Bourbaki – The Story Of The Rockstar Mathematician Who Never Lived

Portrait of D. Kosambi from Wikimedia Commons — further edited and altered by the author (with a silhouette of Bourbaki on the right)

In 1931, a little-known Indian mathematician named Damodar Kosambi published a mathematical article and attributed it to a little-known Russian mathematician named D. Bourbaki. There are plenty of mathematicians that never get recognized, let alone the lesser-known ones. So, what was so special about this particular publication?

Well, here’s the catch: The mathematician named Bourbaki did not exist! What is even more fascinating is that this paper was just the beginning. Following this, “Bourbaki” revolutionised the field of pure mathematics by publishing a series of influential books and papers.

If Bourbaki did not exist, who was publishing all this mathematical literature? Why did Kosambi attribute his work to a mathematician who did not exist? There are so many questions and so many mysteries to uncover here. This is the story of Nicolas Bourbaki — the rockstar mathematician who never lived!

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Pranks and Publications — The Russian Mathematician

The story begins at the prestigious school: École normale supérieure (ENS) in France. In the early 1900s, a student named André Weil had attended the school. During his time there, a new professor had presented a certain “theorem of Bourbaki.” Later on, it turned out that this new professor was just an upperclassman who was pulling a prank. Somehow, the narrative and the humour of this prank stuck with Weil.

After graduating from ENS with a doctorate, Weil taught Mathematics at an Indian University for a short while. Over there, he met the mathematician named Damodar Kosambi. Kosambi was involved in a power struggle with one of his colleagues.

To help Kosambi establish intellectual superiority over his colleague, Weil proposed a cheeky plan to him. The plan was to publish an article with material attributed to a certain “Bourbaki” to show off to everyone in the department.

Kosambi took the suggestion, and attributed his work to a little-known Russian Mathematician named D. Bourbaki! The little prank from the ENS upperclassman was slowly taking a form of its own. Little did they know that this would kick-start a mathematical revolution.

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Wars and Gangs — The World of French Mathematics

Fast forward a few years, Weil was an upcoming mathematician who was teaching at the University of Strasbourg. In the meantime, the first world war had wiped out a significant proportion of French mathematicians. Unlike the Germans who shielded their mathematical and scientific talent, the French had deployed everyone under an egalitarian scheme. This had backfired.

As a result, a lot of the work done by the French mathematicians of this era got lost. Weil and other French mathematics instructors were forced to use dated texts and lecture notes. At the University of Strasbourg, a fellow mathematician named Henri Cartan complained to Weil about the dire situation.

Eventually, the situation irritated them to such an extent that they decided to gather a bunch of fellow-minded academics to see if they could do something about it. They assembled at a Café in Paris in 1934. There were six mathematicians in total: André Weil, Henri Cartan, Jean Delsarte, Claude Chevalley, Jean Dieudonné, and René de Possel.

They collectively decided that they would work on fundamental mathematical literature that fixed the issues they were plagued with as mathematics instructors.

They also eventually decided that they would publish all of their work under the alias “Nicolas Bourbaki.” This way, they could avoid issues with copyrights and potential individual claims. Thus, the “Bourbaki” group was born!

The Rockstar Mathematician Makes His Mark

Over the next few years, the group worked intensively on a fundamental and rigorous approach to mathematics. Some members of the group left and others came in. But the collective spirit of the group remained strong. Bourbaki released an influential series of books known collectively as Éléments de mathématique (Elements of Mathematics).

This work treated topics such as set theory, abstract algebra, analysis, topology, lie groups, and lie algebras. Apart from this, Bourbaki also published influential mathematical articles. The group’s best work is widely believed to have been done through the 1950s and the 1960s.

Even today, the Bourbaki approach to defining functions as injective, surjective, and bijective is used widely. Apart from this, they also influenced work in other fields such as the humanities and psychology. Legendary psychologist Jean Piaget was impressed with their work and was influenced by Dieudonné’s mathematical model of mother structures.

Bourbaki was also known for their sense of humour. They openly criticized anyone who was not convinced of Bourbaki’s approach to mathematics. They even announced Bourbaki’s daughter’s wedding. Eventually in 1968, when they could not hold it a secret anymore, they came out by printing an obituary for Bourbaki which was filled with mathematical puns and humour.

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What Happened to Bourbaki?

Fast forward to the present day, the Bourbaki group still lives on. Over the years, the group has remained small, averaging about twelve members at any given time. New members of the group are vetted carefully and Bourbaki selects them upon mutual interest and consent. On the one hand, the group guards the identities of present members as a secret. On the other hand, past members openly discuss their experiences and Bourbaki’s approaches.

Bourbaki conducts regular seminars and even has an internal newsletter. In the seminars, both internal and external members present their ideas. They discuss ideas very critically and only publish literature that they unanimously agree upon as being rigorous and aligned with the group’s goals.

Where is Bourbaki Headed Next?

From the 1980s until the early 2000s, the influence of Bourbaki vaned due to infrequent publishing. But this has changed in more recent years. Bourbaki has increased its publication rate. Information is shared openly on their website (linked under the references section below) and they even have a Twitter handle.

They have now split their work into two categories:

1. One category focuses on documenting the structural fundamentals of mathematics — what Éléments de mathématique originally aimed to achieve.

2. The other category focuses on areas of new mathematical research.

Modern mathematics has seemed to pose problems for the conventional Bourbaki approach (as it seems less flexible to change). But the group seems to be determined to tackle the challenges and continue its adventure.

Final Remarks

Personally, I feel that Bourbaki is too stringent with their approach; they are strictly against illustrations and use only text, for example. Many mathematicians have criticized their approach as being “elitist”.

One of my all-time heroes in the field of mathematics, Benoit Mandelbrot decided to emigrate to the United States partly because he wished to escape Bourbaki’s influence in France.

With all this said and done, Bourbaki’s success proves that mathematics is open to such unconventional approaches. Through the thick and the thin, Bourbaki continues to bring flair and spirit to the world of mathematics!

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Reference: Association des collaborateurs de Nicolas Bourbaki.

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Further reading that might interest you: The Thrilling Story Of Calculus and Logarithms: The Long Forgotten Stroy Of Scientific Progress.