Steven Gaal
In Memoriam
Steven Alexander Gaal was born as István Sándor Gál on February 22, 1924, in Budapest, Hungary. He received his Ph.D. in 1947 from the University of Budapest under Frigyes Riesz and Lipót Fejér. His thesis problem had its origin in a letter Paul Erdős wrote to Pál Turán, in which he mentions a prize problem posed by the Netherlands Mathematical Society. Gaal solved it and with Erdős jointly published the solution, giving him an Erdős number of 1, which he re-earned in a subsequent two-part collaboration in 1955.
After obtaining his Ph.D., Gaal served as an instructor at the University of Szeged and as an assistant professor in Budapest. He then went to the Centre National de la Recherche Scientifique (CNRS) in Paris, where he was from 1948 to 1950 with the rank of Attaché de Recherches; his supervisors were Jean Favard and Jacques Hadamard. It also was in Paris that Gaal first met Paul Erdős. Then Atle Selberg, of trace formula fame, was instrumental in bringing Gaal to the Institute for Advanced Study in Princeton, where he served as Selberg’s assistant from 1950 to 1952. In 1953, he became Instructor and then in 1954 Assistant Professor at Cornell University, and was a Research Associate at Yale University from 1958-60. He and his wife Lisl both joined the faculty of the School of Mathematics at the University of Minnesota in 1960. Steven came as an Associate Professor and was soon promoted to Full Professor in 1963. During his time at Minnesota, he supervised 5 Ph.D. students.
Gaal's research interests included both number theory and analysis. Robert Langlands, another very prominent number theorist, has said in a published interview that "...during this year [in Yale] a major event for me ... was a course of Stephen Gaal on analytic number theory, more precisely, on Hecke theory. His intent was to prepare himself, and incidentally us, for the study of the work of Atle Selberg ... I listened to Gaal's lectures with enthusiasm ..." Gaal’s foundational 1949 paper on Diophantine approximations has recently had an enormous impact on the study of greatest common divisor (GCD) sums, including surprising connections to the Riemann zeta function. While at the University of Minnesota, he also wrote 2 well-regarded books: Point Set Topology and Linear Analysis and Representation Theory; both were later reprinted by Dover. He also wrote a manuscript entitled Lectures on Algebraic and Analytic Number Theory, which was printed by Jones Letter Service.
In 2004, Gaal was honored at the Hungarian Academy of Sciences 80th anniversary as one of the "big five" group of distinguished Hungarian mathematicians. The other honorees were Janos Horvath, János Aczél, Ákos Csaszar and László Fuchs. Gaal went to Hungary to participate in the festivities where he gave a talk entitled When Is a Fibonacci Sequence Periodic? Gaal retired in 1993 and subsequently moved to Nevada, where he spent the last years of his life. He passed away on March 17, 2016, and is survived by his former wife Lisl (also an emeritus faculty in the School of Mathematics), daughters Barbara and Dorothy, their husbands, and three grandchildren.
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