Nicolas Bourbaki was influential. He was also unusual, given that he didn’t exist. The reality behind the name, and the impact of ‘his’ work is the subject of this volume from Amir D Aczel, the maths writer best known for the book on Fermat’s Last Theorem that wasn’t by Simon Singh.

Bourbaki was the pseudonym of a group of young 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 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. Bourbaki was thus somewhere between a secret society and a prank. His first appearance was in a nonsensical paper by D Kosambi 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 mathematics must be nonsense).

The ever-evolving Bourbaki group had as much fun as you can with maths, preferring anarchic meetings to chalky classrooms. A sense of mischief prevailed: when the editor of Mathematical Reviews 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 basics. It emphasised the general and abstract, taking little interest in practical applications or even numeracy. Aczel argues 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 a book about stucturalism, it just doesn’t hang together, with no strong narrative to tie together its disparate threads.