De Kant à Gentzen, en passant par Brouwer, Hilbert et Frege

The aim of this paper is to analyse the reference to space and time in the foundation of mathematics. First, we describe the reference to time in Brouwer’s intuitionism and in Hilbert’s formalism in order to show that the reference to time leads to different restrictions on what can be considered a mathematical proof. We then study three attempts, by Frege, by Hilbert around 1900, by Gentzen, to eliminate the reference to time and ground mathematics on the intuition of space.