- Mashaal, Maurice.
Bourbaki: A Secret
Society of Mathematicians.
Translated by Anna Pierrehumbert.
Providence, RI: American Mathematical Society, [2002] 2006.
ISBN 978-0-8218-3967-6.
-
In 1934,
André
Weil and
Henri Cartan,
both young professors of mathematics at the University of
Strasbourg, would frequently, when discussing the calculus
courses they were teaching, deplore the textbooks available,
all of which they considered antiquated and inadequate.
Weil eventually suggested getting in touch with several
of their fellow alumni of the
École
Normale Supérieure who were teaching similar courses
in provincial universities around France, inviting them to collaborate
on a new analysis textbook. The complete work was expected to
total 1000 to 1200 pages, with the first volumes ready about
six months after the project began.
Thus began one of the most flabbergasting examples of “mission
creep” in human intellectual history, which set the style
for much of mathematics publication and education in subsequent
decades. Working collectively and publishing under the
pseudonym
“Nicolas
Bourbaki” (after the French
general in the Franco-Prussian War
Charles
Denis Bourbaki), the “analysis textbook” to be
assembled by a small group over a few years grew into a project
spanning more than six decades and ten books, most of
multiple volumes, totalling more than seven thousand pages,
systematising the core of mathematics in a relentlessly abstract
and austere axiomatic form. Although Bourbaki introduced new
terminology, some of which has become commonplace, there is
no new mathematics in the work: it is a presentation of
pre-existing mathematical work as a pedagogical tool and
toolbox for research mathematicians. (This is not to say that
the participants in the Bourbaki project did not do original
work—in fact, they were among the leaders in mathematical
research in their respective generations. But their work on
the Bourbaki opus was a codification and grand unification of
the disparate branches of mathematics into a coherent whole.
In fact, so important was the idea that mathematics was a
unified tree rooted in set theory that the Bourbaki group
always used the word mathématique,
not mathématiques.)
Criticisms of the Bourbaki approach were many: it was
too abstract, emphasised structure over the content which
motivated it, neglected foundational
topics such as mathematical logic, excluded anything
tainted with the possibility of application (including
probability,
automata theory, and combinatorics), and
took an eccentric approach to integration, disdaining the
Lebesgue
integral. These criticisms are described in detail, with
both sides fairly presented. While Bourbaki participants
had no ambitions to reform secondary school mathematics
education, it is certainly true that academics steeped in
the Bourbaki approach played a part in the disastrous
“New Math”
episode, which is described in chapter 10.
The book is extravagantly illustrated, and has numerous boxes and
marginal notes which describe details, concepts, and the
dramatis personæ in this
intricate story. An appendix provides English translations
of documents which appear in French in the main text.
There is no index.
La
version française reste
disponible.
January 2008 