Genius Who Never Was

How a group of mathematicians got a collective identity and changed their discipline forever

In 1931, d kosambi, Goa-born mathematician-historian who later did valuable work in numismatics and wrote the classic The Culture and Civilisation of Ancient India in Historical Outline 1965, published a paper in the Bulletin of the Academy of Sciences of the Provinces of Agra and Oudh, Allahabad. It was titled 8220;On a Generalisation of the Second Theorem of Bourbaki8221;, and was intentionally nonsensical. Kosambi referred to 8220;the little-known Russian mathematician, D Bourbaki, who had been poisoned during the Revolution8221;.

Not only was there no such Second Theorem, there was no such mathematician. There had been a much decorated French general called Bourbaki in the 18th century, who even had a street named after him in Paris. In 1927, a mathematics student at the Ecole Normale Superieure invoked a 8220;Theorem of Bourbaki8221; in a ritualised annual prank. Among the students present then was Andre Weil, who later played an integral role in the formulation of the 8220;new math8221; that changed the discipline after the War, imbuing it with rigour and structure.

Weil, an ardent student of Sanskrit and the Bhagavad Gita, had found a teaching position at Aligarh Muslim University in 1929. At the age of 23, he was given the responsibility to revitalise the mathematics department. Among the teachers he brought in was Kosambi, who8217;d studied at Harvard and whom he8217;d met in Benares. Weil told Kosambi about the Paris prank, and planted the idea for another one in his mind.

Bourbaki survived the spoof. On December 10, 1934, he was resurrected by Weil fourth from left in the photograph above and a group of bright young mathematicians as Nicolas Bourbaki. The six of them were early in their teaching careers in universities around France, and they gathered at a cafeacute; in Paris8217;s Latin Quarter to write the curriculum for calculus and mathematical analysis. They decided to collectively write under the name, Nicolas Bourbaki. Members would join and exit Bourbaki, but over the next forty or so, years the group would play a decisive role in shaping mathematics.

In The Artist and the Mathematician: The Story of Nicolas Bourbaki, the Genius Mathematician Who Never Existed, Amir D Aczel strikes a fine balance. He draws enough from the lives of the group8217;s members to show how dependent it was on these special individuals having been fortuitously in communication with each other, but he never over-romanticises the mavericks. Aczel, author of Descartes8217;s Secret Notebook and Fermat8217;s Last Theorem, places the fascinating history of Bourbaki in the context of the intellectual and artistic temper of the times.

The Bourbaki mathematicians were essentially reacting to the reigning Poincare consensus, which eschewed rigour for intuitiveness. They set the tone in the planning of that curriculum itself. They decided that they would not assume anything that had been written in the past. In addition, it would be abstract and axiomatic.

This was a time when everything was being rewritten. Claude Levi-Strauss took the social sciences towards structuralism, with its emphasis on the production and perception of meaning. Einstein and Planck had changed physics from its Newtonian certainties. Pablo Picasso and Georges Braque were creating modern art, exploring ways in which colour and space could be used to find the kind of connectivity gained for physics by Einstein8217;s four-dimensional space. By focusing on the idea of structure in mathematics, Bourbaki similarly did work in set theory and topology. Aczel says softly: 8220;It can be said that no working mathematician in the world today is free of the influence of the seminal work of Nicolas Bourbaki.8221;

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Later, into this group drifted compelling characters like Alexandre Grothendieck, who in 1966 got the Fields Medal, the 8220;Nobel prize of mathematics8221;, and is widely reckoned to be one of 20th century8217;s most influential mathematicians. In the early 1990s he withdrew to solitude, burning tens of thousands of pages of original work and setting off for the Pyrennes. He has, by Aczel8217;s account, not been heard from in years.

It8217;s an almost mystic representation for the decline of Bourbaki. Perhaps, as Aczel says, Bourbaki had already achieved its goals. But its history is a stirring reminder of how crucial integrity is in taking human thought forward.