [[Richard Askey]] and [[Paul Nevai]] 

{{Authority control}}

{{DEFAULTSORT:Szego, Gabor}}
[[Category:1895 births]]
[[Category:1985 deaths]]
[[Category:20th-century Hungarian mathematicians]]
[[Category:American people of Hungarian-Jewish descent]]
[[Category:Mathematicians from Austria-Hungary]]
[[Category:Hungarian emigrants to the United States]]
[[Category:Hungarian Jews]]
[[Category:Mathematical analysts]]
[[Category:People from Kunhegyes]]
[[Category:Stanford University Department of Mathematics faculty]]
[[Category:Washington University in St. Louis mathematicians]]