Karen V. H. Parshall" A Parisian Café and Ten Proto-Bourbaki ...

l'
tools. Although Rocard's suggestions were tabled until men formed an elite in a highly hierarchical systemi
some future rneeting, some of them ultimately found a they were the designated aspirants to the leadership of
p_lace in one of the projects on differential equations. French mathematics.
Elie Cartan was also called in----at the tenth meeting- Paris, of course, was the best place for them to meet.
to help out the Comrnittee on integral equations, and They frequently went to the iapital city to keep in
although no formal decision was reached at that time, touch with its scientific life, to visit fellow mathemati-
like Rocard's, some of his advice was also later heeded. cians, and to frequent bookstores and libraries. Most of
Born between 1899 and 1909, the regular participants them also commuted twice a month, on Mondavs, to
were graduates of the École Normale Supeileurefwith take pârt in a Sèminaire de mathématiques, which Àet at
the exception of Mandelbrojt who received rnost of the recently built Institut Henri-Poincaré. They usually
education in Poland and came to Paris for his doctor- held their Committee meetings in the hours bêfore the
ate. They shared a corunon background, but did not semlnar.
know or use the same mathernatical tools, and they did Gaston lulia, professor at the Paris faculté des sciences,
not even work in the same specialties. Many of them officially convened this seminar which was primarily
had traveled abroad after their doctorate or while do- organized and animated by a handful of devbtees. Àt
ing their doctoral research, as fellows of some granting the beginning of each year, the organizers would
agency, the most generous of which was the Rockefel- choose the theory which was going to be the topic of
ler Foundation. Although their hosts were not always the year, and draft a list of possible talks and speakers
real mentors to them, those fellows who spent re- (usually recruited from their own ranks). The
search time in Denmark, Germany, Hungary, Italy,
Sweden, Switzerland, and the United States became
acquainted with areas of research, methods, and resources
which were not common in their native
France. Partly as a result of their contacts with foreign
mathematicians in France or in other countries, some
participants were more familiar with set-theoretical,
axiomatic, algebraic, or topological methods. Others
remained closer in their work to function-theoretical
questions and analytic methods on which the reputation
of French mathematics had been built. Their ëommittee
discussions reflected this heterogeneity.2l
As mathematical researchers, the proto-Bourbakis
had each already published several papers.22 Furthermore,
they were the recipients of fellowships, prizes,
and other distinctions. In fact, most of these men received
several of the prizes of the Académie des Sciences
de Paris early in their careers.23 As professors,
they had also followed the then current pâttern of taking
a position in a French prov'rncial t'nculté des sciences
before seeking a call to Paris. In 1934-1935, Henri Cartan
and André Weil taught in Strasbourg, Delsarte and
Dubreil were in Nancy, Dieudonné had a position in
Rennes, and Mandelbroit, de Possel and Coulomb in
Clermont-Ferrand. Chevalley and Leray were grantees
of the Caisse nationale that yéar.2a From their pôvincial
vantage points, they had the freedom to experiment
with new ideas and fresh approaches which might
have been less accepted in Paris. Nevertheless, these
,Julia
seminar," as it was called, studied the following topics
between 1933 and 1939: group theory and algebras,
Hilbert spaces, topology, the works of Élie Cartan, algebraic
functions, and calculus of variations. Its obiective
was neither to serve as a teaching seminar nor to
inform the audience on current liteàrure. Rather, it
offered, to its speakers as well as to its audience, an
opportunity to work through large parts of recently
developed theories and methods. It forced the speakers
to synthesize in{ormation which was otherwise
scattered in the literature. Since the seminar had virtually
no official institutional ties, it provided a free
forum for criticism. There, the members of the Committee
eventuâlly assimilated, together, the approaches
which they later tried to integrate into their
collective expository writng.25
The Committee had neither money nor a set administrative
structure. Delsarte acted as "secretary" or
"manager." He wrote up minutes and sent around
reminders, but he had no particular powers. A de facto
hierarchy developed quickly, however, based on a
mixed measure of mathematical excellence and exoertise,
intellectual sophistication, strength of voice, ànd
determination. Indeed, the meetings of the Committee,
like the later gatherings of Bourbaki, reportedly
took place amid great noise and confusion. This should
come as no surprise, given that a Latin Quarter café
served as their laboratory. Still, the ambience of the
Latin Quarter of the mid-30s-with its strikes, demonstrations,
and political street fights-did not totally
dominate the group's meetings. As a mathematical
2r
On trips and traveling fellowships, see Beaulieu, Bourbaki. Ilne team, it largely managed to remain staunchly apoliti-
Histoile, YoL 1, pp. 69-105.
2
On average, the proto-Bourbaki had published 23 papers, with a
minimum of 4 and a mayjmuin of 75, according to a rough count.
æ
On prizes and other distinctions, see Beatljiu, Boutbaù. LIne Histoirc,
Vol. 1, rp. 87-114.
'?a
On teaching posts and provincial French frrultés iles scimces, see
Bourbaki. Une Histore, Vol. 1, pp.
5
The texts of the talks were mimeogûphed. A near complete set is
deposited at the libÉry of the Institut Henri-Poincaré in Paris. For
the list, see Bourbaki. Une Histoire, Yol. 2, pp, 63*65. On the Julia
Seminar, see Borl,rh. Ufie Histoire, Vol. 1, pp. 133_132.
'n4122.
32 TrIE MATHEMATICAL tNrELucENcER vo|-. 15. No. 1.1993