Nicolas Bourbaki
Nicolas Bourbaki is the collective pseudonym of a group ( collective of authors ) mainly French mathematicians who since 1934 in a multi-volume textbook of mathematics in French, the Éléments de mathématique, worked and repeatedly drove forward a year at various locations in France in seminars their joint book project. Supposedly Bourbaki worked at the University of Nancago (pseudonym: contracted from Nancy and Chicago, the universities, where were some of the leading Bourbakisten then, Jean Dieudonné called his villa in Nice, Villa Nancago ). The publications are in the tradition of the axiomatic foundation of mathematics.
Task
Bourbaki did not see it as his task to create new mathematical knowledge. Rather, existing mathematical knowledge should be re- processed and made available in a compelling context. Served as a basis function based on that the school of David Hilbert axiomatic presentation of set theory, there was no doubt as to their outstanding performance at the time of the founding of Bourbaki.
Structure and notation of the plant are extremely rigid. The argument is basically from general to specific. Everything that is said is justified from the foregoing it. So the reference system in the first six books is completely linear: Any reference refers to an earlier Bourbaki text. References to other works are considered superfluous.
The original goal was to treat only topics that were necessary for a systematic construction of the foundations of mathematics. Were Eliminated so the lattice theory, number theory, and of course the entire applied mathematics. The geometry is considered with the treatment of topological vector spaces as done.
Subsequent criticism of the educational shortcomings representation answered Bourbaki member Pierre Cartier in a 1997 interview: There is a misunderstanding when some people thought that it should be so taught as it was shown in the books. One can imagine the first books of Bourbaki as an encyclopedia of mathematics that contains all necessary information. That's a good description. If you look at it as a textbook, it is a disaster.
Operation
One of the basic rules of the group included the anonymous publication under the joint pseudonym, the merciless editorial discussion of each proposal and the resignation upon reaching the fiftieth year of life. The composition of the group and the way they work remained shrouded in mystery for a long time; only at the age began the founding members to speak publicly about Bourbaki. We now know that Jean Dieudonné had the largest share of the first draft and the final editing of the published volumes.
During the meeting, the group discussed often very violent designs of individual textbook chapters, decided countless changes, and handed over the manuscripts then each new authors for further processing. At the next meeting, but no one was bound by the decisions previously taken; it was criticized again and decided on a new makeover. Each chapter typically learned ten makeovers, which dragged on for eight to twelve years. Each member had veto power.
The members met three times a year, often in hotels in the country and in holiday resorts, the leisure activities and accommodation were financed by the increased income from the book sales. The notification magazine La Tribu served the communication within the group.
Results
1939 appeared the first of a total of 40 volumes, which in turn are grouped into six books:
After the work has largely come to a standstill. It still appeared:
As the last band came 1983, the spectral theory ( Volume IX ) was added. The last chapter so far and the last release of Bourbaki was the Chapter 10 to commutative algebra, 1998.
The most successful volumes were perhaps the on Lie groups and commutative algebra. The repeatedly interspersed digressions to mathematics history was Jean Dieudonné out separately as Bourbaki's Eléments d' histoire de mathématique (1960, 1969). He also wrote an overview of the modern mathematics " Bourbakisicht ": panorama of pure mathematics as seen by Bourbaki 1982.
History
The six founding members of the group were Henri Cartan, Claude Chevalley, Jean Delsarte, René de Possel, Jean Dieudonné and André Weil. They had completed shortly before the École Normale Supérieure and taught now on French provincial universities. In their teaching they found the available textbooks inadequate and hopelessly out of date, especially compared to the same flowering German axiomatic school to David Hilbert and Emmy Noether and Emil Artin in Göttingen in Hamburg, where some of the founding members had studied. In the center of mathematical research in France at that time was there the traditionally strong analysis, represented approximately by Jacques Hadamard, while algebra and number theory were hardly maintained. In their occasional meetings they decided to write their own textbook on analysis, and soon came to the conclusion actually having to rewrite the entire foundations of mathematics. Originally, they estimated it to take three years. In fact, it took four years to even appeared only the first chapter. On one of their first meeting, the group chose the name Bourbaki, according to a legend that has become a joke students of École Normale Supérieure and indirectly by General Charles Denis Bourbaki from the Franco-German War of 1870 /71.
Soon after founding the group Szolem Mandelbrojt was called, in the 1940s, Laurent Schwartz, Samuel Eilenberg, Jean Leray (which was only briefly a member ) and Jean -Pierre Serre. In later years, Young was recruited among the most gifted student of members: the young mathematicians took a trial basis in a meeting of the group, where it was expected of them to actively contribute to the discussion, which was often performed passionate and seemingly chaotic. In the second half of the 20th century belonged to Bourbaki also included Paul Dubreil (briefly ), Jean Coulomb ( even for a short time), Charles Ehresmann, Pierre Cartier, Pierre Samuel, Alexander Grothendieck, Jacques Dixmier, Jean -Louis Koszul, Roger Godement, Armand Borel, Alain Connes, Serge Lang, Francois Bruhat, John Tate, Pierre Deligne, Adrien Douady, Bernard Teissier, Michel Demazure, Jean -Louis Verdier, Arnaud Beauville, Jean -Christophe Yoccoz, Charles Pisot, Claude Chabauty, Hyman Bass, Michel Raynaud, Joseph Oesterlé, Guy Henniart and the Nobel laureate economist Gerard Debreu. Both Grothendieck and long left the group but early in the battle. Many Grothendieck students from the 1960s, the group, however, dominated.
For about twenty years, there are no significant releases more. Towards the end of the twentieth century said Cartier, Bourbaki was a dinosaur whose head was too far away from his cock.
The slow decline of the group has a number of reasons that might be summarized as:
- Bourbaki has completed its task: With the first six or eight books, the original task to write down the essential foundations of mathematics, was completed.
- There are now, crucially under the influence of Bourbaki, a wide range of modern textbooks in an axiomatic style.
- The rigid spelling makes it extremely difficult to incorporate new mathematical developments.
- The claim to represent the whole of mathematics in a closed system has proved to be unfeasible for practical reasons. After leaving Dieudonne there was no one who really looked over the entire body released so far.
In addition, there was a long, unpleasant dispute with the publisher in the late 1970s.
To date, there is L' Association des Collaborateurs de Nicolas Bourbaki, the company organized the employees of NB ', three times a year, the famous Bourbaki seminars ( Séminaire Nicolas Bourbaki ). These are international conferences, which are attended usually more than 200 mathematicians. You can now find place at the Institute Henri Poincaré.
Aftereffect
The strictly logical style of Bourbaki has helped shape today's mathematics crucial.
Specifically, we owe Bourbaki the sign of the empty set, the sign for the implication, the abbreviations N, Z, Q, R, C for the quantities of natural, whole, rational, real and complex numbers ( besides the spelling with the double stroke ) and the words bijective, injective and surjective for properties of functions.
In France Bourbakische axiomatic often still dominated the entire higher education in mathematics as a major or minor; foreign observers such as Vladimir Arnold Igorewitsch keep this dogmatic formalism for a crime against the students.
The Bourbakiströmung reached into the 1960s on the education about ( " New Math" ), one of the initiators Jean Dieudonné was.