Bourbaki & Zero

This post is about Andre Weil's autobiography, The book 'The Artist and the Mathematician: The Story of Nicolas Bourbaki, the Genius Mathematician Who Never Existed' by Amir D Eczel, Dr. Banwari Lala Sharma and the group 'Zero in the lines of  Bourbaki in the Allahabad University.

The group photograph is of the participants in a conference of Algebraic and Differential Topology in February 1988. Dr. Banwari Lal Sharma is sitting second from right, Dr. Pramila Srivastava is sitting on extreme left, Dr Ramji Lal is standing on the last row and is second from left, my wife Neeta is sitting on the ground and is second from right.

André Weil was well known French mathematician for his work in number theory and algebraic geometry. His sister Simone Weil was well known philosopher. Like Robert Oppenheimer, Weil taught himself Sanskrit.  He was greatly influenced by Gita and Hindu philosophy. Once he wrote a letter to his philosopher sister explaining the importance analogies in mathematics by adverting to Gita. He wrote as Vishnu has ten different avtars, a simple mathematical equation could manifest itself in different abstract structures. It was because of his influence many French mathematicians had liking to Hindu metaphysical words. Mathematical equations and functions are often reborn in complex ways.  Alexander Grothendieck, who transformed the modern mathematics would prefer to call them as new avatars.

Weil also taught for two years 1930-32 at Aligarh Muslim University (AMU), that never realised his importance. AMU tried to remove him but eventually Weil left himself, went back to France first and then to USA. 

After going back from AMU, Weil and other French mathematicians from the field of pure mathematics, felt the need to form a group to jointly produce textbooks that they could all use for teaching. During a conference in Paris, Weil organised a meeting on 10 December 1934 to form Bourbaki group that wrote books in the name of Nicolas Bourbaki. He was a founding member and the de facto early leader of the mathematical Bourbaki group. The group produced excellent books that advanced the field of pure mathematics.

Andre Weil has written his autobiography in French. It has been translated into English and is titled 'Andre Weil: The Apprenticeship of a Mathematician', In this, there is full chapter of his stay in India. 

Amir D Eczel has written worth reading book on the group titled, 'The Artist and the Mathematician: The Story of Nicolas Bourbaki, the Genius Mathematician Who Never Existed'. It talks about different members of the group. The Book also explains as to why it went into decline. They could not anticipate the changes and they did not listen to Alexander Grothendieck and excluded him from the group.

Henri Cartan was leading algebraic topologist and was founder member of the Bourbaki group. His father Elei Cartan was also famous mathematician in the field of differential geometry. 

Dr. Banwari Lal Sharma was professor of mathematics in Allahabad University. He never taught me as he was in France when I was studying for my graduation from 1968-70 but he had taught my sister, my brother and later was my wife's supervisor for her PhD. He was very well known in his field and perhaps one of the most renowned teacher in the modern times. He had done his DSc from Universite De Paris Sud under guidance of Henri Cartan. 

Dr. Sharma also formed a group in the lines of Bourbaki group in Allahabad. It was called 'Zero'. This group also wrote a book on modern algebra. It was the best book on the subject. I had it for a few years but can no longer trace it. Unfortunately, the book was cyclostyled and is no longer available.

Both the books are worth reading. 

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