Wednesday, January 31, 2007


Lance Fortnow recently devoted a post to The Bourbaki Lecture. Reading his post, reminded me that I had in mind of scribbling a couple of lines on the book Bourbaki: A Secret Society of Mathematicians by Maurice Mashaal, Pour la Science - AMS, 2006, 168 pp. I came across that book while looking for another one at the university library, and decided to borrow it. I am glad I did!

For one, I did not know that André Weil (1906-1998) introduced the symbol for the empty set that we now universally use. (A whole issue of the Notices of the AMS is devoted to Weil.) Nor did I know that Boubarki coined the terms injection, surjection and bijection, and invented the notion of filter. Not to mention the striking similarity between André Weil and Eugenio Moggi! (Eugenio, I hope that you don't mind me mentioning this!)

More seriously, I really enjoyed reading that book, and I warmly recommend it. It tells what was good, and what was bad, with Bourbaki and its view of mathematics. It is also full of eminently quotable sentences from the Bourbaki members. Examples?

"You can't do good work in applied mathematics until you can do good work in pure mathematics." (Jean Dieudonné (1906-1992), cited on p. 119)

"[...] logic is the mathematician's hygiene, but it does not provide his meals. The big problems constitute the daily bread on which he lives." (André Weil in The Future of Mathematics, 1948) Shame on you Weil!

The closing paragraph of the book is poignant:

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

Indeed, not to mention that the members of Bourbaki have included some of the greatest mathematical minds of the last century.

Great minds can also make great mistakes (for instance, Bourbaki's disdain of probability theory had a very negative effect on French work in that very important area of mathematics, and Bourbaki was very dogmatic in his view of mathematics), and one of the virtues of the book is that these are not swept under the carpet. Read it, and form your own opinion on this non-existent, and most prolific mathematician.

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