Abstract

We survey Brouwer's intuitionistic mathematics and Markov's constructive recursive mathematics by examining axioms assumed in each school and mathematical theorems derived from the axioms. It is known that Bishop's constructive mathematics is a core of the varieties of mathematics in the sense that it can be extended not only to intuitionistic mathematics and constructive recursive mathematics, but also classical mathematics. We compare a new trend of constructive mathematics, called a minimalist foundation, with Bishop's constructive mathematics.