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Prominent Poles

Antoni Szczepan Zygmund , Polish-American mathematician, founder of Chicago school of analysis

Photo of Antoni Zygmund, mathematician

Born:  25 December, 1900, Warsaw, Russian partition of Poland (presently Poland) Died: Died: 30 May, 1992, Chicago, Illinois, USA

Summary. Encyclopedia Britannica: “Polish-born mathematician who exerted a major influence on 20th-century mathematics, particularly in harmonic analysis, a field utilized in science and technology for the formulation of descriptions of periodic phenomena such as waves, vibrations, and regularly repeating structures.” National Medal of Science citation: For outstanding contributions to Fourier analysis and its applications to partial differential equations and other branches of analysis, and for his creation and leadership of the strongest school of analytical research in the contemporary mathematical world.

Early days. Both his father Wincenty Zygmund and his mother - Antonina Perowska; were of peasant origin. Antoni had three younger sisters Jadwiga, Felicja and Maria. He attended elementary school in Warsaw, which he completed in 1912. He then entered the high school Seventh Gymnasium, Warsaw. After two years of secondary education World War I broke out in 1914 and Antoni, together with the rest of the Zygmund family, were evacuated to Poltava in the Ukraine. Antoni continued his education in Poltava, then in 1918, he returned to independent Poland. He attended the Kazimierz Kulwiec's Gymnasium for a year. In 1919 was awarded his school certificate and entered University of Warsaw. At the University Zygmund was taught by Janiszewski, Mazurkiewicz and Sierpinski. Zygmund, however, was most influenced by Aleksander Rajchman and by Stanislaw Saks who had been his school friend. Rajchman was interested in the theory of trigonometric series. He held lectures and a seminar on this topic for a few selected students. This gave Zygmund a life-long interest in the trigonometric series. There was a forced break in Zygmund's studies in 1920 when he was called up for the army. He did not see active service in Polish-Russian war, however, and was able to return to his studies.

Professional career. In 1922 he was appointed (as was his friend Saks) to be an instructor in the Department of Mathematics at Warsaw Polytechnic School. Zygmund obtained his Ph.D. from the University of Warsaw in 1923 for a dissertation on the Riemannian theory of trigonometric series written under Aleksander Rajchman's supervision. His formal supervisor, however, was Mazurkiewicz since Rajchman was too junior to officially undertake the supervision role. From 1922 to 1929 he taught at the Polytechnic School of Warsaw, being promoted from junior to senior instructor after obtaining his doctorate. In 1925 Zygmund married Irena Parnowska. In 1926 he submitted his habilitation dissertation to the University of Warsaw and began teaching there. He continued to hold his position at the Polytechnic School as well. Zygmund's early work, as one might expect, continued to develop ideas from his doctoral studies with Aleksander Rajchman. For example in 1926 he published six papers in Mathematische Zeitschrift in French. He spent the year 1929-30 in England supported by a Rockefeller fellowship. The first half of this year he spent at Oxford, and then in the second half he studied at Cambridge. In 1930 he was appointed to the chair of mathematics at the University of Stefan Batory in Wilno, Poland (presently Vilnius, Lithuania). There he met Jozef Marcinkiewicz - they collaborated until the outbreak of World War II. . Irena Zygmund worked in Wilno as a school teacher until the birth of their first son Jerzy in 1935. After meeting Paley at Cambridge in 1930-31, Zygmund wrote five joint papers with him, and both of them together with Norbert Wiener wrote Notes on random functions (1933). The joint Zygmund-Paley work played an important role in Zygmund's book Trigonometric Series (1935). It is a classic that, together with later editions, is still the definitive work on the subject. Remarkably a third edition appeared in 2002. This edition contains a foreword by Robert A Fefferman in which he writes:- In light of the importance of Antoni Zygmund as a mathematician and of the impact of "Trigonometric series", it is only fitting that a brief discussion of his life and mathematics accompany the present volume, and this is what I have attempted to give here. I can only hope that it provides at least a small glimpse into the story of this masterpiece and of the man who produced it. Another major work, this time written with his long standing friend Saks, was Analytic functions published in Polish in 1938In 1939, at the start of WWII, Zygmund was drafted into the Polish army as a reserve officer. Zygmund returned to Wilno but then, on 10 October 1939, Wilno was returned to Lithuania. In 1940 Zygmund escaped with his wife and son from German controlled territory to the United States. After a short time at the Massachusetts Institute of Technology he was appointed to Mount Holyoke College in 1940 where he remained until 1945 spending the year 1942-43 at the University of Michigan. In 1947 he was appointed to the University of Pennsylvania, then, to the University of Chicago where he remained until he retired in 1980. In 1948 he met Calderón. Not only did Zygmund have the role of Calderón's teacher and advisor, but was also his mentor and became his main collaborator. In 1950 Zygmund published Trigonometric Interpolation. Zygmund created one of the strongest analysis schools of the 20th century, making Chicago into a major analysis research centre. Together with Richard L Wheeden, Zygmund wrote Measure and integral (1977).He supervised over 40 doctoral students in his years at Chicago.

Honors and awards. He received honorary doctorates from Mount Holyoke College, Washington University, the University of Torun (Poland), the University of Paris, and the University of Uppsala (Sweden). He was elected to the Polish Academy of Sciences in 1959. In 1961 he was elected to the National Academy of Sciences (United States), then in 1964 to the Argentina Academy of Sciences. Further academies elected him such as the Spanish Royal Academy of Sciences and the Academy of Palermo in 1967. In the same year he was elected to the American Academy of Arts and Sciences and London Mathematical Society. In 1972 he was elected to the Polish Mathematical Society. He also received prizes and awards such as the Steele Prize by the American Mathematical Society, the award of Alfred Jurzykowski Foundation in 1972, and the National Medal of Science presented to him by President Reagan at a White House Ceremony in 1986.

Private. Zygmund suffered many sad losses during his life. His doctoral student at Vilnius, Ela-Chaim Cunzer, was a victim of the Holocaust and so was Saks, his friend from childhood and later his collaborator His student and collaborator Mazurkiewicz died in 1945, largely as a consequence of the Warsaw uprising. Rajchman, Zygmund's doctoral supervisor, was executed by the Nazis. His young collaborator Paley tragically died in a mountaineering accident. Irena, his wife, died on 6 August 1966.

St.Andrews university
Article by: J J O'Connor and E F Robertson
GAP is Copyright (C) 1986--1997 by Lehrstuhl D fuer Mathematik, RWTH Aachen, Aachen. Germany and Copyright (C) 1997-2001 by School of Mathematical and Computational Sciences, University of St. Andrews, St. Andrews, UK
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Other sources:
Encyclopedia Britannica
The Mathematics Genealogy
Univerity of Chicago

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