The Artist and the mathematician

The Artist and the Mathematician: The Story of Nicolas Bourbaki, the Genius Mathematician Who Never Existed . Amir Aczel's book has a strange title, but then the story of Bourbaki is rather strange. Originally a joke, the Bourbaki name became a focus for updating the syllabus of mathematics in French universities, and eventually grew into a huge project to rewrite mathematics from the bottom up. As such it had great influence in the mathematical world, bringing a new sense of rigor to the way mathematics is done, as well as leading to initiatives such as New Math in the USA.

Aczel tells the stories of the various mathematicians who made up the Bourbaki group, such as André Weil, and Laurent Schwarz, but most of all the enigmatic Alexandre Grothendieck. The Second World War.played a significant part in the lives of these mathematicians, and the members of the group often had strong political views. Indeed the book emphasises the link between Bourbaki and the philosophy of Structuralism - how it emerged from Existentialism and in turn gave way to Postmodernism. Some readers might prefer a book which concentrates more on the mathematics, rather than ranging into linguistics, anthropology and art, but I felt that Aczel's work provides a useful overview of the development of various twentieth century philosophical movements.