# Dr Thomas Woolley

Thomas Woolley is a mathematical biologist at Oxford University working in stochastic pattern formations in nature, specifically stingrays. Thomas also works extensively in communicating mathematics to the public including appearing regularly as a mathematical consultant on the television show ‘Dara O’Briain: School of Hard Sums’.

I would say that this really is the golden time for mathematical biology

**On becoming interested in maths**

My interest in mathematics really started quite late, you know, you hear these…well, I won’t compare myself to a genius but all the geniuses out there, you know, they started…the story of Gauss, he solved one of his father’s problems when he was still in diapers. But I started rather late, I didn’t understand fractions ‘til, ooh, at least secondary school, but it just took one great teacher to sort of say, ‘Well, think about one millionth, that’s a really tiny amount, think about this square, if I did one millionth of a square, it’d be less than the ink that I put on the square’. And that was it, it was just that moment of epiphany that I understood what a millionth was, and from then on mathematics just sort of clicked.

And so from then on, I found the teachers were as passionate as I was and they were all just pushing me, and I was just a sponge to soak up their ideas. So…but where I really got into mathematical biology, that came from, again, a fabulous lecturer and it was one of the first maths courses that I did where you got to use mathematics. Because, as an applied mathematician, I want to use my mathematics. Pure mathematics is very beautiful, you get to prove theorems and they work and they will work forever. Applied mathematics is very dirty, what you prove now – it’s like physics, essentially – what you prove now may not be true next week but you’re using it, you’re solving problems, and what I work on is mathematical biology and biology has a whole load of problems still and that’s why I’m interested in it.

**On how people can connect with maths**

It’s incredibly important visualising data, and particularly nowadays when we’re inundated by so much data, and that’s why you have these websites popping up – Information Is Beautiful – because they found ways that make all these numbers understandable. And the important thing about being a mathematician is that it’s really not about the numbers; either it’s how you understand their structure or, as an applied mathematician, you want to say, well, what are those numbers telling me? It’s not the fact that this is ‘five’, it’s the fact that this is more or less than we should expect and so I firmly take this point that numbers really hide the beauty of mathematics, numbers really for us are just the tools. You know, you wouldn’t ask a carpenter about this wonderful box that he made with ornate carving, you wouldn’t say, well tell me about your chisel, tell me about your hacksaw. You want to know about the box and that’s what the mathematician sees as his maths.

**On mathematical biology**

So mathematical biology really started in Oxford, it was a guy called Jim Murray, there had been bits before this but it was never really seen…there’s a quote, I can’t remember who it’s from, but it was, um, ‘their maths is bad but their biology is worse’ and that’s really how it was seen, it was mathematicians encroaching onto an area that we really had no business being in.

So it took a guy called Jim Murray – fabulous genius of a man – to really go and speak to biologists, to really see what their problems were, and their problems range over everything. So he, Jim Murray himself, he has worked on the respiratory system, the cardiac system, he’s worked on the shockwave of a spine as an ejector seat is pulled. So, apparently – this is a great anecdote – he would drop corpses down lift shafts to see the traveling wave up a spine.

He’s done everything from that end to ecology, and how marriage works, so how people interact with each other. And some work on…my original piece of work was on fish spots, so I was carrying on his work and Alan Turing’s work on how do patterns get created, why aren’t fish all one colour, why do zebras have stripes and things, and that’s sort of where I fitted in.

But mathematical biology, it took a while, but we’re gaining more respect and I would say that this really is the golden time for mathematical biology, because they’re beginning to respect us and we’re beginning to understand the tools that we have that we can transfer.

**On the problems in mathematical biology today**

In terms of big problems at the moment, I would say there is a huge statistical problem, essentially. So for a long time, biologists have used statistics but they’ve never really understood them, and I suppose I’ve made lots of enemies of biologists there, but they’ve learnt a test, they’ve put their information in and that’s the answer they get, they don’t know why. And so, what I’d really like to see is biologists and statisticians getting together and the biologists to trusts the statisticians to say well, OK, here’s my data, what does it mean and why does it mean that? They’ll be much more robust in their results because they will understand why they’re testing it in the way they are.

But as for specific questions, what really is the big one? Of course the gene revolution was incredible but I think getting to the really small ideas of what genes do, that’s a really powerful one at the moment, that different alleles in the population can create different effects and understanding how they interact, because…the idea of the blue eyes, that you have two genes which encode that: if you had both you’ll get blue eyes, but if you only have one you’ll get brown or some other colour. But their interactions are much more complicated than that and so, if we can really peg down how gene and gene products interact, that’s when you’ll get the gene revolution pushing forward, because we’ve been able to identify genes for a long time now, we’ve been able to say well, you have cancer, we see this gene, but we don’t know what that gene is doing, and that’s why mathematical biology is important, because we can make a model of what that gene is doing, we can test it, we can see if it’s doing what the data says. If it’s not, we can rework it, we will get our model as close as we can to the data. Once we have that model, we can then tell you lots more about the system than an experiment could. We can say what it’s doing and how it’s doing it.

**On seeing maths everywhere**

I would say I don’t unless prompted, I don’t feel the world is mathematical, because I do enjoy that wonder of not knowing, it’s kind of like a magic trick. You know, you see a magic trick and you like being entertained, you don’t want to know how it’s done, but when you start thinking about it…so if I was with friends and they start questioning it, I will find myself saying, well, how is that done? There is that nice idea of pure entertainment, you get to look at a nice tree, say, but how does that tree form itself, how is it able to produce all of those individual leaves, how is it able to manage as an ecosystem? And then that’s where you start thinking about the fractal structure and things like that. So I would say as a person, in the real world, I can live without maths, but it’s so much better when you think of it with maths.