In this talk, I will address a peculiar characteristic of the French tradition in philosophy of mathematics, namely the attention to the productive character of mathematical thought. Fruitfulness of mathematical thought is conceived in different ways by the most representative thinkers belonging to this tradition. Firstly, I will focus on Jean Cavaillès’ idea of an autonomous production of objects and his attention on gestures. Then, I will contrast his view with Albert Lautman’s one who emphasises dialectic as a productive power within the mathematical thought and elaborates an authentic metaphysics of mathematics. Finally, I will consider Gilles Châtelet as a more recent elaboration in this particular tradition in the field of philosophy of mathematics which offers a very broad philosophical understanding of mathematical thought.

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