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, structure, space, models, and change. History On ...

and Professor of Mathematics at the

University of Minnesota The University of Minnesota, formally the University of Minnesota, Twin Cities, (UMN Twin Cities, the U of M, or Minnesota) is a public land-grant research university in the Twin Cities of Minneapolis and Saint Paul, Minnesota, United States. ...

—

Minneapolis Minneapolis () is the largest city in Minnesota, United States, and the county seat of Hennepin County. The city is abundant in water, with thirteen lakes, wetlands, the Mississippi River, creeks and waterfalls. Minneapolis has its origins ...

Education

Gaal received his Ph.D. under

Frigyes Riesz Frigyes Riesz ( hu, Riesz Frigyes, , sometimes spelled as Frederic; 22 January 1880 – 28 February 1956) was a HungarianEberhard Zeidler: Nonlinear Functional Analysis and Its Applications: Linear monotone operators. Springer, 199/ref> mathema ...

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 Fejér studied mathematic ...

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 (28 July 1914 11 November 1918), often abbreviated as WWI, was one of the deadliest global conflicts in history. Belligerents included much of Europe, the Russian Empire, the United States, and the Ottoman Empire, with fightin ...

, Hungary was dismembered and the Austro-Hungarian 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 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. He had a long collaboration with fellow Hungarian mathematician Paul Erdős, lasting ...

, 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, most populous city of France, with an estimated population of 2,165,423 residents in 2019 in an area of more than 105 km² (41 sq mi), ma ...

, where he was employed by the CNRS (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 teac ...

. 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 and Henri Cartan. After emigrating to the United States, he held positions at

Yale Yale University is a private research university in New Haven, Connecticut. Established in 1701 as the Collegiate School, it is the third-oldest institution of higher education in the United States and among the most prestigious in the wor ...

and Princeton before joining the faculty of the School of Mathematics at the

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 awarde ...

was instrumental in bringing Gaal to the

Institute for Advanced Study The Institute for Advanced Study (IAS), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent schola ...

Princeton, New Jersey Princeton is a municipality with a borough form of government in Mercer County, in the U.S. state of New Jersey. It was established on January 1, 2013, through the consolidation of the Borough of Princeton and Princeton Township, both of whi ...

. While in Princeton, Gaal met

Albert Einstein Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest and most influential physicists of all time. Einstein is best known for developing the theory ...

, 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 In mathematics, a zeta function is (usually) a function analogous to the original example, the Riemann zeta function : \zeta(s) = \sum_^\infty \frac 1 . Zeta functions include: * Airy zeta function, related to the zeros of the Airy function * A ...

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 generaliz ...

. 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 80th anniversary as one of the "big five" most distinguished Hungarian mathematicians. The other honorees included John Horvath, János Aczél,

Ákos Császár Ákos Császár ( hu, Császár Ákos, ) (26 February 1924, Budapest – 14 December 2017, Budapest) was a Hungarian mathematician, specializing in general topology and real analysis. He discovered the Császár polyhedron, a nonconvex polyhedr ...

and

László Fuchs László Fuchs (born June 24, 1924) is a 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