18. Chapter II : Applying abstraction

II. Applying abstraction

The study of mathematics began with the research for solutions to concrete problems: a sculptor searching for the perfect proportions, an architect designing a temple, a sailor navigating the sea at night.

Anchored in reality, mathematics allows for abstractions that, in turn, help us to describe, understand, and even predict and – to certain extents – control reality itself. 

This intrinsic connection and permeability between the abstraction of mathematics and the tangibility of the real world enrich our understanding of both.

Despite its reputation of being too abstract and disconnected from reality, mathematics is undoubtedly the discipline with the widest range of applications, precisely thanks to its abstraction.

Mathematics is everywhere, natural or artificial: it is encoded in our calendar as well as in the stars.  It helps us to move, vote, compose music and to know what the weather will be tomorrow. We use it to organise our society, in every science, in every technology.

And, of course, it has many interconnections with artistic expression, sharing its history, raison d’être, and questions. Artists are inspired by it, and often apply it in their creations, as much as mathematicians sometimes turn to artistic practices to investigate and demonstrate their hypothesis. 

Applicability, efficiency and ubiquity of both mathematics and art are so universal that, among all domains of knowledge, they have been given special status over time, from highly philosophical, supernatural, even divine.