Hello!

I'm Josh Grant, and this is my math newsletter.

In the past while, I've realized that I've always been a little interested in mathematics as a topic. As I've gone through life, my little interest has grown to a major interest. But lately I've been thinking, over and over: what is mathematics, anyway?

So I thought I'd write my way through it. And if folks out there find this interesting too, then let's learn together.

Where to start?

I'm not sure how to start this project, so I'll start with where I'm coming from.

My Mathematical CV

Here is a rough CV of my mathematical "career" as it were:

I was raised in Kitchener, Ontario. I went to elementary and high school there. It turns out that a world class mathematics school was up the road from me.

In Grade 12, I scored second in my high school in the Euclid math contest, with a score of 60 out of 110 (if I recall correctly). I believe the highest score was 61 or 62, so I wasn't far off from the highest. Overall around 20 students (again, based on my memory) took this test.

I attended Trent University in Peterborough, Ontario, choosing to major in mathematics. I chose a single major unlike most of my colleagues who usually took math with physics, biology or computer science in some combination of a major/minor or joint major. I graduated with a BSc on the Dean's list.

At Trent, some courses I took included: Real Analysis; Complex Analysis; Groups, Rings, and Fields; Introduction to Topology; Dynamical Systems; Mathematical Modelling; and Social Choice Theory (Voting Systems, Fair Division, and some Bargaining Theory)

In my third year, I competed in the Putnam math contest. I scored 2 out of 120. Around 6 students took this test at Trent. Notably, professors came up to me unprompted and congratulated me on scoring points, which gives some idea of the difficulty of the test.

In the summer between third and fourth year, I had the delightful experience of attending the Atlantic Association of Research in Mathematical Sciences (AARMS) summer school, held at Dalhousie University in Halifax, Nova Scotia. I took two graduate-level courses; Internet Mathematics/Complex Networks, and Introduction to Wavelets.

In the summer after I graduated, I took a two-week workshop in Mathematical Biology at the University of Alberta in Edmonton, Alberta. This was a good but intense workshop covering all aspects of mathematical biology, from ecology to human physiology.

Since I enjoyed school and had lots of support from professors and friends, I decided to pursue graduate studies. I attended The University of Western Ontario (now simply known as Western) in London, Ontario. My area of research was in mathematical biology, and in particular was The Evolution of Cooperation and Evolutionary Theory.

I gave two presentations as a graduate student, both on results related to a sexual Moran model (much less interesting than it sounds) I worked with. The first conference was the Society for Mathematical Biology's Annual Meeting in 2008 in Toronto, Ontario, Canada. The other conference was the Canadian Applied and Industrial Mathematics Society's Annual Meeting in 2009 in London, Ontario, Canada

## And the other stuff

Something that my "formal" mathematical training and CV doesn't convey is all of the mathematical conversations and people I've met along the way.

I've had many conversations with people where folks ask questions like "What do you plan to do with a math degree? Teach?" (at one point, yes), "Do you like accounting?" (not at all), or "What do you do in math research?" (for the pure math case, I'm not entirely sure.) I've also had a lot of visceral reactions to saying I'm studying or interested in math. In one interaction I had during undergrad, someone asked me what I was studying and when I said math, they replied "Ew!". Many people have told me they hated calculus or stats in school. Mathematics as a topic elicits strong reactions from people.

I've also met a lot of wonderful people and been able to experience new places because of math. The first time I took a flight as an adult was to go to summer school in Halifax. I've met people from nearby places and from overseas studying math, as well as meeting folks from a diverse walks of life. And generally speaking, I've enjoyed social events based around mathematical topics. So I feel there's a social element to mathematics that I find very enjoyable.

My mathematical career also led me to new intellectual places. Somehow I got interested in mathematical biology, despite never being interested in biology until university. And I also had an interest in game theory, which is how I found out about game theory in biology and theories of evolution. None of that sounds like mathematics, but in some cases is completely is mathematical in nature. How exactly does one get from taking linear algebra courses to learning about theoretical population dynamics?

All of this makes me ask the question: What is math, anyway? I know mathematics is a large subject, one that basically no one could know completely in a single lifetime.

But what is mathematics, then? Let’s find out together.