It was while reading philosophy in Leiden that Stefan Buijsman’s eyes were really opened to how much fun mathematics could be. He applied to Stockholm University, and is very happy with the supervision he had there as a doctoral student.

Record-breakingly young PhD studies how children learn mathematics

Svenska 2020-11-03

Stefan Buijsman has always thought faster than others, and received a doctorate in philosophy of mathematics at only 20 years of age. He is now considering subjects from what mathematics actually is, to how children learn mathematics, and what artificial intelligence entails for us all.

Stefan Buijsman, from the Netherlands, is excited by major philosophical issues, and doing research suits him perfectly. He is doing research at the Institute for Futures Studies in Stockholm and has a PhD focusing on philosophy of mathematics, which means that he is investigating mathematics from a philosophical perspective.

Stefan Buijsman’s current research project is funded by the Swedish Research Council and is about how children learn mathematics. The project compares and links together the research available in two disciplines, philosophy and psychology, on how children learn mathematics.

“There are many philosophical theories of how children learn mathematics, but philosophers have rarely talked to psychology researchers about this. In psychology, there is important knowledge on how the brain works, and exciting empirical experiments that show what happens in practice when children learn mathematics. I want to develop the theories in philosophy of mathematics based on this knowledge,” says Stefan Buijsman.

He is currently working from his home country, the Netherlands, as the corona pandemic has caused plans to change.

“I was planning to spend one of the three project years as a guest researcher at the University of Leiden, but the pandemic has meant that I will be staying for longer,” says Stefan Buijsman, who is now working from home in his flat in The Hague. He is accompanied by his girlfriend, who is sitting in the room next door studying history of art.

Do we have an inherent sense of numbers?

In one part of the research project, Stefan Buijsman follows psychologists who investigate how the brain handles amounts, for example when comparing the number of sheets of paper in two piles. People can determine whether one of the piles contains more sheets of paper than the other one, without actively counting them.

“There is debate whether the brain counts them on the quiet, but I believe that the brain uses other information, such as how tall the piles appear to be, how closely packed the sheets are, and so on. It is a clever process, but it has nothing to do with numbers.”

Stefan Buijsman hopes that his research will lead to better ways of teaching children mathematics.

“Some researchers think that children have an inherent sense of numbers, but I do not. A child can point to cakes and count “one, two, three”, but when you ask the child to fetch three cakes, they will fetch any number, entirely at random. I think you have to start by teaching children what numbers symbolise, and how they are structured.”

The language a child speaks has been shown to influence how quickly they learn mathematics, Stefan Buijsman tells us. Some languages give children a better picture than others of how numbers relate to each other.

“In Chinese, for example, the number eleven is called ‘ten-one’. Chinese children learn to count earlier than children with languages such as English, which uses expressions like ‘eleven’. English-speaking children might therefore need help to understand the structure.”

Was inquisitive as a child

Stefan Buijsman was born in 1995 and grew up in Leiden in the Netherlands. His father was a computer engineer and his mother a housewife with her hands full. Stefan Buijsman and his three younger siblings needed a lot of stimulation.

“When I was two-three years old, I wanted to visit a museum every week, and I could be difficult if I was not allowed to. I was very inquisitive and keen to learn about things.”

In the Netherlands, children start school at the age of four, and Stefan Buijsman had great expectations of all the interesting things he would learn. He was already able to read and write.

“I was really disappointed when I started school, and it was quickly decided that I could skip the first school year.”

He was later allowed to skip more years, and completed the first eight school years in five calendar years, but despite this he was constantly bored.

“I had good friends, and I went to school every day, but I was rather unhappy and never felt challenged.” During most of upper secondary school, I did nothing in lessons, and did not get particularly good grades. In mathematics, I barely scraped a pass.”

To university aged 15

When Stefan Buijsman was 15, he started reading computer science at Leiden University, and gradually understood what mathematics could be used for. However, mathematics did not become really fun until he took a couple of courses in philosophy to broaden his outlook.

“Then I had to consider the larger questions, such as why mathematics works and how it works, the real ideas behind it.”

Stefan Buijsman switched from computer science to philosophy, and finished his master’s degree in philosophy at Leiden University in 2014. He then wanted to continue on the route he had taken, but found no opportunity to do a doctor’s degree in the philosophy of mathematics in the Netherlands.

“Sweden invests much more in research, and there were opportunities there. I applied to Stockholm University, as philosophy research is really good and active there. The two professors I hoped to have as supervisors also worked there.”

Could work at his own speed

The professors, Peter Pagin and Dag Westerståhl, agreed to supervise Stefan Buijsman, and he is grateful for all the work they did.

“For the first time in my life, I didn’t have to adapt to slower class mates, and could work at my own speed, which was very stimulating and fun!”

When his thesis was completed in 2015, Stefan Buijsman was only 20 years old. He was thereby the youngest person to be awarded a doctorate in modern-day Sweden. He does not really know himself what it is that makes him so fast.

“I read at the same speed as others, but I think I am faster at creating an overview of the knowledge available. I can see more rapidly what is missing, how things can be compared, and how they hang together.”

Pluses and Minuses

Besides his research, Stefan Buijsman writes popular science books. His book Pluses and Minuses (Swedish: Siffrorna i våra liv) shows how mathematics is present everywhere in everyday life.

“I want to explain why mathematics is important, and how mathematics affect us all. I also wanted to remove the mystique surrounding mathematics, show that what lies behind a complicated formula can be easy to understand.”

What Stefan Buijsman would really like to do is to create interest in children and youngsters who do not like mathematics, but he realises that it might be difficult to make them read the book. He is therefore happy if it is ready by teachers and parents, who can then pass on the ideas.

One amusing example he gives is how easily you can be tricked by statistics – it is possible to show a high correlation between the number of films featuring the actor Nicholas Cage, and the number of persons who drown in swimming pools!

“I want people to have a critical attitude, and to know what they should take notice of when interpreting figures. Mathematics is just a tool. It can be used in the right way, or the wrong way.”

Wants to research artificial intelligence

His latest book is about artificial intelligence, and in the future he would really like to research AI.

“There are many important philosophical issues relating to artificial intelligence. With self-teaching algorithms, no-one knows why a computer ends up with a certain answer. The process is so complex that it cannot be grasped.”

He tells us about the time when Amazon allowed a self-teaching algorithm to propose which persons the company should employ. It turned out that the program only recommended men.

“The algorithm had drawn the conclusion that men were better than women, because Amazon had previously employed more men than women. They could not get round the problem, so Amazon had to go back to using humans to make the selection.”

Positive towards Swedish research support

One of the questions Stefan Buijsman would like to investigate is how artificial intelligence worked during the coronavirus pandemic. For example, a major internet retailer had problems in April, when buying patterns changed from one week to the next. Suddenly, products such as face masks and alcogel were top sellers.

“This was a new situation for the programs that managed the retailer’s warehouse. The programs started making mistakes, and didn’t order enough products to restock the warehouse.”

Stefan Buijsman is glad that he has had the chance to have a taste of AI also in his current research project. Overall, he is positive towards Swedish research support.

“In the Netherlands, there is little funding, researchers are forced to criticise their colleagues to increase their own chances of getting certain grants, and knowing the right persons can be crucial. In Sweden, the process for getting research support is both simpler and better.”

Text: Eva Annell
Photo: Merlijn Doomernik