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.

Zygmund graduated from the University of Warsaw (Ph.D. 1923) and taught there (1926–29) and at the Polytechnical School in Warsaw (1922–29). After a year in England on a Rockefeller fellowship, he became professor of mathematics at the University of Wilno (later Vilnius, Lithuania). In 1940, following a period of service in the Polish army, he fled his war-scarred homeland to the United States. After successive posts at Mount Holyoke College and the University of Pennsylvania, Zygmund joined the faculty of the University of Chicago, where he remained until his retirement in 1980.

Zygmund's legacy for nearly six decades of teaching included more than 80 Ph.D. students and hundreds of second-generation mathematical descendants. In 1986 he received the U.S. National Medal of Science for creating the so-called Chicago School of Analysis, which focused on Fourier analysis and its applications to partial differential equations. He wrote Trigonometric Series (1935 and later editions), Analytic Functions (1938, with Stanislaw Saks), and Measure and Integral (1977, with R.L. Wheeden). Zygmund held membership in the national academies of science of the United States, Poland, Argentina, and Spain.