Mandelbrojts ancestors came from Lithuania. He studied in Warsaw and Kharkiv, where he was particularly influenced by Sergei Bernstein. He continued his studies in Paris continues (amongst others with Édouard Goursat, Henri Lebesgue, Paul Montel, Emile Picard ) and in 1923 received his doctorate at the Sorbonne in Jacques Hadamard. With Hadamard, he published a book on the Taylor series. 1924 to 1926 he was a Rockefeller scholarship in the U.S., where he was from 1926 to 1927 Lecturer at Rice University in Houston. In 1928 he was Maître de conférences at the Université Lille Nord de France and 1929 Professor in Clermont -Ferrand, where he was a colleague of René de Possel. With Possel he visited every second Monday seminars at the Institute Henri Poincaré in Paris. Through contact with former fellow students, it was found that both in the early 1930s, members of Bourbaki were. Mandelbrojts interest, however, was the classical analysis. With Henri Cartan he worked on harmonic analysis and published in 1935 the book Séries de Fourier et classes quasi- analytiques de Fonctions. In 1938 he became a professor at the Collège de France, but had to France after the occupation by German troops left in 1940 and went again to the Rice University in Houston. There he published (1969, he published another book on Dirichlet series ) 1942 Analytic functions and classes of infinitely differentiable functions, and in 1944 his lectures on Dirichlet series. Even after returning to his chair at the Collège de France, he remained connected with Rice. In 1972 he went into retirement. With Paul Lévy, Maurice Fréchet and Laurent Schwartz he gave in the 1960s out the works of Hadamard and wrote it with Levy, Malgrange and Malliavin whose biography.
In 1950 he was invited speaker at the International Congress of Mathematicians (ICM ) in Cambridge (Massachusetts ) ( Théorèmes d' unicite de la théorie des fonctions ).
His doctoral include Yitzhak Katznelson, Hans Reiter, Paul Malliavin and Jean -Pierre Kahane. Szolem Mandelbrojt was the uncle of the mathematician Benoît Mandelbrot.