Preface
L
et's say it straightaway: Nicolas Bourbaki is not an individu
but a group of mathematicians, almost all French. Formed
1935, this colorful group consists of a dozen members and r
mains active today. Despite being unknown to most of the general pu
lic, these mathematicians changed the face of mathematics during t
sixties and seventies.
Bourbaki neither invented revolutionary techniques nor prov
grandiose theorems—and neither did it try to do so. What the grou
did bring, primarily through its imposing treatise Elements de mat
ematique, was a new vision of mathematics, a profound reorganiz
tion and clarification of its components, lucid terminology and not
tion, and a distinctive style. It seduced many mathematicians, to su
an extent that Bourbaki's philosophy has pervaded the internation
mathematics community. This has increased the influence of Fren
mathematics throughout the world.
It was not only Elements de mathematique that contributed to Bou
baki's fame. The exceptional quality of the group's members also co
tributed fundamentally to the quality of the group. Andre Weil, a k
figure in Bourbaki since its creation, was one of the greatest math
maticians of the century. The other mathematicians who helped foun
the group, including Henri Cartan and Claude Chevalley, were also
international stature. More recent members include prestigious figur
of mathematics such as Laurent Schwartz, Alexandre Grothendiec
and Jean-Pierre Serre. The members of Bourbaki all carried out ind
vidual mathematical work, earning them a range of high internation
honors. Several of them, notably Claude Chevalley, Laurent Schwart
Alexandre Grothendieck, and Roger Godement, also committed mu
of their time to philosophy and politics. The group's philosophy al
found its way into the New Math revolution of the seventies. While Bou
baki regretted this extension of their work, like Antigone they watche
in fear as their views broke free from the group and started to lea
their own existence.
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