In June’s blog post, we feature an interview with Dr. Thomas Woolley, Senior Lecturer of Mathematics, Cardiff University.

**When did you first become interested in mathematics and biology?**

My story will be familiar to many academics. There was that one teacher, Howard Hall, in secondary school that really made mathematics sing for me and I knew I wanted to know more. Mathematics at university then built on my ideas of rigour and instilled a true understanding of how beautiful a proof could be. But nothing really grabbed me until the third year undergraduate course in Mathematical Biology. For the first time we were actually using mathematics to do something beyond the abstract. Prof. Eamonn Gaffney demonstrated that you don’t need the most difficult or cutting edge mathematics to say something extremely useful and powerful about a biological mechanism.

And the final section on Turing patterns blew me away. I knew that was what I wanted to study in my life. The mathematics and the final product were both incredibly beautiful and Turing’s tragic story wrapped the science and history together in an irresistible package.

**Was the decision to do a Ph.D. an obvious and easy choice?**

In all honesty I had no idea what I wanted to do for a job in life and I had the mantra that I will keep doing mathematics until it gets boring. I had thought about the standard directions of banking and had done an internship in my second year. I HATED it. Thankfully, that must have shone through because they didn’t offer me a job afterwards. However, if I had been offered the job then it would have been difficult to turn down the job security (and the wage!). But I’d like to think that I make the best of the opportunities provided and following my interests has meant that mathematics hasn’t gotten boring yet.

**How did you come to run your own group?**

Persistence. Academia is a long game with few opportunities and it can wear you down. But if it makes you happy you keep going.

**What are your main research questions and why are they interesting?**

This is probably a bad admission, but I don’t have an “all-encompassing-research-goal-which-I must-answer-lest-my-life-have-been-for-naught”. And I know this is not trendy. All universities and funding panels want to know your BIG IDEA that will CHANGE THE WORLD. Not to say that there is anything wrong with this, but this is not how I work. My interests lie in diversity. I see myself as having a vast array of modelling skills and I want to apply them to the problem that will help us the most. This work philosophy is the reason why my publications span diverse areas such as: Turing patterns, neurodevelopment, chick digit formation, tumour invasion, cell movement and many more areas that use models that are: discrete, continuous, stochastic, deterministic, mechanical, algebraic and numerical.

Currently, my interests are in understanding a piece of biological work from collaborators on tumour elimination in the pancreas. I thought it would be easy. But that is the beauty of mathematical biology. Even if the logistic equation has been used a thousand times, using it in the right setting can still provide new insights and push our knowledge forward both mathematically and biologically.

**What makes you passionate about your work?**

Conversations with biologists. It is such a different world to mathematics. Where mathematics is confident, rigorous and constant, biology is dogmatic, messy and transient. This is not to denigrate biology, it is just the nature of the beast. With physics and chemistry you can do experiments under lab conditions and get repeated results no matter where and when you do them. In biology you can do the same thing to the same cell twice and generate two completely different outcomes! Thus, as a science it is fundamentally more difficult. This is where I fit in and what I enjoy most. Namely, through conversations with biologists I try to understand enough of their experiment to use the right framework to model it. From there we work together to probe the experiments and model in tandem, asking such questions as:

- What ideas are consistent with the outputs?
- Once we have a model that reproduces reality, what happens when we perturb it?
- What are the limitations of what the model says can happen?

Thus my passion is knowing that I’ve pushed our biological understanding forward and knowing that I’ve provided a stepping stone for the next experiment to build on.

**Do you have any advice for someone considering a career in mathematical biology?**

If mathematical biology is your passion do a course, or dissertation, in something else first, before you focus on a doctorate in math bio. What I am finding is that it is not “new ideas” that push our field forward, it is “old” ideas from other fields that find a new niche in math bio and they push our understanding forward. For example, network theory, Bayesian probability and topological data analysis all started in different fields, but their application to biological data sets have revolutionised our understanding in neurobiology and neurodevelopment.

This is how I see mathematical biology. It isn’t necessarily a mathematical discipline in itself, it is about developing a wide range of skills and being able to know which tool is best for the job. Thus, taking that other course in fluids, or machine learning, or operations research, will help you develop new ideas in mathematical biology.

**What do you like to do in your spare time outside of work?**

Mechanical puzzles, escape rooms and board games. I find it very difficult turn my mind off, so even when not researching I still want to be problem solving and I find such pursuits as opening a puzzle box highly delightful. Unfortunately, these are all quite stationary pursuits and so to get myself out more I have just joined an archery club. Who knows how these skills will help, or be helped by, my mathematics.

**Any final comments or advice?**

A good answer quickly is often more useful than a great answer slowly. To unpack this a little, as mathematicians you’re taught to prove ideas that will last forever. This can take a long time, which may make the answer useless (see the COVID-19 pandemic as an excellent example of this). As I’ve said before it is much more important to apply the right idea to a biological scenario rather than a new idea. Thus, don’t worry if your mathematical model will be supplanted in a short time. Biology is still a young science and doesn’t have an axiomatic basis of laws. Just try to focus on answering that next question as best as you can.