# Bunch-Hellemans, The mathematics of Nicolas Bourbaki

In 1939 the first volume of Elements de mathématique (“elements of mathematic” — without the s to suggest that all mathematic(s) is a unit) by Nicolas Bourbaki appeared. This influential work, which eventually ran to 40 volumes, sought to recast all of mathematics into a consistent whole with the same symbolism used throughout. The author was identified in a 1949 biographical note as having been formerly with the Royal Poldavian Academy. Somewhat later he moved to the Mathematics Institute of the University of Nancago.

If these institutions seem a bit unfamiliar, do not be surprised. Like the redoubtable N. Bourbaki, they do not exist. Instead, Bourbaki is a pseudonym used by a group of mainly French mathematicians, including Jean Dieudonné, Henri Cartan, André Weil, and Samuel Eilenberg, with some other mathematicians loosely affiliated. The group formed itself in 1935, starting with graduates of l’Ecole Normale Supérieure. A fictitious Général Claude Bourbaki had been associated with the school since 1880, with his name adopted from a real 19th-century French general Bourbaki.

The aim of Nicolas Bourbaki was to lay out all of mathematics according to the ideas of the Formalists, who had been led by the German David Hilbert. Bourbaki introduced its own vocabulary and symbolism, which were influential worldwide during the 1960s and 1970s, but now are viewed as too complex (although some of the vocabulary and symbols continue in use). Each volume is written by a committee and critiqued at a congrès featuring fine wine and gourmet food, paid for by Bourbaki’s royalties. The group has kept young by limiting the age of its members to 50. In addition to the books, Bourbaki continues to sponsor frequent seminars.

Although the true identity of Nicolas Bourbaki has been known to mathematicians for many years, the members of the group have continued to pretend. When the mathematician Ralph P. Boas wrote an article about the group in a popular publication, the editors received a letter from Nicolas Bourbaki himself, protesting the article and claiming that there is no real Ralph P. Boas, but only a group of mathematicians claiming to be Boas.

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