Fastidious, absent-minded and just a bit mad… Do mathematicians really resemble the image evoked by jokes and popular stories? Once upon a time mathematicians were also physicists, philosophers and lots of other things at the same time. Today they are specialized, sometimes they teach, but we don’t know what they really do. The key to understanding mathematicians’ activity is the word “model”, a tool that was used – from the Middle Ages to the modern era – in order to build formal representations of the world: cathedrals, starry vaults, categories of fish, economic systems. Mathematicians develops patterns, and although the latter are caricatures of reality rather than accurate descriptions of it, they are often beautiful, elegant and incredibly effective. The extraordinary power of mathematics proves that, far from being a mere science of numbers and shapes, it is a general and pervasive language, a veritable alphabet of the world.

Angelo Guerraggio teaches Mathematics at the Università dell’Insubria in Varese and also heads the PRISTEM research center at the Bocconi University in Milan.