Stuart King

What is your first memory with mathematics, the first thing that made you want to pursue it?

It’s not particularly a first memory, but if I were to think back to what made me interested in mathematics, there was a book about chaos theory that I remember reading and being very excited by. As an A Level student I was a bit obsessive about maths and I have distinct memories of sitting in the college canteen doing Sierpinski’s Triangle by hand, following the algorithm and actually getting something really convincing and being quite pleased with it. So, I think the kind of desire to chase mathematics as a career probably stems from that, and that time when I was finding the joy from it and the satisfaction of doing maths. I was really bound up in maths and physics and seeing where they overlapped, particularly in applied mathematics.

Do you prefer teaching or research or is it an equilibrium where they both benefit each other?

It’s both, I don’t think that I’d like to lose either part of the job. For example, if I have a break from teaching and I have a period of time where I have to focus on research, I find it quite difficult. I enjoy structure, so I’m not a person that likes the idea of having a month to just do one or the other, so I wouldn’t want to give it all up. I like exploring the subjects that I’m interested in, and I would likely still be doing some research even if it wasn’t part of my job, but luckily I get to be paid to do something I enjoy.

Do you find that teaching lends to research?

What I’ve found over the years is that when you have to teach something, you begin to understand it better. That’s something that teaching has helped with, regarding research, it essentially makes the foundation in core parts of mathematics all that much more concrete. However, the best thing about teaching, I’ve found, is the energy that students have; that’s probably the most rewarding part. Teaching to an empty room wouldn’t be nearly as enjoyable without the engagement you get from students working on projects and pieces they’re really interested in, especially when they discover something for the first time. I find that exciting, especially when I get an opportunity to point out all the fun things in that area that might get them even more interested. It’s similar to lectures, when you can see the penny drop for everybody in the audience and they notice the connections and reasons behind topics; I think that’s a really nice thing to experience.

What are you looking at in your current research?

We’ve just published a new item to do with edge tracing in images, that’s been a fun project. We started off with a particular problem that was motivated by eye imaging, and needing to be able to trace layers in an “optical chromatic tomography” image of somebody’s eye. Inside this image, there’s a picture of the layering at the back of the retina, and one of the tasks we wanted to be able to do is trace the layers there and study those. These have a relationship to blood flow into the brain, due to its positioning, and it’s one of the best ways we can understand this. One of the things we had to do was develop some different image tracing algorithms that were robust to different types of noise, since it can be really noisy imaging. So, we’ve done some new methodology looking at that problem, and then we’ve got other work in progress around different image enhancement ideas.

It aims to improve medical imaging, this is very often not optical modalities, but other things, and they come back as, typically, black and white images. This is because they’re not really about transmitted light; they’re more about the measurement of something like x-rays, CTs, etc. What this means is you’ve got potentially quite noisy images, that can be quite difficult to unpack and get information about. I think there’s some exciting stuff, connecting that to the medical outcomes, diagnosis and diagnosis support.

Do you find it fulfilling to work on projects you will be able to see actively used?

I would say I prefer the tangible things, which are usable applications of mathematics. I prefer the mathematics that is driven by its applications, compared to completely pure mathematics done for the sake of mathematics. For example, I was previously working on topics related to fluid dynamics and waves and I found that really interesting. For me, that’s the heart of what applied mathematics is about, trying to model things that are happening in the real world, in whatever context, because applied mathematics is everywhere. This, while still coming at it from a mathematical perspective, compared to other disciplines like geosciences or physics for example. That’s what makes mathematicians important in these projects, it’s, in part, bringing the rigor and understanding, and why these ideas might or might not be able to work. That’s something mathematicians are very mindful of, knowing when you can, and can’t, apply a methodology and what needs to be developed in order to make something better.

What is your advice to students, ones that want to start at Edinburgh or current students?

To current students, I would certainly say to make the most of the things that are on offer, Edinburgh is a melting pot of ideas, courses, clubs, and all of the things going on in the city. Looking back, I perhaps spent too much time studying, it’s important for when you’re no longer a student and looking for your next step, having that balance of experiences for future job interviews or further education.

To prospective mathematics students, a good way to think about maths is to think about where it pops up, the applications. Think about the different applications, and how many different routes, there are out there to get excited about. This is what interested me as an undergraduate and helped me understand the pure side. That’s often how a lot of mathematics gets developed, it starts with having to solve a tangible problem, and then someone goes “oh we could generalise it” and it’s then generalised until it becomes a part of mathematics.

Finally, what have been the most exciting developments in your field in recent times?

Certainly, for me, it’s that people are beginning to apply deep neural networks to understand fluid problems. In terms of general applied mathematics, the impact of neural networks is big at the moment; it’s beginning to be felt almost everywhere. That’s certainly one of the most interesting developments, and it’s exciting to think about what we might be able to do in the future.