Listening to the Music of Reason: Nicolas Bourbaki and the Phenomenology of the Mathematical Experience

• Main Author: TILL DÜPPE
• Format: Article
• Language: English
• Published: University of Windsor 2015-10-01
• Series: PhaenEx: Journal of Existential and Phenomenological Theory and Culture
• Online Access: https://phaenex.uwindsor.ca/index.php/phaenex/article/view/3935

Jean Dieudonné, the spokesman of the group of French mathematicians named Bourbaki, called mathematics the music of reason. This metaphor invites a phenomenological account of the affective, in contrast to the epistemic and discursive, nature of mathematics: What constitutes its charm? Mathematical reasoning is described as a perceptual experience, which in Husserl’s late philosophy would be a case of passive synthesis. Like a melody, a mathematical proof is manifest in an affective identity of a temporal object. Rather than an exercise for its own sake, this account sheds a different light on both the epistemic limitation of mathematical science, and the discursive problem of social responsibility in mathematics – two issues at the heart of Husserl’s critique of science as well as of mid-20th century mathematics, for which Nicolas Bourbaki stands as a monument of rigor.