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Letter to the Editors
Bourbaki’s
Structures
and Structuralism
The Mathematical Intelligencer encourages comments
about the material in this issue. Letters to the editor
should be sent to either of the editors-in-chief, Chandler
Davis or Marjorie Senechal.
I
Ihave read with interest Osmo Pekonen’s review of Amir
Aczel’s book, The Artist and the Mathematician,inThe
Mathematical Intelligencer, Vol. 31 (2009), No. 3. I had
already read the book and had been surprised again and
again by Aczel’s complete freedom with historical facts
(see, for example, his comparison of Andre
´Weil, born in
1906, with Alexander Grothendieck, born in 1928).
But here I will concentrate on just one important point:
The supposed relation of Bourbaki’s structures to structur-
alism. This is a pure intellectual fraud, propagated by many
people from the social sciences and repeated by Aczel.
Bourbaki’s structures and structuralism had independent
births, even if we wave hands and refer to the Zeitgeist.
But let us be precise.
The idea of structure appeared in mathematics before
Bourbaki in the theory of abstract algebra of commutative
fields (E. Steinitz, ‘‘Algebraische Theorie der Ko
¨rper,’’ Jour.
fu
¨r die reine und angewandte Mathematik 137 (1910), 167–
309), in linear algebra, and also in the beginning of the
theory of continuous groups with Elie Cartan. Bourbaki
was directly inspired by them (Pierre Cartier, personal
communication, April 2010).
The word ‘‘structure’’ appeared independently in Claude
Levi-Strauss’s book Anthropologie Structurale (1958). When
structuralism became a fashion in the 1960s, referring to
Bourbaki in structuralist essays was a way of giving some
scientific credit and weight to works of variable quality.
When I asked Claude Levi-Strauss about the origin of the
word ‘‘structure’’ in his work, he answered (letter to the
author, Nov. 16, 1990): ‘‘Ne croyez pas un instant que
Bourbaki m’ait emprunte
´le terme ‘‘ structure’’ ou le con-
traire, il me vient de la linguistique et plus pre
´cise
´ment de
l’Ecole de Prague.’’ (Do not believe for one minute that
Bourbaki borrowed the word ‘‘structure’’ from me, or the
contrary; it came to me from linguistics, more precisely,
from the School of Prague.)
This, I hope, puts an end to any discussion about the
origin of ‘‘structures.’’
Jean-Michel Kantor
Institut de Mathe
´matiques de Jussieu
4, Place Jussieu,
Case 247-
75005 Paris, France
e-mail: kantorjeanm@gmail.com
Ó2010 Springer Science+Business Media, LLC, Volume 33, Number 1, 2011 1