From the philosophy of contemporary mathematics

Abstract

The purpose of this research is to stand on an aspect of the philosophy of contemporary mathematics, by tracing its relationship to logic, and highlighting this relationship from the proposal presented by the constructivist school represented by Henri Poincaré in this regard, and how it made mathematics based on the idea of proof Mathematics, something that the logical school denies represented in the proposition presented by Bertrand Russell by considering mathematics to be based on what he calls research mathematics: that is, logic, and from it the “axiom of response” takes the place of proof by regression, and it is the result of what is known In Russell's theory of logical patterns, "La théorie des types logiques", and from here the problem that we would like to address can be limited to the following: What is the relationship between logic and mathematics and which are the founders of the other?