Nicolas Bourbaki

The Bourbaki Congress of 1938 (from left to right: S. Weil, C. Pisot, A. Weil, J. Dieudonné, Claude Chabauty, C. Ehresmann, J. Delsarte).

Nicolas Bourbaki is the collective name of a group of French mathematicians who, in the 1930s, set out to revise the fundamentals of mathematics with a much greater demand for rigor than was then the norm. current in this science. Founded in 1935, the group began the publication of its monumental Elements of mathematics in accordance with the new canon of rigor and the axiomatic method, claiming to cover the bases of all mathematics.

Origin of name

The eponymous "Bourbaki" refers to a French general, Charles Denis Bourbaki. It was adopted by the group as a reference to a student anecdote about a misleading mathematical lecture, and also possibly a statue.

Organization

From the beginning they tried to maintain the cute fiction that Nicolas Bourbaki was a "poldavian" mathematician. That is why the name of its members, which change over time, is one of the best kept secrets (as is the way they are organized), although it is known that the majority are French. On their website they already acknowledge that the group was initially founded by Henri Cartan, Claude Chevalley, Jean Coulomb, Jean Delsarte, Jean Dieudonné, Charles Ehresmann, René de Possel, Szolem Mandelbrojt and André Weil. They were former students of the Ecole Normale Supérieure in Paris who, at the initiative of Cartan and Weil and under the rallying cry "everyone should be interested in everything", set out to write new texts for their classes. It seems certain that the best French mathematicians of the mid-20th century (Jean-Pierre Serre, Alexandre Grothendieck, Laurent Schwartz, Pierre Samuel, Jean-Louis Koszul, Armand Borel, Pierre Cartier, Roger Godement) have at some point been part of the group, as well as some of another nationality (Samuel Eilenberg, John Tate).

Jobs

Until the year (2006) he has written the volumes of:

• Theory of sets
• Algebra
• Overall
• Actual function
• Topological vectorial space
• Integration
• Switching algebra
• Differentiable Variety and Mathematical Variety
• Lie and Lime Algebra Group
• Spectral theory.

These volumes contain historical notes that have been published separately, forming some appreciated, although still very incomplete (2006) volumes whose corpus receives the name Elements of the History of Mathematics.

Impact

• Its impact on contemporary mathematics has been enormous, and since the 1950s it can be said that its demand for rigor has been universally accepted in mathematics, along with the particular style in which they express it, being very different the current texts of prebourbakians. This success has become unnecessary the continuation of his work, since the 1960s all the texts are already written according to their requirements. However, the Bourbaki Seminar continues to be developed in Paris, where the main advances of mathematics are presented each year.

• The "tragedy" of this titanic attempt to base all mathematics is that they chose as a starting point the theory of assemblies and, when in the 1950s and 1960s the theory of categories appeared as a supposed unifying principle of all known mathematics, they decided with full knowledge of cause not to follow that labyrinth (“that hell” in their own words) thus renouncing their initial purpose.

• The University of Valladolid institutionalized the celebration of a party last Friday of every month of November to commemorate the group of mathematicians.
• They called "Muera Euclides". They have not achieved it, even basic geometry has expanded and computer geometry has emerged. The basic mathematics on conjunctitious and algebraic knowledge was based, failed as foreseen by René Tomm and Lev Pontriaguin.

• The American musical duo Twenty One Pilots, mentioned in his song "Morph", published in 2018: "He'll always try to stop me, that Nicolas Bourbaki. He's got no friends close but those who know him most know. He goes by Nico, he told me I'm a copy. When I'd hear him mock me, that's almost stopped me.". His name styling as twenty øne piløts refers to the empty set. They also refer to this collective in the simple Nico and the Niners, Nico is the abbreviation of Nicolas and "the niners" refers to it being created by 9 people. The last reference is in [1], as among the images you can see one of the photos of the symbol creator ø.