Dr. Tom Crawford, a mathematician at the University of Oxford, is known for his engaging approach to mathematics. He received his PhD in Applied Mathematics with a focus on Fluid Dynamics from the University of Cambridge, and also holds a Master’s degree in Mathematics from the University of Oxford, where he studied at St. John’s College.

Dr Crawford is currently a Special Election Fellow in Mathematics at St Edmund Hall, University of Oxford. He is also the public engagement lead at Oxford University’s Continuing Education Department. He teaches mathematics to first and second year undergraduates at St Edmund Hall, as well as to visiting students at the same institution.

In addition to his academic roles, Dr. Crawford is widely recognized for his outreach efforts through the Tom Rocks Maths website and eponymous YouTube channel, where he strives to make mathematics more accessible and fun.

Dr. Crawford was among the speakers at the fall edition of the Ratio popular science forum. The Economy.bg team met with him during the event to talk about mathematics with love – what makes us like it or not, can it be fun, what it actually teaches us, what it has to do with penalties and catching Pokémon, and more…

Why math?
In school, it was my favorite subject. I think personally, my brain works in patterns. When I see the world, I see patterns, I see numbers. And so for me, finding math as a subject was just finding the right way for my brain to work anyway. I just love it. I love the fact that the entire universe can be described in math.

When did you realize that math was your thing?
The way I see the world is the way mathematicians try to describe it. I think I can give you a very clear example. I was very lucky recently and I climbed Mount Kilimanjaro, the highest peak in Africa. It was really fun, I loved it, I got to the top and like everyone else, I was just admiring the view. It was incredible. But I could also see another peak in the distance on another mountain, Mount Meru, and my brain started, “I wonder how far away that is? Can I work it out with trigonometry? Can I figure out the angle and can I calculate the height of this other mountain?” So definitely like most people, I could appreciate the beauty of the nature that was there, but my brain couldn’t help but also think about how I could use my knowledge of math to try to answer that question. And I think that’s generally how I see the world. For me, because that’s how I perceive reality, that’s how my brain works, I’m just drawn to math. So I don’t feel like I ever had to choose math as a subject or I ever suddenly realized that it was my thing. I think it just fits perfectly with the way my brain wants to perceive the world.

What do you actually do as a mathematician?
I’m quite unique as a mathematician. As well as teaching, I also have a role in public engagement. I’m the public engagement lead at the University of Oxford, which means I make YouTube videos, I give public talks. So that’s a big part of what I do. As a mathematician, I think about problem solving. Whether it’s trying to figure out how to teach a certain topic to my students, to help them understand some of the more difficult problems [that’s problem solving]. I do research, I look at the spread of pollution in the ocean, which is a problem. And again I try to figure out how we can use equations and mathematical models to understand how pollution spreads and predict how it’s going to spread. Then we can go and clean up where the pollution is going to be. I think in general, mathematical research is about asking a question, but then you try to answer it using the tools of mathematics. So in that sense it’s not that different from any other scientific research. You’re just using maybe a slightly different set of tools to answer the question.

What are the Millennium Prize Problems?
The Millennium Prize Problems were announced in 2000, the millennium, and they are 7 of the biggest unsolved problems that mathematicians are currently facing. One was actually solved a few years later by the Russian mathematician Grigori Perelman. The other six remain unsolved. In short, one of them is the Riemann hypothesis, which talks about the distribution of prime numbers. So, is there a model for how prime numbers are arranged? My favorite is the Navier-Stokes equations, which are related to fluid mechanics, which is my field of research. I study the ocean, which is a fluid. But more generally, we study all sorts of different things that behave like fluids. We have these equations that describe fluids, but we don’t understand them mathematically. They work. They’re used by engineers and physicists to solve problems and build rockets that fly into space. But we don’t really understand them. I think that’s a pretty hard concept for people to navigate because only mathematicians really care about understanding them. If we can use them, why do we need to understand them, which is a fair question. But from a mathematical perspective, we really want to understand what’s going on with these equations.

You have very specific teaching methods. If we could imagine how math relates to disease modeling, how do you relate it to the shape of water and colours?
I think you can use math to talk about anything. I really believe that once you have the tools and the skill set of a mathematician, once you learn how to manipulate equations, how to create a mathematical model, you can apply it to anything – colors, the shape of water, any of these things. I can give you my two favorite examples. I really like video games, and I play a lot of Pokemon. I decided that I would take everything I know as a mathematician and apply it to Pokemon, the video game, and figure out how to catch Pokemon. How can you improve your chances of catching a Pokemon? So we take math and apply it to fictional creatures. My favorite sport is soccer. So I take penalty kicks for my team, and I’m pretty good at taking penalty kicks. And I thought, “Okay, what makes me good at taking penalties?” I did some mathematical analysis and I found the perfect place to aim your shot when you take a penalty. So there’s a specific spot in the goal where you’re going to maximize your chance of scoring a penalty. You calculate that mathematically, and then it turns out that’s exactly where I was aiming all along. I hadn’t done the math before. I had learned from my experience in football. Most people, like players, you know, professional players, don’t do math, they learn from experience. But I just love the fact that you can model it mathematically and explain why that’s the best place to aim your penalty. So to me, that’s just the beauty of mathematics – once you have that skill set, you can apply it to anything – Pokemon, football, water, whatever you want to try and figure out.

Did you catch the Pokemon?
I finished the game. I caught all the Pokemon. Yeah, absolutely. The other thing I find fun with Pokemon is trying to model Pokemon and pretend they’re real. You have all this description, they have all these properties, you know, like fire-breathing dragons and electric mice like Pikachu. And you’re like, “Okay, okay, what if Charizard, (the fire dragon) was real? How much would you have to feed Charizard if it was a real creature? If you had a Pikachu at home, could you use it to charge your phone?” These are funny questions, but you can answer them mathematically.

Many students feel intimidated by math. What advice would you give to young people who struggle with this, and how can parents and teachers better support them?
We as mathematicians are aware of this and we need to address it. I guess there can be a sense that sometimes students who love math really do like it, and a lot of other people just don’t. It’s a love-it-or-hate-it kind of subject. It seems to have this reputation. And I think one of the main reasons for that is that the way math can be presented can often be quite dry. It can feel a bit boring. If you’re like me and your brain works that way, you love it regardless, right? And those are the people who really love the subject. For everyone else whose brain maybe doesn’t work in that very specific way, my approach or the way I would advise parents and students is to find a way to teach math that makes sense to the student. So for example, if you have a class of 13- or 14-year-olds, maybe they’re interested in sports or video games. The examples that I gave. So if you then talk about that and put it in that context – so the penalty problem that I mentioned, trying to work out the perfect spot to take your penalty kick, that’s actually a geometric problem because your goal is a rectangle. Your goalkeeper covers a semi-circle shape.

Your target is a circle. You’re trying to match shapes. So if you present the problem as, “Let’s figure out how to take a penalty kick,” hopefully a lot more of the students will be interested in learning the answer, right? If they’re playing soccer specifically, they’re like, “I want to know how to take a penalty kick. That would be great. That’s really helpful.” But then you say, “Okay, okay, to solve it, we have to solve this problem.” And that’s a shape problem. Now that you get to this point, it looks like a homework problem. But you’ve already told them that you’re doing this to help them get better at soccer. So the students say, “Okay, I understand why we’re doing this. I’m excited to know the answer. I want to know the answer. This will help me get better at soccer.” So if you can find other examples like that and other ways like that, like how do you catch Pokemon? The way is to use those different topics and areas that students are already interested in, and then present the math in that context. And then they want to engage.

You know, instead of saying, “You need to know this,” they say, “Oh, please tell me this extra thing I need to answer,” because they want to answer the question. That’s how I see it. If you think you’re not a math person, think about what you do, what you enjoy, one of your hobbies, your passions, your interests. There will be a way to apply math to it. And that would be my advice – think in that context, and then you’re much more likely to want to learn it and keep persevering and be motivated to learn it [math], because you’re answering a question that you really want to know the answer to.

Why do you think STEM is an important area of ​​education?
I think it’s very applicable to the world that we live in, to our lives. It’s such an important part of the world now with our phones, with all the cameras that you use, the microphones. All of this is built because we understand how sound waves work, how video recording works. Everything is really driven by understanding light, by understanding waves. So I feel like just the technology-driven world that we’re in now means that if you have a background in STEM, you just generally understand more about what’s going on. If you understand things, it’s easier to use them to your advantage. When you do a STEM subject, it teaches you how to solve problems. And that’s why I enjoy math so much. Because at its core, math is about solving problems. You might not feel like it when you’re doing homework in school, but if you kind of break it down, it’s like, “Here’s a question that I want to answer. Here are the rules that I have to follow. So those are the constraints.” It’s like the resources that you have available to you. And you have to get the answer. So you know it could be: here’s an equation where you’re allowed to multiply, divide, manipulate the equation to find x. Again, this sounds a lot like a math problem. But it’s the same as, “I have to drop my kids off at school and go get coffee with my friend. And I have to do this before 11:00.” This is an algebra problem. How long does each of those two things take? What’s the traffic going to be like? So, I think everyone does algebra problems every day just in terms of planning their day. But people don’t think of it as solving a math problem. I think studying STEM, studying math, just helps you develop those problem-solving skills that you can then apply to absolutely every aspect of your life.

What can math teach us?
Problem solving, 100%. One of my favorite studies that I’ve come across in the last 7 or 8 years as a teacher is about a group of statistics students at a university in the United States who were followed for about 10 years. [The study] found that the students who studied more math and did better on their math exams overall made better decisions in life. Now obviously it depends on your definition of better. You know, they exercised more. They’re much less likely to smoke. They’re much more likely to practice safe sex. That’s their definition of better decisions. They would make better financial decisions. But I feel like there’s an important message there, because by studying math, by understanding math, what it does is it teaches you how to solve problems. So if you really understand how to solve a problem, you’re more likely to make better decisions because when you’re trying to make a decision, you’re more likely to understand the risks.

Even think about the pros versus cons of a given decision. It’s a very analytical, logical approach. It’s like I have this situation, this decision that I have to make. There’s nothing wrong with that, but a lot of people would just act impulsively, based on emotions. Math can teach you to take a step back, to think about things very logically and think about pros and cons, advantages, disadvantages. What is the right decision for me to make in this situation? And that doesn’t mean that you only make good decisions. I’m a prime example of that. But you know, we all make questionable decisions. It’s part of being human. But I think that’s a very real, practical skill that you learn as a mathematician. And that’s why I like the study so much, because it actually shows with evidence with this group of students that over a period of 10 years, they made better decisions overall. So to me, that’s a huge, very practical application of what math can teach you.

Why is it important to talk about science?
I think that as scientists, the things that we’re studying and trying to understand now are so advanced and so abstract that it’s really hard for a member of the general public to follow what a professor or a scientist is doing right now. And now scientists are doing amazing things and they’re very good at communicating with other scientists. That’s what I do. Then those scientists work together and go further and further down the path of discovery. What we as scientists in general are not great at is telling everyone else what we’re doing. I think in the past it might have been a little easier to do because what we were doing was closer to reality and closer to people’s everyday lives. Now it seems so far away that there’s a gap. So, events like this, talking about science, bringing scientists together to explain to the public, that’s what I do, and I’ll do my best to help you understand what I do, even though it’s a little crazy, you know, black holes, other dimensions, million-dollar math problems, whatever. But we’re going to do our best to help everyone else at least have a sense of what’s going on in science and why it’s exciting. You know, the students here could potentially be doing these kinds of things in the future. So I think it’s really important to me to talk about science, because as a scientist you have to tell people what you’re doing. You have to make sure that everyone else is aware of the great things that you’re doing, they want to hear about it. But it’s a skill to be able to do that.

Why did you decide to participate in the Ratio Forum?
I’ve been here [Bulgaria] once before and I really enjoyed the trip, so I was really excited to come back. This is my first time at this event, and there are hundreds of people here who are really excited to learn a little bit of math. So for me, this is really exciting. I’d love to talk to anyone about my topic. I just get excited and enthusiastic when I talk about my topic. And so, I think again, not by design, but by accident, I’m pretty good at getting other people excited and interested in the topic, because, as my students would say, my enthusiasm is contagious. When they see me get excited about a problem, they get excited because I’m excited, and then all of a sudden everyone’s like, “Oh, let’s do some math problems!” I think for some reason, that’s just how I am when I talk about math, and being able to do that in front of people, hopefully, will help change their minds. As you said, there’s a very common perception about math that some people decide very early on that it’s not their thing. And what I’m trying to say is that it doesn’t have to be your life. You don’t have to become me. But I hope to get them to think even a little bit, “Okay, maybe I should give it a second chance. Maybe I should be less sure that I don’t like math. Maybe I’ll just try again and look at it in a more fun and playful way, in a way that makes sense to me through my hobbies. And maybe I’ll enjoy it if I try it again.”

What’s next in Maths?
I had a really interesting conversation a few months ago with a mathematician named Martin Hairer. He’s a Fields Medalist, a very big, prestigious award. He’s a really cool guy, and he actually said that he happens to be working on one of the millennium problems right now. So when you have a mathematician of that caliber trying to solve one of these problems, it really excites me, because I think if anyone can do it, it’s probably him. He and his team of researchers are trying to really solve the Yang-Mills problem. So I think in terms of what’s next, I hope in the next 5 to 10 years the Yang-Mills problem is solved. That would be huge for mathematics. It would be huge for the millennium problems, and I think it could potentially have really interesting applications and implications for society, because it’s all tied to quantum theory and the way we understand the universe.

*Fields Medal or Fields Medal/ Fields Medal is an award given every 4 years by the International Mathematical Union to mathematicians under the age of 40 for outstanding achievements in mathematics, in accordance with the will of Canadian mathematician John Fields (1863–1932). As president of the 7th International Congress of Mathematical Scientists in Toronto in 1924, Fields proposed that at each subsequent congress two mathematicians under the age of 40 be awarded a gold medal in recognition of their outstanding achievements. The award began after Fields’ death in 1936. It is widely believed that the Abel Prize and the Fields Medal are substitutes for the Nobel Prizes, which do not have a category for mathematics, and the most significant awards that a mathematician can receive. The award consists of a gold medal and a cash prize of 15,000 Canadian dollars, which is divided between two, three or four scientists.