Nicolas Bourbaki | Biography

Nicolas Bourbaki does not exist. This name is used as a pseudonym for a group of mainly French mathematicians who started publishing collectively in 1939 (the year of birth given above). The stated aim of the Bourbaki group is to produce a modern overview of mathematics relevant to university students.

The founding members of the Bourbaki group were all graduates from the Ecole Normal Superieure, in Paris. The original members were Henri Cartan, Claude Chevalley, Jean Dieudonne, Jean Deslarte, and Andre Weil. Their aim was to produce a modern text book for French University students to replace the classic work by Goursat. With their desire to keep the work up to date and fresh, a rule was adopted such that members upon reaching their 50th birthday would have to relinquish their membership in the group.

The first book in this series, Elements of Mathematics, was published in 1939 and it had as its aim the drawing together of all the different strands of modern mathematics. All of the works are concerned with the treatment and the relationship of the differing mathematical topics covered. There is no room for diversions such as the people involved in the discoveries of the various principles. The history and people involved have been looked at briefly in volume 36, Elements d'historique des mathematiques. To keep each volume fresh, the Bourbaki group would meet annually for one or two weeks. At these meetings all would contribute ideas and knowledge of the areas to be covered, after having spent the preceding year researching them from first principles. Then one member would produce the first draft which would be circulated to all other members for comments and corrections. At the next meeting the work in progress was greatly discussed and handed to another author to continue. This would continue until the work was judged to be completed by all. This method of composition with numerous rewrites ensured the work comprised the latest material, was not obviously by one author, and was not an encyclopaedia written by a panel of experts, each submitting a chapter on his own area of expertise.

Although the work of Bourbaki is highly regarded, the field of mathematics is so complex today that a book of this nature is no longer accessible to students embarking on their University mathematics course; and it is now recognized that the books are aimed at those who have at least a good working knowledge of the contents of the first year or two of a mathematics course. It is true to say that for many practical purposes the Elements of Mathematics is really only accessible to the graduate student and beyond. By 2000 over 45 volumes had been published in French with the majority being translated into English.