Mathematician of the Week

Mathematicians working on the space race did calculations by hand, and suddenly that was automated and changed the whole way of working. But the problems didn’t disappear; a different kind of understanding was required to apply the new tools. The same happens with AI: you have to understand what is relevant and what is not. And when you work with real-world phenomena, where everything is enormously complex, human intuition remains irreplaceable.

I would not consider any research project as truly ‘completed,’ but I am proud of the work in which we use traveling wave solutions of nonlinear evolution equations to solve real world problems.

I say that I’m a statistician with pride! It means that I have been rigorously trained, that I have a broadly applicable skill set, and that I’m always open to new and interesting problems.

I thought, ‘This does not belong in the math department! How is math going to have anything to do with leopards and spots?’ But I went to the talk, and ... I understood that math can play a role in science, in biology, in medical science, and developmental biology, and I had never seen that before. That was when I knew I wanted to be an applied mathematician, because I saw real benefit of math in those areas. I wanted to be like this person I saw giving this talk.

We start with an important problem from biology and then we translate it into a problem in mathematics, computer science, statistics or physics, we work on it, but always keeping an eye on the original motivation and the relevance to biology.

Truly, the math here is counterintuitive. It’s rich. It’s hard. It’s deep. And through luck or through sheer force of will, the kinds of math that I’m trained to do actually give you insight into the problem, so that’s a treat for me.

Even though she never took the time to celebrate her landmark proof — nor felt any consequent ego boost — at least Wang can now say with utter certainty that tubes pointing in every direction in 3D space can’t overlap very much.

I'd say my main motivation is knowledge in itself. That said, the existence of a link with the real world, however remote, is important to me. I think it would be hard for me to work on subjects that are totally disconnected from questions that are rooted in the real world.

Maths is non-invasive – there's no need to operate – so we can use equations to describe the circulatory system in order to better understand human physiology and why certain pathologies occur.

That’s what I find really exciting about maths, you find these connections between these things that don’t seem to be connected at all. So similar maths can be used to describe arms races and arguments between married couples. As soon as someone says this to you, you can see the analogy and it becomes really obvious. But it’s not really obvious until you transcribe it into mathematical language.

When you perform a calculation, sometimes there’s really clever tricks you can use or some ways that you can be an actual human and not a computer in the performing of the calculation.

Biology gives us mathematicians a rich collection of challenging problems to work on, but we mathematicians also give biologists rigorous mathematical approaches—modeling, rigorous analysis, data analytics and computation—to provide insight into the things they cannot do in the lab.

Think about what it means to find something beautiful. For me, I recognize in myself a feeling of joy, awe, and reverence. It gladdens the heart and lights up the eye. Mathematics is beautiful as it elicits the same emotions in us. We may recognize it as elegant or different. It is awe-inspiring and joy-inspiring at the same time. For example, consider the experience you have after understanding something arduous, glimpsing truth, or a way of doing things in a new way… with all these things you get that feeling.

I get to take something that I’m good at, which is statistics, and apply it to a thing that I love.

To me personally, structure is very satisfying. You are not just answering one question; you are really seeing some huge, global phenomenon going on. This is how I like the world to be, where I can completely understand what is going on. So if I have a question, then I can go and look at this systematic picture that I have in mind, and I can find out the answer to this question.

Tyrants cannot stop us from doing mathematics. There is at least something they cannot take away from us.

I think part of my love for math and statistics was, seeing the beauty and the complexity of it and the wonder of it and knowing that it’s so much bigger than me. The deeper I got into math and stats, the more I realized there’s so much I don’t understand.

I've only had a few real eureka moments in my research career, and they're fantastic, and I can picture them. You don't know they're those moments until afterwards, and you realise what's happened.

So, we’re working together, mathematicians, computer scientists, working with machine-learning researchers, biostatisticians, even medical practitioners and engineers, and policymakers to bring this all together to provide solutions. So that’s a very exciting area to be working in now.

But then, this moment when all of a sudden you get an idea in this process of trying to understand the problem and finding out how to solve it, you get an idea and then follow this idea through and see that it actually works, this is really cool.

Mathematical creativity, analytical and lateral thinking, a joy of puzzles, and perseverance in the face of difficult problems are all equally important in my view.

Today it is obvious to me that if a problem is interesting from a biological point of view, then there is almost always a mathematical question behind it, which is really fascinating.

As a young kid, my parents would take us to the science museums so that we could pick one area to study seriously as an adult. But the problem was that I liked everything! So that’s why I moved into applied maths. With that, you can do everything, from science to engineering and even social sciences.

I trusted the famous saying that “mathematics is the language of the universe.” I thought mathematics lies at the core of scientific knowledge. If I had only one life, I wanted to be connected with the most essential language of our universe.

Throughout history, we see that much of science has been built on mathematics that was developed before that science or those applications were even imagined. For example, today’s entire digital economy and world relies on the fact that we can encrypt information, that we have some way to reasonably easily encode things so that only people with a certain key can decode them. All of today’s encryption systems are built on number theory, on properties of prime numbers in particular, and on mathematics that was developed before there were computers.