Polycephalic Euclid?

collective practices in Bourbaki's history of mathematics

Anne-Sandrine Paumier

David Aubin

pp. 185-218

in: Volker R. Remmert, Martina R. Schneider, Per Kragh-Sørensen (eds), Historiography of mathematics in the 19th and 20th centuries, Basel, Birkhäuser, 2016

Abstract

In this paper, we argue that Bourbaki's historiography, which has been extremely influential among mathematicians and historians of mathematics alike, reflected the special conditions of its elaboration. More specifically, we investigate the way in which the collective writing practices of the members of the Bourbaki group in both mathematics and the history of mathematics help to explain the particular form taken by the Elements of the History of Mathematics (1960). At first sight, this book, which has been seen as an "internalist history of concepts," may seem an unlikely candidate for exhibiting collective aspects of mathematical practice. As we show, historical considerations indeed stood low on the group's agenda, but they nevertheless were crucial in the conception of some parts of the mathematical treatise. We moreover claim that tensions between individuals and notions related to a collective understanding of mathematics, such as "Zeitgeist" and "mathematical schools," in fact structured Bourbaki's historiography.