Marius Sophus Lie was a Norwegian mathematician. He largely created the theory of continuous symmetry and applied it to the study of geometry and differential equations. He also made substantial contributions to the development of algebra.
Oscar Zariski was a Russian-born American mathematician and one of the most influential algebraic geometers of the 20th century.
Antoni Zygmund was a Polish mathematician. He worked mostly in the area of mathematical analysis, including especially harmonic analysis, and he is considered one of the greatest analysts of the 20th century. Zygmund was responsible for creating the Chicago school of mathematical analysis together with his doctoral student Alberto Calderón, for which he was awarded the National Medal of Science in 1986.
Stanisław Saks was a Polish mathematician and university tutor, a member of the Lwów School of Mathematics, known primarily for his membership in the Scottish Café circle, an extensive monograph on the theory of integrals, his works on measure theory and the Vitali–Hahn–Saks theorem.
Ernest William Hobson FRS was an English mathematician, now remembered mostly for his books, some of which broke new ground in their coverage in English of topics from mathematical analysis. He was Sadleirian Professor of Pure Mathematics at the University of Cambridge from 1910 to 1931.
Ralph Hartzler Fox was an American mathematician. As a professor at Princeton University, he taught and advised many of the contributors to the Golden Age of differential topology, and he played an important role in the modernization of knot theory and of bringing it into the mainstream.
John William Scott "Ian" Cassels, FRS was a British mathematician.
Leonard Eugene Dickson was an American mathematician. He was one of the first American researchers in abstract algebra, in particular the theory of finite fields and classical groups, and is also remembered for a three-volume history of number theory, History of the Theory of Numbers. The L. E. Dickson instructorships at the University of Chicago Department of Mathematics are named after him.
Walter Rudin was an Austrian-American mathematician and professor of Mathematics at the University of Wisconsin–Madison.
In mathematical analysis, the rising sun lemma is a lemma due to Frigyes Riesz, used in the proof of the Hardy–Littlewood maximal theorem. The lemma was a precursor in one dimension of the Calderón–Zygmund lemma.
In harmonic analysis, a field within mathematics, Littlewood–Paley theory is a theoretical framework used to extend certain results about L2 functions to Lp functions for 1 < p < ∞. It is typically used as a substitute for orthogonality arguments which only apply to Lp functions when p = 2. One implementation involves studying a function by decomposing it in terms of functions with localized frequencies, and using the Littlewood–Paley g-function to compare it with its Poisson integral. The 1-variable case was originated by J. E. Littlewood and R. Paley and developed further by Polish mathematicians A. Zygmund and J. Marcinkiewicz in the 1930s using complex function theory. E. M. Stein later extended the theory to higher dimensions using real variable techniques.
Edward James McShane was an American mathematician noted for his advancements of the calculus of variations, integration theory, stochastic calculus, and exterior ballistics. His name is associated with the McShane–Whitney extension theorem and McShane integral. McShane was professor of mathematics at the University of Virginia, president of the American Mathematical Society, president of the Mathematical Association of America, a member of the National Science Board and a member of both the National Academy of Sciences and the American Philosophical Society.
History of the Theory of Numbers is a three-volume work by Leonard Eugene Dickson summarizing work in number theory up to about 1920. The style is unusual in that Dickson mostly just lists results by various authors, with little further discussion. The central topic of quadratic reciprocity and higher reciprocity laws is barely mentioned; this was apparently going to be the topic of a fourth volume that was never written.
Moderne Algebra is a two-volume German textbook on graduate abstract algebra by Bartel Leendert van der Waerden, originally based on lectures given by Emil Artin in 1926 and by Emmy Noether (1929) from 1924 to 1928. The English translation of 1949–1950 had the title Modern algebra, though a later, extensively revised edition in 1970 had the title Algebra.
Adolph Winkler Goodman was an American mathematician who contributed to number theory, graph theory and to the theory of univalent functions: The conjecture on the coefficients of multivalent functions named after him is considered the most interesting challenge in the area after the Bieberbach conjecture, proved by Louis de Branges in 1985.
Harris Hancock was a mathematics professor at the University of Cincinnati who worked on algebraic number theory and related areas. He was the brother of the horse breeder Arthur B. Hancock.
Robert Edmund Edwards (1926–2000), usually cited simply as R. E. Edwards, was a British-born Australian mathematician who specialized in functional analysis. He is the author of several volumes in Springer's Graduate Texts in Mathematics.
Victor Lenard Shapiro was an American mathematician, specializing in trigonometric series and differential equations. He is known for his two theorems on the uniqueness of multiple Fourier series.
Robert McDowell Thrall (1914–2006) was an American mathematician and a pioneer of operations research.
Friedrich Georg Schilling was a German mathematician.
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