The Relationship between Intuition and Invention in Mathematics: A Consideration from the Points of View of Henri Bergson and Henri Poincaré

Abstract

The French authors Henri Bergson and Henri Poincaré call attention upon intuition and its relationship to mathematical invention. Both authors believe that intuition is an intellectual process that requires individual experience both physical and mathematical. They also claim that the results of intuition are to be observed in the surface of consciousness, i.e. in mathematical language. Additionally, both authors believe that intuition is necessary for mathematical invention. This paper shows the coincidences between Bergson and Poincaré concerning the relationship between intuition and invention. It investigates how its definition leads to the understanding of intuition as a process and, finally, how the idea of a dynamic scheme—introduced by Bergson to explain invention—is implicitly present in Poincaré’s thought.