Gábor Szego
Encyclopedia
Hungary
Hungary , officially the Republic of Hungary , is a landlocked country in Central Europe. It is situated in the Carpathian Basin and is bordered by Slovakia to the north, Ukraine and Romania to the east, Serbia and Croatia to the south, Slovenia to the southwest and Austria to the west. The...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
. He was one of the foremost analysts
Mathematical analysis
Mathematical analysis, which mathematicians refer to simply as analysis, has its beginnings in the rigorous formulation of infinitesimal calculus. It is a branch of pure mathematics that includes the theories of differentiation, integration and measure, limits, infinite series, and analytic functions...
of his generation and made fundamental contributions to the theory of Toeplitz matrices
Toeplitz matrix
In linear algebra, a Toeplitz matrix or diagonal-constant matrix, named after Otto Toeplitz, is a matrix in which each descending diagonal from left to right is constant...
and orthogonal polynomials
Orthogonal polynomials
In mathematics, the classical orthogonal polynomials are the most widely used orthogonal polynomials, and consist of the Hermite polynomials, the Laguerre polynomials, the Jacobi polynomials together with their special cases the ultraspherical polynomials, the Chebyshev polynomials, and the...
.
Life
Szegő was born in KunhegyesKunhegyes
Kunhegyes is a town in Jász-Nagykun-Szolnok, Hungary. It is located at around ....
, Hungary
Hungary
Hungary , officially the Republic of Hungary , is a landlocked country in Central Europe. It is situated in the Carpathian Basin and is bordered by Slovakia to the north, Ukraine and Romania to the east, Serbia and Croatia to the south, Slovenia to the southwest and Austria to the west. The...
into a Jewish family. He married Anna Nemenyi in 1919, with whom he had two children.
In 1912 he started studies in mathematical physics
Mathematical physics
Mathematical physics refers to development of mathematical methods for application to problems in physics. The Journal of Mathematical Physics defines this area as: "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and...
at the University of Budapest
University of Budapest
The Eötvös Loránd University or ELTE, founded in 1635, is the largest university in Hungary, located in Budapest.-History:The university was founded in 1635 in Nagyszombat by the archbishop and theologian Péter Pázmány. Leadership was given over to the Jesuits...
, with summer visits to the University of Berlin and the University of Göttingen, where he attended lectures by Frobenius
Ferdinand Georg Frobenius
Ferdinand Georg Frobenius was a German mathematician, best known for his contributions to the theory of differential equations and to group theory...
and Hilbert
David Hilbert
David Hilbert was a German mathematician. He is recognized as one of the most influential and universal mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many areas, including invariant theory and the axiomatization of...
, amongst others. In Budapest he was taught mainly by Fejér
Lipót Fejér
Lipót Fejér , was a Hungarian mathematician. Fejér was born Leopold Weiss, and changed to the Hungarian name Fejér around 1900....
, Beke, Kürschák
József Kürschák
József Kürschák was a Hungarian mathematician noted for his work on trigonometry and for his creation of the theory of valuations. He proved that every valued field can be embedded into a complete valued field which is algebraically closed. In 1918 he proved that the sum of reciprocals of...
and Bauer and made the acquaintance of his future collaborators George Pólya
George Pólya
George Pólya was a Hungarian mathematician. He was a professor of mathematics from 1914 to 1940 at ETH Zürich and from 1940 to 1953 at Stanford University. He made fundamental contributions to combinatorics, number theory, numerical analysis and probability theory...
and Michael Fekete. His studies were interrupted in 1915 by the World War I
World War I
World War I , which was predominantly called the World War or the Great War from its occurrence until 1939, and the First World War or World War I thereafter, was a major war centred in Europe that began on 28 July 1914 and lasted until 11 November 1918...
, in which he served in the infantry, artillery and air corps.
In 1918 while stationed in Vienna, he was awarded a doctorate
Doctorate
A doctorate is an academic degree or professional degree that in most countries refers to a class of degrees which qualify the holder to teach in a specific field, A doctorate is an academic degree or professional degree that in most countries refers to a class of degrees which qualify the holder...
by the University of Vienna
University of Vienna
The University of Vienna is a public university located in Vienna, Austria. It was founded by Duke Rudolph IV in 1365 and is the oldest university in the German-speaking world...
for his work on Toeplitz determinants
Toeplitz matrix
In linear algebra, a Toeplitz matrix or diagonal-constant matrix, named after Otto Toeplitz, is a matrix in which each descending diagonal from left to right is constant...
. He received his Privat-Dozent from the University of Berlin in 1921, where he stayed until being appointed as successor to Knopp
Konrad Knopp
He also authored two texts on functions of a complex variable as well as a problem book:He also produced the sixth edition of the three-volume work :-References:...
at the University of Königsberg
University of Königsberg
The University of Königsberg was the university of Königsberg in East Prussia. It was founded in 1544 as second Protestant academy by Duke Albert of Prussia, and was commonly known as the Albertina....
in 1926. Intolerable working conditions during the Nazi regime resulted in a temporary position at the Washington University in Saint Louis, Missouri
Missouri
Missouri is a US state located in the Midwestern United States, bordered by Iowa, Illinois, Kentucky, Tennessee, Arkansas, Oklahoma, Kansas and Nebraska. With a 2010 population of 5,988,927, Missouri is the 18th most populous state in the nation and the fifth most populous in the Midwest. It...
in 1936, before his appointment as chairman of the mathematics department at Stanford University
Stanford University
The Leland Stanford Junior University, commonly referred to as Stanford University or Stanford, is a private research university on an campus located near Palo Alto, California. It is situated in the northwestern Santa Clara Valley on the San Francisco Peninsula, approximately northwest of San...
in 1938, where he helped build up the department until his retirement in 1966. He died in Palo Alto, California
Palo Alto, California
Palo Alto is a California charter city located in the northwest corner of Santa Clara County, in the San Francisco Bay Area of California, United States. The city shares its borders with East Palo Alto, Mountain View, Los Altos, Los Altos Hills, Stanford, Portola Valley, and Menlo Park. It is...
.
Works
Szegő's most important work was in analysis. He was one of the foremost analysts of his generation and made fundamental contributions to the theory of Toeplitz matricesToeplitz matrix
In linear algebra, a Toeplitz matrix or diagonal-constant matrix, named after Otto Toeplitz, is a matrix in which each descending diagonal from left to right is constant...
and orthogonal polynomials
Orthogonal polynomials
In mathematics, the classical orthogonal polynomials are the most widely used orthogonal polynomials, and consist of the Hermite polynomials, the Laguerre polynomials, the Jacobi polynomials together with their special cases the ultraspherical polynomials, the Chebyshev polynomials, and the...
. 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
Orthogonal polynomials
In mathematics, the classical orthogonal polynomials are the most widely used orthogonal polynomials, and consist of the Hermite polynomials, the Laguerre polynomials, the Jacobi polynomials together with their special cases the ultraspherical polynomials, the Chebyshev polynomials, and the...
, published in 1939, contains much of his research and has had a profound influence in many areas of applied mathematics
Applied mathematics
Applied mathematics is a branch of mathematics that concerns itself with mathematical methods that are typically used in science, engineering, business, and industry. Thus, "applied mathematics" is a mathematical science with specialized knowledge...
, including theoretical physics
Theoretical physics
Theoretical physics is a branch of physics which employs mathematical models and abstractions of physics to rationalize, explain and predict natural phenomena...
, stochastic process
Stochastic process
In probability theory, a stochastic process , or sometimes random process, is the counterpart to a deterministic process...
es and numerical analysis
Numerical analysis
Numerical analysis is the study of algorithms that use numerical approximation for the problems of mathematical analysis ....
.
Tutoring von Neumann
At the age of 15, the young John von NeumannJohn von Neumann
John von Neumann was a Hungarian-American mathematician and polymath who made major contributions to a vast number of fields, including set theory, functional analysis, quantum mechanics, ergodic theory, geometry, fluid dynamics, economics and game theory, computer science, numerical analysis,...
, 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 he was brought to tears. 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 with his father's stationary, are now on display at the von Neumann archive at Budapest.
Honours
Amongst the many honours received during his lifetime were:- Julius König PrizeJulius KönigGyula Kőnig was a Hungarian mathematician. He was born in Győr, Hungary and died in Budapest. His mathematical publications in foreign languages appeared under the name Julius König...
of the Hungarian Mathematical Society (1928) - Member of the KönigsbergKönigsbergKönigsberg was the capital of East Prussia from the Late Middle Ages until 1945 as well as the northernmost and easternmost German city with 286,666 inhabitants . Due to the multicultural society in and around the city, there are several local names for it...
er Gelehrten Gesellschaft (1928) - Corresponding member of the Austrian Academy of SciencesAustrian Academy of SciencesThe Austrian Academy of Sciences is a legal entity under the special protection of the Federal Republic of Austria. According to the statutes of the Academy its mission is to promote the sciences and humanities in every respect and in every field, particularly in fundamental research...
in Vienna (1960) - Honorary member of the Hungarian Academy of SciencesHungarian Academy of SciencesThe Hungarian Academy of Sciences is the most important and prestigious learned society of Hungary. Its seat is at the bank of the Danube in Budapest.-History:...
(1965)
See also
- Fekete–Szegő inequalityFekete–Szegő inequalityIn mathematics, the Fekete–Szegő inequality is an inequality for the coefficients of univalent analytic functions found by , related to the Bieberbach conjecture...
- Rogers–Szegő polynomials
- Szegő inequalitySzegő inequalityIn functional analysis, a mathematical discipline, the Szegő inequality or Pólya–Szegő inequality, named after George Pólya and Gábor Szegő, states that if...
- Szegő kernelSzegő kernelIn the mathematical study of several complex variables, the Szegő kernel is an integral kernel that gives rise to a reproducing kernel on a natural Hilbert space of holomorphic functions...
- Szegő limit theoremsSzegő limit theoremsIn mathematical analysis, the Szegő limit theorems describe the asymptotic behaviour of the determinants of large Toeplitz matrices. They were first proved by Gábor Szegő.-Notation:...
- Szegő polynomial
- Problems and theorems in analysis