What is called ‘thinking’ in mathematics?
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.
