Which Came First, the Circle or the Wheel? From Idea (ιδεα) to Concrete Construction

Idea is a Greek world (ιδεα) which means mental representation, rational scheme or mathematical figure; Plato and Galileo said that nature uses the language of mathematics, whose geometrical patterns come from experiences. But, as F. Enriques noted, in the formalization of these ideas “we should take into account not really the experience, but rather the demands of simplification of our mind, in which they are reflected”. Most of our activities, especially in modern time, consists in realizing concretely abstract mathematical concepts and theories, as in the title of this conference: when form becomes substance. Fab Labs (Fabrication Laboratories) are modern workshops in which everybody can use digital fabrication to create real objects from mathematical ideas, especially from those which came from the phenomenology of space. In the last part I will briefly consider some recent results in higher dimensional algebraic geometric, which can be summarized in few diagrams. I will point out that some of these ideas and diagrams could be directly connected to biology and life sciences.