Science Focus (issue 24)

By Sonia Choy 蔡蒨珩 Any Marvel fan – or even most people, really – will know the Avengers – six superheroes who teamed up to save the world. Mathematics, on the other hand, always has the image of being a rather solitary affair. We have written about a modern-day mathematical Polymath Project on the Twin Prime Conjecture in Issue 020, but these collaborations have been happening for a while – almost a whole century ago, in fact. Meet Nicolas Bourbaki. Assuming the name of a French general who fought in the FrancoGerman war (1870-1871), Nicolas Bourbaki, founded 1934-1935, was in fact a collection of mathematicians writing collectively. The name was chosen in jest (founders of the group had a distaste towards hierarchy), and humor is a running theme throughout the group. The group’s founders were all French [1] – although later incarnations involved mathematicians of other nationalities; they were admirers of the German mathematician David Hilbert, and the German school’s emphasis on precision and rigor of proofs, as opposed to the French school’s more handwavy approach based on intuition. The group’s membership would change throughout the ages – there was an agreement that the current members would be kept secret, although former members discuss their involvement with the group openly. This secrecy is to allow the mathematicians to write as a collective without any individual egos involved and no chance to claim copyright of any sort. Most m e m b e r s agreed to gradually drop out after they turn 50, letting the younger generation take over [2]. In their place, new members are recruited through invitation to their annual conference as “guinea pigs”, and are accepted into the group once all the mathematicians agree to let them join [3]. Bourbaki’s main work was a textbook series on mathematics, known as the Éléments de mathématique (Elements of Mathematics). Originally wanting to write a new textbook for differential calculus [1], the group eventually covered the major areas of mathematics – analysis, algebra and geometry, as well as including more modern areas of active research in later volumes. The group was drawn to abstraction rather than concrete illustration; most of the core six texts (those published before 1954) consist of theorems and proofs written out formally, with little diagrams or examples to illustrate the ideas. The group also wrote articles and hosted a lecture series known as Séminaire Bourbaki (Bourbaki Seminar) in Paris since 1948, adding up to over a thousand lectures as of today. One of Bourbaki’s main activities was its periodic conferences, usually held in a rural location, where its