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.

Bourbaki was founded in response to the effects of the First World War which caused the death of a generation of French mathematicians; as a result, young university instructors were forced to use dated texts.

The group's name derives from the 19th century French general Charles-Denis Bourbaki, who had a career of successful military campaigns before suffering a dramatic loss in the Franco-Prussian War.

During the Franco-Prussian war however, Charles-Denis Bourbaki suffered a major defeat in which the Armée de l'Est, under his command, retreated across the Swiss border and was disarmed.

[8][9] In the early 20th century, the First World War affected Europeans of all professions and social classes, including mathematicians and male students who fought and died in the front.

For example, the French mathematician Gaston Julia, a pioneer in the study of fractals, lost his nose during the war and wore a leather strap over the affected part of his face for the rest of his life.

During his time as a student, Weil recalled a prank in which an upperclassman, Raoul Husson [fr], posed as a professor and gave a math lecture, ending with a prompt: "Theorem of Bourbaki: you are to prove the following...".

[24] The first, unofficial meeting of the Bourbaki collective took place at noon on Monday, 10 December 1934, at the Café Grill-Room A. Capoulade, Paris, in the Latin Quarter.

[35][39][d] As various topics were discussed, Delsarte also suggested that the work begin in the most abstract, axiomatic terms possible, treating all of mathematics prerequisite to analysis from scratch.

[63] Weil reached the United States in 1941, later taking another teaching stint in São Paulo from 1945 to 1947 before settling at the University of Chicago from 1947 to 1958 and finally the Institute for Advanced Study in Princeton, where he spent the remainder of his career.

[68][69] Over time the founding members gradually left the group, slowly being replaced with younger newcomers including Jean-Pierre Serre and Alexander Grothendieck.

[75] Born to Jewish anarchist parentage, Grothendieck survived the Holocaust and advanced rapidly in the French mathematical community, despite poor education during the war.

[92] Although the method is slow, it yields a final product which satisfies the group's standards for mathematical rigour, one of Bourbaki's main priorities in the treatise.

[91][99] Schwartz related another illustrative incident: Dieudonné was adamant that topological vector spaces must appear in the work before integration, and whenever anyone suggested that the order be reversed, he would loudly threaten his resignation.

[93] Bourbaki's culture of humor has been described as an important factor in the group's social cohesion and capacity to survive, smoothing over tensions of heated debate.

When Bertrand Russell and Alfred North Whitehead applied this approach at the turn of the twentieth century, they famously filled over 700 pages with formal symbols before establishing the proposition usually abbreviated as 1+1=2.

Material has been revised for new editions, published chronologically out of order of its intended logical sequence, grouped together and partitioned differently in later volumes, and translated into English.

[141] Several journal articles have appeared in the mathematical literature with material or authorship attributed to Bourbaki; unlike the Éléments, they were typically written by individual members[119] and not crafted through the usual process of group consensus.

After the war, a number of members joined: Jean-Pierre Serre, Pierre Samuel, Jean-Louis Koszul, Jacques Dixmier, Roger Godement, and Sammy Eilenberg.

[177][178] Bourbaki used simple language for certain geometric objects, naming them pavés (paving stones) and boules (balls) as opposed to "parallelotopes" or "hyperspheroids".

At Lévi-Strauss' request, Weil wrote a brief appendix describing marriage rules for four classes of people within Aboriginal Australian society, using a mathematical model based on group theory.

[188] The psychoanalyst Jacques Lacan liked Bourbaki's collaborative working style and proposed a similar collective group in psychology, an idea which did not materialize.

The authors cited Bourbaki's use of the axiomatic method (with the purpose of establishing truth) as a distinct counter-example to management processes which instead seek economic efficiency.

Bourbaki provided a simple and relatively precise definition of concepts and structures, which philosophers and social scientists believed was fundamental within their disciplines and in bridges among different areas of knowledge.

[187][203] In 2016, an anonymous group of economists collaboratively wrote a note alleging academic misconduct by the authors and editor of a paper published in the American Economic Review.

In a book review, Emil Artin described the Éléments in broad, positive terms: Our time is witnessing the creation of a monumental work: an exposition of the whole of present day mathematics.

When asked in a 1997 interview about topics left out of the Éléments, former member Pierre Cartier replied: There is essentially no analysis beyond the foundations: nothing about partial differential equations, nothing about probability.

[216][217] Bourbaki also influenced the New Math, a failed[218] reform in Western mathematics education at the elementary and secondary levels, which stressed abstraction over concrete examples.

During the mid-20th century, reform in basic math education was spurred by a perceived need to create a mathematically literate workforce for the modern economy, and also to compete with the Soviet Union.

[229][230][231] These factors prompted biographer Maurice Mashaal to conclude his treatment of Bourbaki in the following terms: Such an enterprise deserves admiration for its breadth, for its enthusiasm and selflessness, for its strongly collective character.