Polycephalic Euclid?
Résumé
In 1961, the French historian of mathematics Jean Itard ventured the idea that Euclid might have been no more than a nom de plume for a collective mathematical enterprise. This was anything but innocent, at the time when Bourbaki was so successful and well-known, and, more generally, collective aspects determined more and more the mathematical life of the period. In this paper, we look both at the place of collective practices in the historical writing of mathematicians around Bourbaki and at the role played by concepts representing the collective in their historiography. At first sight, although written collectively, Bourbaki's Elements of the History of Mathematics, which has been seen as an "internalist history of concepts", is an unlikely candidate for exhibiting collective aspects. But, as we shall show tension between individuals and collective notion, such as, most famously, "Zeitgeist" which is presented as orchestrating the development of infinitesimal calculus, are constant. It is interesting to unpack the way in which changes in mathematical practices impacted conceptions of the history of mathematics.
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