Bourbaki's first work: a summary
of results in set theory.
Laurent Schwartz
between 1940 and 1970, with the production rate slowing dow
markedly after this. The most recent volume was published in 199
while the one before that had been published fifteen years earlier,
1983.
Elements de mathematique (which currently contains about 70
pages dense with definitions, axioms, lemmas, corollaries, and the
rems)—and especially a few particular volumes—was a worldwi
success and made Bourbaki famous. But the success and fame of t
group stem equally from the distinctive way in which the membe
lived and worked. Such a huge and influential treatise succeeded n
only because of the mathematical talent of its authors, but al
because of the group's enthusiasm, friendship, schoolboy solidarit
and belief in a common goal.
The Bourbaki group is devoid of any hierarchy. All decisions mu
be unanimous, and while there is no official voting, anyone can ve
a proposal. This system particularly applies to decisions about t
treatise. The final version must be accepted by every member, whi
requires, in most cases, many years of work. The writing proce
itself is distinctive as well. The group gives the task of writing t
rough draft of a given section to one or two members. Once the se
tion is written, it is read out loud to all the members, after which t
other members mercilessly criticize the draft. The group the
assigns the task of rewriting the section to a different member. T
process continues until it converges—sometimes wearily—to
manuscript that the members unanimously accept as ready for pu
lication.
However, the lack of hierarchy doesn't imply that all the membe
have equal weight in the group. Some members put more into th
group; some have more influence. Andre Weil, who can be considere
as the group's first leader, is primum inter pares, the first amon
equals. He was also the target of jokes and mockeries less often tha
the other members. Even Jean Dieudonne, a vocal member wh
worked intensely for the group, was aware of Weil's role. Hen
Cartan tells how "one day, Dieudonne said [metaphorically], T won
drink my cafe au lait before Weil.'" In the more recent history
Bourbaki, key members of the group include Jean-Pierre Serre, Mich
Demazure, Pierre Cartier, and Jean-Louis Verdier.
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