My academic autobiography

“His life, for all its waywardness, had a certain anachronistic consistency, reminiscent of that of the aristocratic rebels of the early nineteenth century. His principles were curious, but, such as they were, they governed his actions.” (Bertrand Russell, Auto-obituary, in The Last Survivor of a Dead Epoch, 1937)

I always knew I wanted to study mathematics and I followed a full-time mathematical course load from my first day to my last back home at Stockholm University. But I also craved more. I had a broad intellectual appetite. So in addition to my mathematics courses I took art history, philosophy, and so on. My first semester I took an evening course on the history of classical music. The lecturer would weave a grand narrative and ever so often sit down at the piano and play some select bars to illustrate a point. This remained with me as an image of how I longed to experience mathematics: the technical masterpieces and their broader context each heightening the appreciation for the other.

My mathematical courses, meanwhile, were plain-vanilla technical courses. I could do the exercises and pass the exams easily enough, but I was frustrated that bigger why-questions were not being addressed. I could play the formal game of definitions and proofs, but I wanted to know why anyone would want to define, say, principal and maximal ideals in the first place, and what the purpose of these theorems about them was supposed to be. So I went to the library to find out. And that is what brought me to the history of mathematics, for it was only there that I could find the answers to my why-questions. It was only by studying the history of the subject that I realised, for instance, that all the abstract gobbledygook about rings and ideals that I was being fed in my courses was really just number theory with all the interesting applications left out. Thus my interest in the history of mathematics was always a means to an end; it was always subordinated to teaching and mathematical understanding. And, fundamentally, it still is. In this way the problem of teaching has remained the root of all my scholarly work ever since.

It was no accident, of course, that I found the answers I was looking for in the history books. Mathematicians do not make up arbitrary definitions and start proving theorems about them aimlessly. They work on interesting and natural problems, and introduce new concepts only when they serve a credible purpose in this pursuit. That is how history works, and I think a good argument can be made that it is how teaching should work also. This is why, to my mind, mathematics and its history—and thus in my case teaching and research—form an organic whole.

It was in this mindset that I finished up my masters degree, so naturally I was more excited about teaching than going on to do a Ph.D. right away. I got a two-year position teaching at Marlboro College in Vermont, which was a lovely experience. I had long perceived my affinity with the liberal arts ideal, and I at once felt at home in this environment. With these people I debated Kant in the dining hall, traced conics in the snow, cast horoscopes according to ancient principles, and, most of all, taught mathematics in a thinking rather than robotic fashion. The small class sizes and absence of centrally fixed curricula gave me ample opportunity to translate my long-held ideals into teaching practice. From this moment, if not sooner, I knew that this was a passion I wanted to make a career of.

But first I had to get my Ph.D., of course, and I was still more excited about understanding mathematics historically and contextually than about joining the frontiers of research. So I went to the LSE in London to do a second masters degree in philosophy and history of science. This afforded me the opportunity to study in their own right the kinds of big-picture questions that had kept cropping up in my mind as a reflective mathematics student. My view of mathematics was greatly enriched by these perspectives, but doing such a Ph.D. would have taken me too far from home. I was now a full-fledged humanist who could speak to philosophers and historians like a native, but in my heart I was still a mathematician.

So I went back to the root, the problem of teaching that had started it all. I enrolled in a Ph.D. program in educational mathematics at the University of Northern Colorado. My two years spent there made me a native in the world of mathematics education research as well. I studied what research has shown about learning and cognition, I was inducted into social science research methodology, and I saw reform teaching of all kinds in action at the hands of its most enthusiastic advocates. This was all very valuable, and I was always prepared to devote my life to mathematics education. But ultimately I felt that the current paradigm of mathematics education research was too intellectually restrictive for my tastes. So I left.

From there I went to my current position at Utrecht University, where I completed my Ph.D. in the history of mathematics. This has been the perfect Ph.D. for me. It has brought together all the themes that drove me during my searching years. It has allowed me to be an intellectual and a philosopher, a humanist and a reader of books, while remaining with both feet on solid mathematical ground. My path may not always have seemed the most direct but in retrospect its logic is clear: in writing my thesis on the history of the calculus I have gone full circle back to my early university days and made it my daily bread to explore precisely that elusive richness that I always felt was hiding behind the austere façade of the modern mathematical curriculum.