C for Constructivism

Abstract

According to constructivism, all mathematical entities and truths about them should be the result of a construction. At present this view of the nature of mathematics is essentially ignored by the vast majority of mathematicians. This is perhaps due to historical reasons and is accompanied by deep-rooted dogmas, misunderstandings, misinformation, prejudices, etc. We briefly analyse them and recall some information which could be useful to go beyond them and reach a more balanced view on constructivism. In particular, we suggest that the present accepted attitude of mathematicians is the result of a denial of the problem of foundations of mathematics and of the impact of Godel’s incompleteness theorems. We claim that a constructive view is fully compatible with an evolutionary view of mathematics, which would bring it closer to all other natural sciences and enliven it.