Mathematics can be found everywhere: basic Arithmetic explains us how sales work, Differential Equations explain us how planets orbit around the Sun, Geometry tells us that the Earth is not flat, Combinatorics tells us how many "clinks" will we hear in a toast, Probability tells us how unlikely it is to become rich by buying lottery...

However, sometimes it is hard to explain what Algebra does for us (and here by Algebra I mean actual Algebra); and the truth is that Algebra is beneath every single one of these fields! In this post I want to explain one of my favourite theorems, how its roots are essentially algebraic (although it is a theorem in combinatorics), and how it can be applied to the real world: Pólya enumeration theorem.

However, sometimes it is hard to explain what Algebra does for us (and here by Algebra I mean actual Algebra); and the truth is that Algebra is beneath every single one of these fields! In this post I want to explain one of my favourite theorems, how its roots are essentially algebraic (although it is a theorem in combinatorics), and how it can be applied to the real world: Pólya enumeration theorem.