Times, August 2007
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
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.