Monday, 4 May 2015

Nicolas Bourbaki: A secret mathematician

I had first heard the name of Nicolas Bourbaki when I was at school and developed an interest in mathematics. From what little I read about him, he seemed to be a mysterious secret mathematician, who was keen on transforming the mathematics education scenario at an upper university level. I knew that the books he wrote would be too much for me at that time, and so I forgot all about him. When I entered university and took a course in general topology, I chanced upon a book written by Bourbaki. Out of interest in what the man had to offer, I took a look at the book and it was an exhilarating experience for me. I had never seen a mathematics book like Bourbaki's before. It was terse and laconic. It motivated the subject much better than the book I was then reading. I glanced a bit on the first few sections and left the book as I had little time in that semester left.

That was four years ago, and recently when I read Andre Weil's autobiographical book, The Apprenticeship of a Mathematician, the whole story of how the legend of Bourbaki was created came to the forefront. Weil was one of the founding members of this group of secret mathematicians who styled themselves after a French general and who wrote mathematics textbooks that changed the way mathematics was viewed. This encouraged me to pick up a book in the institute library titled Bourbaki: A Secret Society of Mathematicians by Maurice Mashaal and published in English by the American Mathematical Society (AMS) in 2006.

The book by Mashaal made for some interesting light reading in my spare time, which unfortunately has not been plenty in the last few months. Mashaal's book is for the non-specialist, for the laymen and so sometimes I found it too verbose when there was mathematics involved. The book is set in a light tone, and explores in depth the evolution and influence of Nicolas Bourbaki. It is not one that takes one view or the other. The book is quite balanced and gives in full details many things that would have been difficult to trace about this secret mathematician. The book discusses the opposing views towards Bourbaki and how he might have done as much good as he has done damage to the mathematics education in France and other parts of the world.

Although this book was a nice read, still the mathematician in me was not satisfied. A book on a mathematician should have contained some more mathematics. The editing was not that good either, which is surprising for a book published by the AMS. However, one thing that must be mentioned is the presence of many colourful pictures which have added much pleasure to the reading experience.

This is not the right place to discuss in details about what Bourbaki has done, for mathematics and its education. If I have managed to arouse some interest in the topic then Mashaal's book would be a good starting point. Or else, there is always Wikipedia. The book ends with a beautiful line, which I would like to quote below:

Bourbaki did add a little to "the honour of the human spirit". In an era where sports and money are such great idols of civilization, this is no small virtue.