BOURBAKI , NICOLAS

‘Bourbaki’ is the collective nom de plume of a group of some of the most outstanding of contemporary mathematicians. The precise membership of Bourbaki, which naturally has changed over the years, is a closely guarded secret but it is known that most of the members are French.

Since 1939, Bourbaki has been publishing a monumental work, the Eléments de mathématique (Elements of Mathematics), of which over thirty volumes have so far appeared. In this Bourbaki attempts to expound and display the architecture of the whole mathematical edifice starting from certain carefully chosen logical and set-theoretic concepts. The emphasis throughout theEléments is on the interrelationships to be found between the various structures present in mathematics, and to a certain extent this means that Bourbaki's exposition cuts across traditional boundaries, such as that between algebra and topology. Indeed for Bourbaki, pure mathematics is to be thought of as nothing other than the study of pure structure.

Since the members of Bourbaki are all working mathematicians, rather than pure logicians, in contrast to other foundational enterprises (e.g. those of Gottlob Frege, Bertrand Russell, and A.N. Whitehead) the influence of Bourbaki's writings on contemporary mathematicians and their conception of the subject has been immense.