WNicolas Bourbaki is the collective pseudonym of a group of mathematicians, predominantly French alumni of the École normale supérieure (ENS). Founded in 1934–1935, the Bourbaki group originally intended to prepare a new textbook in analysis. Over time the project became much more ambitious, growing into a large series of textbooks published under the Bourbaki name, meant to treat modern pure mathematics. The series is known collectively as the Éléments de mathématique, the group's central work. Topics treated in the series include set theory, abstract algebra, topology, analysis, Lie groups and Lie algebras.
WThe dangerous bend or caution symbol ☡ was created by the Nicolas Bourbaki group of mathematicians and appears in the margins of mathematics books written by the group. It resembles a road sign that indicates a "dangerous bend" in the road ahead, and is used to mark passages tricky on a first reading or with an especially difficult argument.
WÉléments de mathématique is a treatise on mathematics by the collective Nicolas Bourbaki. Begun in 1939, the work has run to several volumes and remains in progress. The first volumes were published by Éditions Hermann from 1939 in the form of booklets, and later as bound volumes. Following a legal dispute with the editor, publication was resumed in the 1970s by the CCLS, and then in the 1980s by Éditions Masson. Since 2006, Springer Verlag has republished all the fascicles and has published a new volume in 2016, treating algebraic topology.
WHyman Bass is an American mathematician, known for work in algebra and in mathematics education. From 1959 to 1998 he was Professor in the Mathematics Department at Columbia University. He is currently the Samuel Eilenberg Distinguished University Professor of Mathematics and Professor of Mathematics Education at the University of Michigan.
WArnaud Beauville is a French mathematician, whose research interest is algebraic geometry.
WGérard Ben Arous is a French mathematician, specializing in stochastic analysis and its applications to mathematical physics. He served as the director of the Courant Institute of Mathematical Sciences at New York University from 2011 to 2016.
WArmand Borel was a Swiss mathematician, born in La Chaux-de-Fonds, and was a permanent professor at the Institute for Advanced Study in Princeton, New Jersey, United States from 1957 to 1993. He worked in algebraic topology, in the theory of Lie groups, and was one of the creators of the contemporary theory of linear algebraic groups.
WHenri Paul Cartan was a French mathematician who made substantial contributions to algebraic topology. He was the son of the French mathematician Élie Cartan and the brother of composer Jean Cartan.
WPierre Émile Cartier is a French mathematician. An associate of the Bourbaki group and at one time a colleague of Alexander Grothendieck, his interests have ranged over algebraic geometry, representation theory, mathematical physics, and category theory.
WClaude Chevalley was a French mathematician who made important contributions to number theory, algebraic geometry, class field theory, finite group theory and the theory of algebraic groups. He was a founding member of the Bourbaki group.
WJean Coulomb was a French geophysicist and mathematician, and one of the early members of the Bourbaki group of mathematicians.
WJean Frédéric Auguste Delsarte was a French mathematician known for his work in mathematical analysis, in particular, for introducing mean-periodic functions and generalised shift operators. He was one of the founders of the Bourbaki group. He was an invited speaker at the International Congress of Mathematicians in 1932 at Zürich.
WMichel Demazure is a French mathematician. He made contributions in the fields of abstract algebra, algebraic geometry, and computer vision, and participated in the Nicolas Bourbaki collective. He has also been president of the French Mathematical Society and directed two French science museums.
WJean Alexandre Eugène Dieudonné was a French mathematician, notable for research in abstract algebra, algebraic geometry, and functional analysis, for close involvement with the Nicolas Bourbaki pseudonymous group and the Éléments de géométrie algébrique project of Alexander Grothendieck, and as a historian of mathematics, particularly in the fields of functional analysis and algebraic topology. His work on the classical groups, and on formal groups, introducing what now are called Dieudonné modules, had a major effect on those fields.
WAdrien Douady was a French mathematician.
WCharles Ehresmann was a German-born French mathematician who worked in differential topology and category theory. He was an early member of the Bourbaki group, and is known for his work on the differential geometry of smooth fiber bundles, notably the Ehresmann connection, the concept of jet bundles, and his seminar on category theory.
WSamuel Eilenberg was a Polish-American mathematician who co-founded category theory and homological algebra.
WRoger Godement was a French mathematician, known for his work in functional analysis as well as his expository books.
WAlexander Grothendieck was a mathematician who became the leading figure in the creation of modern algebraic geometry. His research extended the scope of the field and added elements of commutative algebra, homological algebra, sheaf theory and category theory to its foundations, while his so-called "relative" perspective led to revolutionary advances in many areas of pure mathematics. He is considered by many to be the greatest mathematician of the 20th century.
WGuy Henniart is a French mathematician at Paris-Sud 11 University. He is known for his contributions to the Langlands program, in particular his proof of the local Langlands conjecture for GL(n) over a p-adic local field—independently from Michael Harris and Richard Taylor—in 2000.
WJean-Louis Koszul was a French mathematician, best known for studying geometry and discovering the Koszul complex. He was a second generation member of Bourbaki.
WSerge Lang was a French-American mathematician and activist who taught at Yale University for most of his career. He is known for his work in number theory and for his mathematics textbooks, including the influential Algebra. He received the Frank Nelson Cole Prize in 1960 and was a member of the Bourbaki group.
WGilles Lebeau is a French mathematician born on 17 November 1954, professor at the University of Nice Sophia-Antipolis, member of the Institut universitaire de France and member of the Académie des sciences.
WSzolem Mandelbrojt was a Polish-French mathematician who specialized in mathematical analysis. He was a Professor at the Collège de France from 1938 to 1972, where he held the Chair of Analytical Mechanics and Celestial Mechanics.
WJoseph Oesterlé is a French mathematician who, along with David Masser, formulated the abc conjecture which has been called "the most important unsolved problem in diophantine analysis".
WLucien Alexandre Charles René de Possel was a French mathematician, one of the founders of the Bourbaki group, and later a pioneer computer scientist, working in particular on optical character recognition.
WLaurent-Moïse Schwartz was a French mathematician. He pioneered the theory of distributions, which gives a well-defined meaning to objects such as the Dirac delta function. He was awarded the Fields Medal in 1950 for his work on the theory of distributions. For several years he taught at the École polytechnique.
WJean-Pierre Serre is a French mathematician who has made contributions to algebraic topology, algebraic geometry, and algebraic number theory. He was awarded the Fields Medal in 1954, the Wolf Prize in 2000 and the inaugural Abel Prize in 2003.
WJohn Torrence Tate Jr. was an American mathematician, distinguished for many fundamental contributions in algebraic number theory, arithmetic geometry and related areas in algebraic geometry. He was awarded the Abel Prize in 2010.
WBernard Teissier is a French mathematician and a member of the Nicolas Bourbaki group. He has made major contributions to algebraic geometry and commutative algebra, specifically to singularity theory, multiplicity theory and valuation theory.
WJacques Tits is a Belgium-born French mathematician who works on group theory and incidence geometry. He introduced Tits buildings, the Tits alternative, the Tits group, and the Tits metric.
WJean-Louis Verdier was a French mathematician who worked, under the guidance of his doctoral advisor Alexander Grothendieck, on derived categories and Verdier duality. He was a close collaborator of Grothendieck, notably contributing to SGA 4 his theory of hypercovers and anticipating the later development of étale homotopy by Michael Artin and Barry Mazur, following a suggestion he attributed to Pierre Cartier. Saul Lubkin's related theory of rigid hypercovers was later taken up by Eric Friedlander in his definition of the étale topological type.
WAndré Weil was a French mathematician, known for his foundational work in number theory and algebraic geometry. He was a founding member and the de facto early leader of the mathematical Bourbaki group. The philosopher Simone Weil was his sister. The writer Sylvie Weil is his daughter.
WJean-Christophe Yoccoz was a French mathematician. He was awarded a Fields Medal in 1994, for his work on dynamical systems.