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Steven Alexander Gaal (February 22, 1924 – March 17, 2016) (also known as István Sándor Gál or I. S. Gál) was a Hungarian- American
mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...
and Professor of Mathematics at the
University of Minnesota The University of Minnesota Twin Cities (historically known as University of Minnesota) is a public university, public Land-grant university, land-grant research university in the Minneapolis–Saint Paul, Twin Cities of Minneapolis and Saint ...
Minneapolis Minneapolis is a city in Hennepin County, Minnesota, United States, and its county seat. With a population of 429,954 as of the 2020 United States census, 2020 census, it is the state's List of cities in Minnesota, most populous city. Locat ...
.


Education

Gaal received his Ph.D. under
Frigyes Riesz Frigyes Riesz (, , sometimes known in English and French as Frederic Riesz; 22 January 1880 – 28 February 1956) was a HungarianEberhard Zeidler: Nonlinear Functional Analysis and Its Applications: Linear monotone operators. Springer, 199/ref> ...
and
Lipót Fejér Lipót Fejér (or Leopold Fejér, ; 9 February 1880 – 15 October 1959) was a Hungarian mathematician of Jewish heritage. Fejér was born Leopold Weisz, and changed to the Hungarian name Fejér around 1900. Biography He was born in Pécs, Au ...
in 1947, although at the time, graduate study in Hungary did not exist in the formal way it is thought of today. There were no formalities of preliminary exams or qualifying exams, no thesis advisor or tuition. After
World War I World War I or the First World War (28 July 1914 – 11 November 1918), also known as the Great War, was a World war, global conflict between two coalitions: the Allies of World War I, Allies (or Entente) and the Central Powers. Fighting to ...
, Hungary was dismembered and the
Austro-Hungarian Austria-Hungary, also referred to as the Austro-Hungarian Empire, the Dual Monarchy or the Habsburg Monarchy, was a multi-national constitutional monarchy in Central Europe between 1867 and 1918. A military and diplomatic alliance, it consist ...
monarchy ended. Two thirds of Hungary's territory was given to other states, some existing, others created and since vanished. Under these conditions, only few higher education faculty could be appointed and students had to learn only from books or one or two old sick professors. Nevertheless, doctoral students managed to create publishable theses. Gaal's thesis problem had its origin in a letter
Paul Erdős Paul Erdős ( ; 26March 191320September 1996) was a Hungarian mathematician. He was one of the most prolific mathematicians and producers of mathematical conjectures of the 20th century. pursued and proposed problems in discrete mathematics, g ...
wrote to
Pál Turán Pál Turán (; 18 August 1910 – 26 September 1976) also known as Paul Turán, was a Hungarian mathematician who worked primarily in extremal combinatorics. In 1940, because of his Jewish origins, he was arrested by History of the Jews in Hun ...
, in which he mentions a prize problem posed by the Netherlands Mathematical Society. Gaal solved it and with Erdős jointly published the solution.


Career

Gaal later went to
Paris Paris () is the Capital city, capital and List of communes in France with over 20,000 inhabitants, largest city of France. With an estimated population of 2,048,472 residents in January 2025 in an area of more than , Paris is the List of ci ...
, where he was employed by the
CNRS The French National Centre for Scientific Research (, , CNRS) is the French state research organisation and is the largest fundamental science agency in Europe. In 2016, it employed 31,637 staff, including 11,137 tenured researchers, 13,415 eng ...
(Centre National del la Recherche Scientifique) at the rank of ''attaché de recherché''. His supervisor was Jean Favard with higher supervisor
Jacques Hadamard Jacques Salomon Hadamard (; 8 December 1865 – 17 October 1963) was a French mathematician who made major contributions in number theory, complex analysis, differential geometry, and partial differential equations. Biography The son of a tea ...
. Gaal met many leading French mathematicians at the CNRS, including
Jean Leray Jean Leray (; 7 November 1906 – 10 November 1998) was a French mathematician, who worked on both partial differential equations and algebraic topology. Life and career He was born in Chantenay-sur-Loire (today part of Nantes). He studied at Éc ...
and both
Élie Élie is the French equivalent of "Elie (given name), Elie", "Elias" or "Elijah."''The Complete Baby Name Book'' 1989 Page 92 "It was revived in the seventeenth century by the Puritans, and is still used, especially by religious Protestant familie ...
and
Henri Cartan Henri Paul Cartan (; 8 July 1904 – 13 August 2008) was a French mathematician who made substantial contributions to algebraic topology. He was the son of the mathematician Élie Cartan, nephew of mathematician Anna Cartan, oldest brother of c ...
. After emigrating to the United States, he held positions at
Yale Yale University is a private Ivy League research university in New Haven, Connecticut, United States. Founded in 1701, Yale is the third-oldest institution of higher education in the United States, and one of the nine colonial colleges ch ...
and Princeton before joining the faculty of the School of Mathematics at the
University of Minnesota The University of Minnesota Twin Cities (historically known as University of Minnesota) is a public university, public Land-grant university, land-grant research university in the Minneapolis–Saint Paul, Twin Cities of Minneapolis and Saint ...
.
Atle Selberg Atle Selberg (14 June 1917 – 6 August 2007) was a Norwegian mathematician known for his work in analytic number theory and the theory of automorphic forms, and in particular for bringing them into relation with spectral theory. He was awarded ...
was instrumental in bringing Gaal to the
Institute for Advanced Study The Institute for Advanced Study (IAS) is an independent center for theoretical research and intellectual inquiry located in Princeton, New Jersey. It has served as the academic home of internationally preeminent scholars, including Albert Ein ...
in
Princeton, New Jersey The Municipality of Princeton is a Borough (New Jersey), borough in Mercer County, New Jersey, United States. It was established on January 1, 2013, through the consolidation of the Borough of Princeton, New Jersey, Borough of Princeton and Pri ...
. While in Princeton, Gaal met
Albert Einstein Albert Einstein (14 March 187918 April 1955) was a German-born theoretical physicist who is best known for developing the theory of relativity. Einstein also made important contributions to quantum mechanics. His mass–energy equivalence f ...
, though the two did not work together. It also was in Paris that Gaal had first met Paul Erdős. Seven years later, they wrote two more joint papers. Over the years, Gaal met Erdős on a number of other occasions, including his last visit to Minneapolis on the invitation of Carleton College, who sponsored his visit.
Robert Langlands Robert Phelan Langlands, (; born October 6, 1936) is a Canadian mathematician. He is best known as the founder of the Langlands program, a vast web of conjectures and results connecting representation theory and automorphic forms to the study o ...
has cited Gaal's influence in his early investigations of zeta functions and
Eisenstein series Eisenstein series, named after German mathematician Gotthold Eisenstein, are particular modular forms with infinite series expansions that may be written down directly. Originally defined for the modular group, Eisenstein series can be generalize ...
. Gaal's former wife, Lisl Gaal (originally Lisl Novak), is an accomplished mathematician in her own right and is well known for her text ''Classical Galois Theory''. In 2004, Gaal was honored at the
Hungarian Academy of Sciences The Hungarian Academy of Sciences ( , MTA) is Hungary’s foremost and most prestigious learned society. Its headquarters are located along the banks of the Danube in Budapest, between Széchenyi rakpart and Akadémia utca. The Academy's primar ...
80th anniversary as one of the "big five" most distinguished Hungarian mathematicians. The other honorees included John Horvath, János Aczél,
Ákos Császár Ákos Császár (, ) (26 February 1924 – 14 December 2017) was a Hungarian mathematician, specializing in general topology and real analysis. He discovered the Császár polyhedron, a nonconvex polyhedron without diagonals. He introduced the ...
and
László Fuchs László Fuchs (born June 24, 1924) is a Hungary, Hungarian-born American mathematician, the Evelyn and John G. Phillips Distinguished Professor Emeritus in Mathematics at Tulane University.
. Gaal gave a talk entitled "When is a Fibonacci sequence periodic?"Tribute to the achievements of five outstanding Hungarian mathematicians
Department of Mathematical Sciences of the Hungarian Academy of Sciences


Books

* (453 pp.) * (208 pp.) * *


References


External links


Erdős, P., and Gál, I. S. (1955). ''On the law of the iterated logarithm''. I. ''Proc. Konikl. Akad. Wetensch Ser A 58'' 65–84
a joint paper by Gaal and Erdős. an
''On the law of the iterated logarithm''. II


* {{DEFAULTSORT:Gaal, Steven 1924 births 2016 deaths Hungarian emigrants to the United States 20th-century American mathematicians 20th-century Hungarian mathematicians 21st-century American mathematicians 21st-century Hungarian mathematicians