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On 2 April, VUB will award seven honorary doctorates with the theme Figures that Matter. Among them are Karine Chemla, Freddy Van Oystaeyen and Padmanabhan Seshaiyer. While they each approach maths from very different angles, they all share a love for their profession. Here they reflect on the challenges that maths and science face today, as well as on the inherent beauty of mathematics.
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Maths, a childhood love
Karine Chemla comes from a family of mathematicians, and in her 20s she went to Beijing to do her PhD. “It was in 1981, not long after the cultural revolution, and I was the first foreign student at the institute for natural sciences in Beijing,” she recalls. She studied the history of maths in China and was assigned five professors. As these professors spoke only Chinese and Russian, she learned Chinese as she went along. “My research, which began as a short-term examination of a subject that interested me, eventually became my life’s work,” she says.
Unlike Chemla, professor Freddy Van Oystaeyen was the first person in his family to go to university. “My father was a dockworker and he always said ‘I’m a docker and you’re a doctor’,” says Van Oystaeyen with a laugh. He discovered his love for maths when as a 10-year-old he spent a whole summer playing a game with plastic cyclists. By throwing a dice, he could advance the cyclists in the peloton.
“What interested me was that, in theory, all the cyclists had an equal chance of winning, because they all had an equal chance of throwing a six,” he says. “I thought therefore that they would come together in the end. To test my theory, I set up all the cyclists around our table. My mother wasn’t allowed to tidy them away for months, and the peloton just kept getting longer. Later I thought about that a lot and realised that they wouldn’t actually meet at an infinite point because the distance would also be infinitely long if you kept rolling the dice.” [Continue story below the picture]
At that point, Van Oystaeyen thought he would become an engineer, the highest profession his father could imagine. Until, that is, at the age of 13 he handed in a piece of work to his maths teacher in which he appeared to have discovered something new. “The teacher had never seen what I’d written before and suggested that I go on to study maths. Before that, I hadn’t known it was an option, but from that moment I was determined to study maths.” He went on to become a key figure in Flemish maths research over the past 50 years, as the originator of non-commutative geometry.
Padmanabhan Seshaiyer also discovered his passion for maths as a boy. He grew up in India and today lives in the US, where he moved in 1994 as student. While Seshaiyer was bitten by the maths bug at a young age, he felt something was missing in his training. “The education system in India was excellent and I was very good at theoretical maths, but I longed to put those theories into practice,” he says. He dreamed of using maths to solve problems in the real world, but there were very few opportunities to do so.
The reputation problem of science and maths
While our three honorary doctors fell in love with maths as children, maths and the exact sciences seem to be struggling with a reputation problem these days. “The 1960s, when I was a student, was a golden age for pure maths,” says Van Oystaeyen. “There was great respect for maths and sciences in general, but today there’s a bit of a crisis for these subjects.” He believes this is in part because there is so much ‘fake news’ in circulation, and in part because science itself can appear corrupt.
“In the applied sciences, many studies aren’t reproduceable. Errors in studies don’t always happen by design, but research results are sometimes manipulated because there’s a pressure to publish,” he says. Statisticians use a tool called a p-value. The lower the p-value, the smaller the chance that the relationship a study demonstrates is based on chance. If the p-value is too high, it’s very likely the relationship is coincidental. So studies with a high p-value are considered irrelevant. “But as people’s careers depend these days on how often they are published, they want to get their research published at any cost,” says Van Oystaeyen.
Another reason for the unpopularity of maths, he believes, is that the field is too vertically orientated. “Out of one definition or quality, the next one comes. It’s like a tower that you keep adding layer upon layer to. Each layer is the basis for the next one. If people don’t understand something, they are stuck at the bottom of the tower. There’s a gap in their basic knowledge and so they can’t understand the next level.”
For Chemla, the fact that maths has been used as a selection criterion is another cause of its reputation problem. “Maths was used to give people a particular rank, and this elitist approach means lots of people see the subject in a negative light,” she says. She also believes more pupils would be interested in the subject if it was presented in a broader historical and philosophical context. “Pupils learn how to carry out mathematical operations, but reflection on maths isn’t part of the curriculum. Why is it an interesting concept? Why did we start using this method and not another? Reflecting on the philosophical and historical aspects would give the subject a more human dimension and make it more interesting for pupils and students.” [Continue the story below the picture]
Not consumers of education, but producers of information
Seshaiyer’s experiences with the traditional education system inspired him to develop another vision of education. Today he is one of the biggest champions of Stem education (Science, Technology, Engineering and Maths), a plan that aims to put more emphasis on these subjects in schools around the world, to prepare young people for careers related to technology, science and maths. In recent years, new acronyms have emerged: people now talk of Steam, with the A from Arts, and Stream, with the R of Reading and wRiting.
“Stream is an integrated way of solving problems,” says Seshaiyer. “I use maths to connect all these fields. The addition of art is useful for gaining practical experience of how mathematics works. Art and reading play a part in the development of skills such as critical thinking and creativity, which are important if you want to solve a problem. Stream encourages cooperation across subject borders, and helps us to reach innovative solutions for a number of the greatest challenges we face today.”
Rather than imposing a curriculum on students from above, Seshaiyer works the other way round and begins with students’ own interests. They carry out projects inspired by the UN’s Sustainable Development Goals. “It’s important that we personalise education, so I let the students submit a problem that interests them and then we go in search of a solution. There was one student, for example, who wanted to find a way to map gang violence in Puerto Rico.”
To do this, they applied the mathematical model that was used to model the spread of the Zika virus. “Zika is unique in that it can be transmitted via both mosquitoes and sexual contact. That transmission is very similar in a sense to gang violence: the gangs are an infectious disease, the adult gangster is the mosquito and the people around you who want to recruit you are like sexual transferability. So we’re using an existing model and applying it to solve other social problems. We need to stop seeing students as consumers of education; they are also producers of information.”
But the idea that people are not just consumers of prepared information is not a new one. It was considered way back in ancient China, as Chemla discovered in her historical research in which she studied mathematical documents from the third century BC. “Most historians assumed that the mathematical texts from that time were simply instructions, which readers followed exactly without thinking for themselves. They thought the users of these texts were stupid, but that’s not the case.”
While most researchers only look at the mathematical operations themselves when analysing this sort of text, Chemla studied the formulation of the text itself. “Many texts explain how to calculate things, for example, ‘reduce to the common denominator’. So the people who used these texts understood what they were doing. That’s fundamental, because it shows that the assumptions about mathematicians from the past were totally wrong.”
The beauty of human creativity and intuition
Letting people think for themselves, letting students explore a problem they’ve chosen themselves, setting maths in a historical and philosophical context… this can all help to make the subject more attractive. But there is also a more elusive aspect to a love for the subject: the beauty of maths. [Continue the story below the picture]
For Seshaiyer, the link between art and maths is a pragmatic one. The A in Stream, for him, represents the translation of mathematical concepts into images that help make the subject more accessible: children learning to multiply through drawing, for example, or using the image of a head of broccoli to explain fractals. But for Chemla and Van Oystaeyen, maths in itself is aesthetic, an art form. Hungarian mathematician Paul Erdős is known for his quote that the beauty of maths cannot be explained: “Asking why numbers are beautiful is like asking why Beethoven’s ninth symphony is beautiful. If you don’t know why, nobody can explain it to you.” Van Oystaeyen agrees, to a certain extent. “You have to understand maths to see its beauty,” he says.
This beauty is primarily in the solution, says Chemla: “If you look at how people have tried to solve mathematical problems, and the unbelievable, unexpected concepts that they’ve discovered, you can’t help but see beauty in that human creativity.” Van Oystaeyen adds: “You have to solve problem A in a particular mathematical context, but in that context you can’t solve it. So, based on your intuition, you have to develop a theory that comes from an entirely different area. Then you come back and solve problem A. That’s the thing mathematicians find the most beautiful: you come back to problem A, having not known you could solve it that way.”
Finding a solution therefore requires tremendous creativity. “Mathematical concepts are linked via an invisible network,” says Van Oystaeyen. “Discover that network and you discover the beauty of maths. What you do is fixed, but there are different ways you can do it.” And intuition plays a major role, he says. “What we consciously think is just a small part of our thinking. Consciousness has many layers. I experienced this once, when a PhD student of mine had a problem he couldn’t solve. After work, I went home and thought no more about it. When I got up the next day, I saw straight away the evidence he needed, right before my eyes. I must have been thinking about it unconsciously as I slept and worked it out. For me, it proves that the invisible network that connects all mathematical structures really exists.”
The problematic business model
For outsiders, the beauty of maths is difficult to grasp and the subject is something rather abstract. But today, there is not enough attention paid to pure, abstract maths, as the focus is on maths that is directly applicable. “It’s about money,” says Van Oystaeyen. “According to the capitalist mindset, something’s value is in its financial yield. It’s much more difficult today than it used to be to get external funding for pure maths. Money goes towards maths that has a direct application for industry or, worse, can be used for military purposes. Only the Research Foundation (FWO) gives money to fundamental mathematical research, but even that is significantly reduced these days.”
That carries a risk, because most of the applied maths we know today was once abstract, Van Oystaeyen says. “Just think of topoisomerase, a process in which DNA splits and bonds with itself, which was discovered through applying button theory, a part of maths that in the past was often seen as abstract nonsense. Medical imaging too is almost always based on pure maths.”
Seshaiyer experienced this, when he helped develop a model to determine whether a stroke patient should be operated on or not. “I could never have dreamed that maths could be so powerful,” he says. He also finds it troubling that science and maths are too often judged in an economic light. “You see it in Stem education too. People see Stem as a way of creating economic diversity and products, but really what’s important is that people work together across subjects and curricula to tackle the great challenges we face as a society.”
- Karine Chemla: Karine Chemla is a historian of maths and sinology. As a young PhD student she went to China to study the history of maths in the country, and today she is research director of the National Centre for Scientific Research in France.
- Padmanabhan Seshaiyer: After his scientific training in India, Padmanabhan Seshaiyer moved to the US to continue his studies in 1994. He is a professor at George Mason University in Virginia and is a strong advocate of Stem education in schools around the world.
- Freddy Van Oystaeyen: Freddy Van Oystaeyen is a mathematician and emeritus professor of maths at the University of Antwerp. Through his discovery of non-commutative geometry, he became one of the key figures of mathematical research in Flanders of the past 50 years.