Communication Dans Un Congrès Année : 2025

What is called ‘thinking’ in mathematics?

Frédéric Jaeck

Résumé

The starting point of this talk will be the existence of a dual mode of thinking in mathematics: one that allows us to manipulate objects according to rules and a game that are co-constructed, and another, more progressive mode, where the structure dictated by the rules and the game gives way to much more diffuse and tangled connections. I will show that these two modes of thinking are in constant and reciprocal contamination, shaping how mathematicians exercise their force of thought. This interplay also reveals a certain depth that always accompanies mathematical propositions, resisting a flat logical interpretation and offering insight into the very nature of mathematical thinking.

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hal-05121477 , version 1 (19-06-2025)

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  • HAL Id : hal-05121477 , version 1

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Frédéric Jaeck. What is called ‘thinking’ in mathematics?. Lunch Time Talk – Center for Philosophy of Science, University of Pittsburgh, Center for Philosophy of Science, University of Pittsburgh, Feb 2025, Pittsburgh, United States. ⟨hal-05121477⟩
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