Abstract

Topology is the mathematical discipline, introduced about a hundred years ago, that studies the problem of the connection between discrete and continuous, which emerged consciously 2500 years ago with the discovery of irrational numbers in the Pythagorean school. Taking inspiration from the example in the eyes of each of us, namely the continuous vision produced by the brain from discrete inputs, we will look at the main stages of the path that led to positive topology, which gives the title to the book [1] recently published. Positive here means both constructed by human beings and free of negations.

We will see that the close interaction between mathematical and philosophical aspects leads to a completely new, more relaxed and simpler general vision, which is at the same time more expressive and closer to applications. To this end, it is crucial to manage all information accurately, to distinguish between abstraction and idealisation, and to scrupulously avoid any assumption that cannot be verified, not even ideally.

[1] G. Sambin, Positive topology. A new practice in constructive mathematics, Oxford U.P., 2025