On a sunny day, the benches are dragged out of the loft of the study association and people spend the afternoon in the sun thinking about mathematical problems and, towards the end of the evening, having increasingly heated discussions with fellow students. Though it would be fun to have this conversation outside on one of those benches, that can’t happen because of the tightened Coronavirus measures. Luckily, mathematician Guus Regts and Maths student Chinook Felix can paint a vivid picture.
Text: Edda Heinsman.
The meeting is being conducted over Skype and there are some online problems, so Guus Regts can be heard but not seen. He’s sporting enough to tell us he’s sitting in his bedroom. He normally works in the living room, but the cleaner’s in there at the moment. Chinook Felix is sitting in her student accommodation. She’s recently made a few small changes to make it a nicer place to work. There are two guitars in the background, but we shouldn’t ask for a guitar solo. ‘I only play at an amateur level’, she laughs.
Graphs and networks
Ask Regts about his research in discrete mathematics and he starts talking about graphs and networks. In an attempt to simplify it, he describes the travelling salesman problem: what’s the shortest possible route that covers a list of cities? After several attempts to explain exactly what he’s working on, he admits that it’s ‘still quite difficult to explain’. His research has interfaces with physics and theoretical computer science. Maybe the problems he’s working on in those areas are more tangible? ‘We’re currently trying to mathematically substantiate questions from statistical mechanics, which to a large extent have been solved at a physics level. These are relatively old questions that we’re trying to dust off and solve.’
And what does ‘theoretical computer science’ mean? ‘Theoretically, once we’ve proven that an algorithm works, there’s no need for us to see if it works for real.’ So you spend a long time puzzling over a problem, and you find a solution, but you don’t want to see how it turns out in practice? Both mathematicians laugh. Regts says, ‘I can only do so many things in a day. We’ve proven it works. I don’t need to see it in action.’ Felix adds, ‘You’ve already proven it!’ But they admit it might be a bit odd to say so. ‘It’s how a mathematician looks at it’, explains Regts. ‘It’s all about the puzzle. You get addicted to finding a solution.’ Felix recognises that. ‘Sometimes you spend all day working on proof. Sometimes that can be very frustrating, but most of the time it’s great, you can really sink your teeth into something. And you feel really clever when it suddenly works out.’
Regts and Felix are clearly enthusiastic about their research and study. ‘When I tell people I’m a mathematician, they often say, “I never understood maths”‘, says Regts. “I’m sorry to hear that, but maths isn’t easy to learn. It’s like learning to read music; you’ve got to embed the basics in your brain. You start with the first note, then the second, and you keep repeating them. Slowly, it starts to get smoother. At a certain point, patterns emerge and you can make your own music. You can see the pennies dropping and students start to really think about problems. It’s great when you see that happen.’
Perhaps the intangibility of mathematics is what puts people off. For example, does Felix know what she wants to do after she graduates? ‘Anything but teaching!’ she says. ‘During one course, I had to give a number of lessons. When I wasn’t having a good day myself, I found it very difficult to keep the students in line.’ Regts, on the other hand, is very enthusiastic about teaching. ‘I was involved in setting up a new course on discrete mathematics. I crammed in as much of the things I find fun as possible. I like being able to improvise during lectures. I hope to make the students as enthusiastic about this discipline as possible.’
Regts says that, in his enthusiasm, he might sometimes go too fast and leave some students behind. Chinook says it’s probably not that bad: an enthusiastic teacher can make or break a subject. And that brings us to the biggest drawback for Regts at the moment: lectures are online. ‘When you go online, you’re switching from 3D to 2D, so the quality of your contact decreases. I don’t know if the students are always following what I’m saying. I can’t see their faces.’
Felix finds it very difficult, not being able to meet up in person. ‘We normally work together a lot. It’s a lot more complicated online.’ She points to a small blackboard in a corner of her work space and says she prefers working on it. That’s why she likes the study spaces so much, in normal times. There are whiteboards on all the walls. ‘Every now and then you have a maths problem that really lends itself to visualisation.’ Then she and a couple of fellow students immerse themselves in their own space and write all over the walls. ‘It must look strange to other students’, she says, thinking about it.
Regts also prefers to use a blackboard. ‘In that sense, nothing much has changed in the last twenty years. A mathematician still only needs a piece of paper and a pen, or a blackboard and a piece of chalk.’ What about the exponential rise of faster computers? ‘Yes, that’s great, but even a computer that’s twice as fast doesn’t help me find a solution any faster in my research. Half of a lot is still a lot’, laughs Regts. ‘So I’m looking for better algorithms to find solutions faster.’
In terms of how he works – with paper and pen – much has remained the same. But a lot has changed in education. As Regts says, there’s now a greater focus on presentation. ‘Ugh’, says Felix. ‘I hate that.’ But she does admit that it’s important. ‘Mathematicians aren’t known for their brilliant public speaking skills. It’s nice to be able to practise in a safe environment, with an audience of fellow students’, says Regts. ‘It’s paying off.’
Many of the courses Felix is taking now are basically the same as when Regts took them, and were the same for many years before that. Nevertheless, Regts says there are definitely developments in the field that are finding their way into the lecture room. ‘Consider quantum computing or machine learning; if you look under the bonnet, they’re powered by rock-solid mathematics. There’s a lot going on in network theory, too.’ ‘There’s still plenty of problems to solve’, Felix adds. ‘Maths doesn’t stand still. It’s never finished.’
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