*Fortean
Times, August 2007
*

**The Artist
and the Mathematician
The Story of Nicolas Bourbaki, the Genius Mathematician Who Never
Existed
**Amir D
Aczel

High Stakes Publishing, 2007

Hb, xii+239, notes, illos, bibl, index, illos, ISBN 978-1-84344-034-5, £12.99

Nicolas Bourbaki
was among the most influential mathematicians of the past. He was also
among the most unusual, given that he didn't actually exist. The
reality behind the name, and the impact of 'his' work on the
intellectual life of the 20th century, is the subject of this latest
volume from Amir D Aczel, the popular maths writer best known for the
book on Fermat's Last Theorem that wasn't by Simon Singh.

Bourbaki was the collective pseudonym for a group of young and gifted
mathematicians, mostly French, who published a remarkable series of
textbooks between the 1930s and 1960s. Their aim was to rebuild
mathematics from the ground up, removing the slack thinking and
conservatism that they saw suffocating teaching in schools. The gestalt
identity was intended to avoid possible claims about intellectual
property, but also to shield the participants from direct criticism
from their academic superiors.

The Bourbaki identity was thus somewhere between a secret society and a
prank. His first appearance was in a deliberately nonsensical paper by
the Indian mathematician D Kosambi which was submitted to, and
published in, an academic journal - shades of Alan Sokal's famous
anti-postmodernist jape (and, if one follows the logic of some of
Sokal's fans, proof that the whole field of mathematics must be a bit
of a nonsense).

The ever-evolving Bourbaki group seemed to have as much fun as you can
with maths, preferring anarchic meetings in the open air to chalky
classrooms. A sense of mischief prevailed - when the editor of
'Mathematical Reviews' publicly exposed the pseudonym, he received
first an angry letter from 'Bourbaki' datelined 'From my ashram in the
Himalayas', and then accusations of being a collective pseudonym
himself.

Bourbaki's work, which inspired the 'New Math' in US schools from the
1960s, stripped mathematics back to its basic elements. It emphasised
the general and abstract, taking little interest in practical
applications or even numeracy. Aczel argues, not always convincingly,
that this approach paralleled or even inspired contemporary trends in
other fields, including structuralist philosophy and anthropology,
cubist art, and the Oulipo school of literature.

While there's plenty of toothsome intellectual history here, the book
is rather less than the sum of its parts. At just over 200 pages, it
never could have been a definitive account of the Bourbaki group and
their work, but neither does it really satisfy as a popular
introduction. The writing is often clumsy, and the explanation of some
key theoretical points frustratingly vague. Perhaps ironically for book
about stucturalism, it just doesn't hang together, with no strong
narrative to tie together its disparate threads.