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Nicolas Bourbaki and the concept of mathematical structure

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The concept of structure is one of the most pervasive ideas of twentieth century mathematics, and it is associated more than with anyone else, with the name of Nicolas Bourbaki. This was the pseudonym adopted by a group of (mostly French) leading mathematicians that undertook the collective writing of a treatise meant to present the entire picture of mathematics centered on the idea of structure. This treatise had a tremendous impact on mathematical research and teaching all around the world at least between 1945 and the 1970s. The idea of structure as associated with Bourbaki also had important echoes in fields like the philosophy of mathematics (structuralism), developmental psychology (Piaget), social anthropology (Levi-Strauss) and mathematical education (the New Math).

In my talk I examine the origins and development of Bourbaki’s idea of structure. I will show that this idea had two totally different and separate aspects that have typically been conflated in misleading ways. One is a general approach to the practice of mathematics, which was only implicit in their work, and which is where Bourbaki’s influence had its greatest effect. The second one was a formal mathematical concept that was meant to underlie all of their conception and to provide an overall uniformity to their treatment of the various mathematical disciplines. This was a rather unsuccessful idea devoid of any consequences on what Bourbaki did, on what other mathematicians could do, of what happened in mathematics in any other way, but at the same time it was the main source of their alleged importance for the philosophy of mathematics or outside mathematics.

This talk is part of the HPS Philosophy Workshop series.

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