The Mysterious Legend of Bourbaki: Le Mathématicien Reclus
By: Kiran Jain
Tags: Mystery, Mathematics, Education, History, Psychology

The Mysterious Legend of Bourbaki: Le Mathématicien Reclus

Deception in a field that is meant to unravel reality

Today, there is a book for almost anything and everything, and one can get access to any question at the turn of a page. However, whatever access we have to theory today has been made possible by the work of scientists over the last century, efforts which compounded over and yielded results.

If you were a high schooler in the earlier half of the 20th century, your access to even the most basic mathematical concepts was restricted due to the lack of authentic and quality knowledge.

A fleet of mathematicians was killed in the First World War, fragmenting the field, causing a lack of a shared mathematical language, and making it extremely difficult to share work.

Mathematics was going through its second puberty, and it looked ugly.

Rise of a new leader

In the late 1930s, a mysterious new Mathematician took center stage in the world of Algebra.

No one knew how he looked, nor did they know where he lived or worked.

This elusive figure went by the obscure name of Dr. Nicolas Bourbaki and published ideas no expert had ever seen before.

Bourbaki miraculously published multitudes of book volumes under the banner Éléments de mathématique (Elements of Mathematics). Several research papers accompanied these volumes.

While the rest of the world was busy hunting down who he was, Bourbaki kept on influencing mathematical theory with enormous rigor. Over the next two decades, Bourbaki’s publications became standard references.

He claimed to be a reclusive Russian genius who would only meet with his selected “collaborators”. He would communicate with the world via telegrams, whether it was to announce his daughter’s wedding or publicly insult anyone who doubted his existence.

He brought in the elements of structure, generality, formal proofing, and abstraction, in a field that had largely been intuitive until that point. Bourbaki’s increasing influence made influential mathematicians such as Benoit Mandelbrot flee from France, as their ideas were based solely on pictures.

Bourbaki forever changed the structure of modern mathematics.

Like everything else in his life, his death was surrounded by an aura of mystery and deception. In 1968, the world received Bourbaki’s obituary, complete with mathematical puns.

Several years after his death, the truth was finally outed. Nicolas Bourbaki wasn’t a man after all. He never existed. He was an imaginary figure created by a bunch of high schoolers, who started this as a prank to disrupt the status quo, for they were disappointed with the existing state of Mathematics.

How it was set up

In 1934, a French teenager had had enough. He’d been studying at the École Normale Supérieure and found his calculus book so disjointed, that he realized someone had to write a better one, or else “Math” would die.

He lobbied his friends and formed a small group to compose a new book. Henri Cartan, Claude Chevalley, Jean Delsarte, Jean Dieudonné, René de Possel, and André Weil were the founding members of this secret group.

They quickly hired new members and decided to publish Éléments de mathématique, and all their subsequent work, under a collective pseudonym: Nicolas Bourbaki, a Russian Mathematician.

Funnily enough, they also fictionalized Bourbaki’s origin story. The story said the Russian mathematician Bourbaki met these young mathematicians in Paris.

The group would meet at the Café Capoulade for regular discussions. There was no leader. Everything they published had to have a unanimous agreement. Their passionate, heated discussions sought for rigorous, formal proof. There was no place for things like ‘intuition’ — abstraction and generality were necessary.

Their texts began with a set of simple axioms, laws, and assumptions. From there, they went on to derive complex theorems.

They gave new, clear definitions to some of the most important mathematical objects, including the function.

Their work allowed mathematicians to establish logic that could be translated across the function’s domains in both directions.

Their systematic approach to abstract principles was in stark contrast to the popular belief that math was an intuitive science, and an over-dependence on logic constrained creativity.

The legacy

Bourbaki Congress of 1938 (Source)

Despite his apparent death, the group bearing Bourbaki’s name lives on today. Though he’s not associated with any single major discovery, Bourbaki’s influence is still very influential. Additionally, the modern emphasis on formal proof owes a great deal to his rigorous methods.

Nicolas Bourbaki may have been imaginary — but his legacy is real.