How should we understand mathematics? Take numbers. Are numbers real things, about which we discover, that 1 + 1 = 2? Or are numbers things that we made up, as part of a story that 1 + 1 = 2? In other words, is mathematics like physics, or is it more like writing fiction? In answering these questions, philosophers often talk about how we can learn mathematics. What do we have to do to get to know something about mathematics? That's different if numbers are real, or things we made up.

Philosophers have disagreed about these questions for thousands of years. Even now there are many the nature of mathematics, and how we learn mathematics. In his dissertation, Stefan Buijsman has surveyed these theories, and argues that none of them describe the practices of ordinary people’s mathematics. For example, one theory says that we can only know that 1 +1 = 2 if we have a proof. But most people don't have a mathematical proof that 1 + 1 = 2, and couldn't give one if we asked.

“All of these theories are made with professional mathematicians in mind. That's a problem for philosophy. Right now, we have no idea what people are doing when they're taking a mathematics class in high school or calculating how much change they need in a store”, says Stefan Buijsman, Ph.D in philosophy at Stockholm University. “I don't have an answer yet, but psychology and pedagogy can help us. They give us an idea of what abilities people can use when they’re doing simple mathematics. We then know what ingredients we can use when making new theories”

At 20 years of age, Stefan Buijsman is probably the youngest in Sweden ever to complete a Ph.D. He is from The Netherlands and at the time of the dissertation exactly, on the day, as old as the current holder of the Dutch record. Stefan Buijsman finished high school at 15, and got a master’s degree in philosophy at 18.

“The main reason why I finished my PhD in 1,5 years is the supervision at Stockholm University. I tend to work faster than most people, no idea why. If my supervisors hadn’t spent a lot of time helping me, it would have taken much longer. People nowadays just assume that I’m older. There’s generally a brief shock when they find out how old I am, but apart from that, socially and at work it’s not really that different.”

## About the research

“Philosophy of Mathematics for the Masses – Extending the scope of the philosophy of mathematics”