The greatest mathematician that never lived - Pratik Aghor
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When Nicolas Bourbaki applied to the American Mathematical Society in the 1950s, he was already one of the most influential mathematicians of his time. He’d published articles in international journals and his textbooks were required reading. Yet his application was firmly rejected for one simple reason: Nicolas Bourbaki did not exist. How is that possible? Pratik Aghor digs into the mystery.
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Nicholas Bourbaki was one of the most influential mathematicians of the twentieth century whose contribution is cardinal to how mathematics is done today. However, there was just one problem – he did not exist. Who or what was Nicholas Bourbaki?
There is much to learn from the case study of Nicholas Bourbaki. One big takeaway is to identify and learn from general structures. Another would be emphasis on rigor. Here is a blog that I had written years ago which also cites some good references for further reading about the history of Bourbaki. In particular, this podcast and these articles provide a good start on the history of Nicholas Bourbaki:
http://mathshistory.st-andrews.ac.uk/HistTopics/Bourbaki_1.htmlhttp://mathshistory.st-andrews.ac.uk/HistTopics/Bourbaki_2.html
However, Bourbaki’s was not the only approach of pedagogy in mathematics. For example, see Vladimir Arnold’s essay ‘On Teaching Mathematics’. Arnold famously had anti-Bourbaki views about teaching mathematics.
Bourbaki’s approach was somewhat of a reaction to Henry Poincare’s reliance on intuition. To read Poincare’s philosophy of mathematics read:
https://plato.stanford.edu/entries/poincare/http://mathshistory.st-andrews.ac.uk/Extras/Poincare_Intuition.html-http://vigeland.caltech.edu/ist4/lectures/Poincare%20Reflections.pdf.
The philosophies of Arnold and Poincare, accomplished mathematicians/physicists themselves, show that Bourbaki’s method should not be the only way. Some critics of Bourbaki, such as Vladimir Arnold, have found their adherence to fundamental mathematics limiting.
In any case, intuition (as advocated by Poincare and Arnold) and rigor (as advocated by Bourbaki) are both right in their own ways and both are important in making progress in mathematics and in general, sciences.
There is much to learn from the case study of Nicholas Bourbaki. One big takeaway is to identify and learn from general structures. Another would be emphasis on rigor. Here is a blog that I had written years ago which also cites some good references for further reading about the history of Bourbaki. In particular, this podcast and these articles provide a good start on the history of Nicholas Bourbaki:
http://mathshistory.st-andrews.ac.uk/HistTopics/Bourbaki_1.htmlhttp://mathshistory.st-andrews.ac.uk/HistTopics/Bourbaki_2.html
However, Bourbaki’s was not the only approach of pedagogy in mathematics. For example, see Vladimir Arnold’s essay ‘On Teaching Mathematics’. Arnold famously had anti-Bourbaki views about teaching mathematics.
Bourbaki’s approach was somewhat of a reaction to Henry Poincare’s reliance on intuition. To read Poincare’s philosophy of mathematics read:
https://plato.stanford.edu/entries/poincare/http://mathshistory.st-andrews.ac.uk/Extras/Poincare_Intuition.html-http://vigeland.caltech.edu/ist4/lectures/Poincare%20Reflections.pdf.
The philosophies of Arnold and Poincare, accomplished mathematicians/physicists themselves, show that Bourbaki’s method should not be the only way. Some critics of Bourbaki, such as Vladimir Arnold, have found their adherence to fundamental mathematics limiting.
In any case, intuition (as advocated by Poincare and Arnold) and rigor (as advocated by Bourbaki) are both right in their own ways and both are important in making progress in mathematics and in general, sciences.
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Meet The Creators
- Educator Pratik Aghor
- Director Iuri Araujo, Guilherme Araujo
- Narrator Addison Anderson
- Animator Iuri Araujo, Guilherme Araujo
- Storyboard Artist Iuri Araujo, Guilherme Araujo
- Art Director Iuri Araujo, Iuri Araujo
- Music Cem Misirlioglu
- Director of Production Gerta Xhelo
- Editorial Director Alex Rosenthal
- Producer Bethany Cutmore-Scott
- Editorial Producer Dan Kwartler
- Script Editor Alex Gendler
- Fact-Checker Eden Girma
