Matematica Costruttiva

Constructive mathematics uses intuitionistic rather than classical logic. This makes it an algorithmic form of mathematics, as its adherence to intuitionistic logic allows us to interpret its theorems as algorithms. This characteristic of constructive mathematics has the potential to change the opinion of mathematicians on this enterprise: from deviant and non-standard practice, in the near future it could become central component of ordinary mathematics. In the present article, I shall survey the principal aspects of constructive mathematics, including its most remarkable differences with the classical tradition. I shall further hint at differences with other kinds of mathematics that also use intuitionistic logic. Finally I shall illustrate the motivation that some prominent constructive mathematicians of the Bishop school have adduced for their constructive turn.