Introduction

Abstract

Theoretical physics has developed hand-in-hand with mathematics.

The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve.

Eugene Wigner (1960)$^{1}$

Modern mathematics is the formal study of structures that can be defined in a purely abstract way, without any human baggage. Think of mathematical symbols as mere labels without intrinsic meaning. It doesn’t matter whether you write “two plus two equals four”, “2 + 2 = 4” or “dos mas dos igual a cuatro”. The notation used to denote the entities and the relations is irrelevant; the only properties of integers are those embodied by the relations between them. That is, we don’t invent mathematical structures – we discover them, and invent only the notation for describing them.

Max Tegmark (2014)$^{2}$

$^{1}$Wigner, E. in “The Unreasonable Effectiveness of Mathematics in the Natural Sciences,” Communications in Pure and Applied Mathematics (John Wiley & Sons: 1960).

$^{2}$Tegmark, M. in Our Mathematical Universe: My Quest for the Ultimate Nature of Reality (Random House: 2014).