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Abstract
The crucial role which Bachelard attributed to mathematics within his historical epistemology to understand the “new scientific spirit” at work at the beginning of the 20th century is well known. Nonetheless, the application to mathematics of the classical Bachelardian epistemological categories (obstacle, rupture, sanctioned history and lapsed history), which were first conceived for physics or chemistry, raises several issues. In this article, we aim to study Bachelard’s mathematical epistemology for itself. We will first point out the natural connection between the issue of a Bachelardian mathematical epistemology and two classical
topics, namely the relationship with Brunschvicg’s epistemology and the claim for discontinuity. In a second step, starting from the evolution of Bachelard’s thought towards a more committed rationalism, we will question what this evolution implies for mathematics by insisting on the notion of epistemological act sketched out by Bachelard. We will finally compare Bachelard’s and Cavaillès’ mathematical epistemology.