Aside from my academic research, I enjoy thinking about the mathematical aspects of the world around us and communicating mathematics to non-academic audiences. On this page you can find some writings and videos aimed at a broader audience.

My research fellowship from the Engineering and Physical Sciences Research Council generously allows me to spend part of my time on outreach activities. If you’d like me speak at your school or event, please get in touch.

## Videos

In 2022 I produced a video about the pattern of waves making up the wake of a ship or a duck. This is a common topic in university-level fluid mechanics courses, but my intention was to give a fairly complete explanation without assuming any knowledge beyond high school maths:

This video received an honorable mention in the 2022 Summer of Math Exposition.

In October 2022 I appeared in a 24-hour maths game show, with a 30 minute segment on a 1-dimensional version of Conway’s Game of Life. You can still watch the recording and play with copy of the google spreadsheet.

In 2024 I made a two-part video on iterations and chaos. The first part reviews some textbook material on the concept of iterations and how to visualise them. The second part has the more ambitious goals of understanding the titular claim of a 1975 paper by Tien-Yien Li and James A Yorke: period three implies chaos. The first part of this miniseries was my entry for that year’s community-run edition of the Summer of Math Exposition, #SoMEpi.

## Blog posts

If you want to get an idea about my research area, have a look at blog posts below. There is a lot of maths between what is taught in school and the highly specialised topics of today’s research. In fact, these intermediate levels contain some exciting insights that aren’t too difficult to explain:

- Waves of predatorsIn mathematical biology, one of the simplest models of population dynamics is the Lotka-Volterra model. It is a system of two differential equations, modelling the interaction of the populations of two species: a predator and a prey. The mathematics behind it has a surprising connection to the dynamics of waves in a shallow canal.
- Four different dynamical systemsThis multimedia post features four different dynamical systems to illustrate some properties of that relevant to my research: we’ll talk about the difference between “integrable” and “chaotic” dynamical systems, and the difference between “continuous-time” and “discrete-time” dynamical systems.
- What is… a variational principle?Variational principles play fundamental role in much of mathematical physics and are a key topic in my own research. That’s a lot to cover, so let’s start with a little story…
- What is… an integrable system?The oversimplified answer is that integrable systems are equations with a lot of structure. The kind of equations we are thinking about are differential equations, which describe change…

## In print

Chalkdust is a “magazine for the mathematically curious”.

I wrote an article on Hamiltonian mechanics and Noether’s theorem for issue 15.

## In the classroom

If you visit Loughborough University with your school, you may end up in a workshop with me. (If you’re a teacher wanting to arrange a campus visit, contact the School and College Liaison.) I also deliver maths sessions for events such as Inspiring Minds: STEM and visit schools.

Some topics I enjoy doing sessions on are:

- The mathematics behind the rainbow. Oakham School published a lovely summary of this lecture after I delivered it there.
- Combinatorial game theory. This workshop involves playing and analysing a few 2-player games with simple rules, but interesting strategies.
- Measuring infinity and fractal dimensions. How do we measure infinite sets? What does it mean when we say an object is 2-dimensional, 3-dimensional, etc? Are there objects of non-integer dimension? These are some of the questions we’ll encounter as we try to tame the strange concept that is infinity.

Feel free to contact me if you’d like me to give a lecture or workshop at your school or event.