Since choosing to major in maths at university and even more now that I am starting my honours year in maths, I have often received weird looks or comments from people saying that they “could never study maths” or worse yet, people telling me that maths is boring. I am sure many others who study maths are similarly frustrated by these types of comments. In my blog post I will explain my reasons for studying maths and why you should too.

The reason I originally chose maths is because I wasn’t sure what I wanted to do and a degree in maths felt like it left the most doors open. This brings me to my first reason you should also study maths. Maths is ubiquitous in all STEM fields and beyond. For anyone who is trying to choose what to study, choosing maths will only open up more pathways. For example in the summer between 2021 and 2022, I had the opportunity to work in a psychology lab studying how people perceive colours differently. I spoke to the head of the lab about why he chose me to work there over people who have studied psychology, he said it was precisely because I had a background in mathematics. The way that you learn to think through studying maths and the ability to model real world phenomena is applicable anywhere so if you do maths you won’t limit yourself to one field. I have since discovered that instead of leaving doors open, a degree in maths will open ones which were closed.

Despite my admittedly unexciting reason for choosing maths, I have learned to appreciate maths in itself. The reason I continue maths is because wherever in maths I look there is an elegant or beautiful or playful theorem that appears out of nowhere and I can’t get enough of them.

The first time I experienced this feeling of awe and appreciation for a theorem was when I first read a proof that there are infinitely many primes. I will present the proof here and hopefully someone reading this will experience what I felt.

We start the proof by considering a set of finitely many primes S.

We then multiply all the primes in this set and get a number N.

Since N is divisible by every number in S, N+1 will be divisible by none of them.

This means that either N+1 is a prime number or there is a prime number not in S which divides N+1. Either way there is at least one prime number not in S and therefore we cannot have finitely many prime numbers.

Pretty neat proof hey?

I hope that you found this proof fun and exciting enough to consider studying maths yourself.

**Jack Mills**

**Monash University**