Bodil Branner is one of the founding members of EWM. Her interview, by Poul G. Hjorth, was published in the Newsletter of the European Mathematical Society No. 84, June 2012. We thank the editors for the permission to post it in EWM website.
Q - When and how did you become interested in mathematics?
A - This is not easy to answer because I think I have really always been, but perhaps without being conscious about it. My father would often play number games with me. He was so important to me and was a great support for me. Actually, upon entering high school I had to make a choice about a science curriculum or a more classics-and-languages curriculum and I was much in doubt. My Latin teacher at the time was very inspiring. Finally, I chose mathematics. Many in my family were academics but none in the exact sciences. I soon found out that I had a flair for maths and physics. My physics teacher in particular was very inspiring. In the second year, there was an arrangement at the city hall, where representatives of tertiary education were present and you could ask them questions. I had booked time for speaking with a theologian, a librarian and a mathematician. The mathematician was Professor Svend Bundgaard. I spoke with him for nearly an hour. When I left, there was no doubt left in my mind: I had to go into mathematics. And I have never regretted that decision. My mother disapproved somewhat. My father was very supportive.
Q - So you entered the University of Aarhus majoring in mathematics. Were there any subjects or teachers in particular that caught your attention?
A - I was immediately faced with another decision. It was possible to major in mathematics only or to major in mathematics combined with another science topic. Bundgaard was to play a decisive role in my education. Bundgaard lectured in analysis; I asked him and he told me to combine maths with physics so I would get a broad view of science. He was such an authoritative but also charismatic figure at the institute in those years. So I followed both mathematics and physics courses. I remember in particular quantum mechanics, which was incredibly interesting. In the long run, though, mathematics won out. Those years were years of rapid growth, energy and internationalization for the new mathematics department. Algebraic topology was a strong subject and I did my thesis with Leif Kristensen. Master’s students had their own environment on the top floor with shared offices. We had a good and productive working situation. After I graduated, I stayed with the department as a teaching assistant for two years. At the time I had married Sven and we already had two children. It was in the late 1960s.
Q - What was the employment situation, particularly with respect to female mathematicians, when you got your first university employment?
A - At the time, there was no PhD in the Danish system. For that, one would have to go abroad. Many of my friends and colleagues did that, and Sven and I planned to go to the U.S. But rather suddenly, Sven, who is a chemist, decided to seek employment in industry, in Copenhagen. We needed to move to Copenhagen. I consequently had to find some sort of employment in Copenhagen. I considered becoming a high school teacher but the high schools (gymnasiums) would not even talk to me because I had not taken a teaching competency exam. Bundgaard, however, intervened. He had found out that there was a vacancy at the mathematics department at the Technical University (now DTU) in Lyngby, near Copenhagen. He made the introductions for me and recommended me so enthusiastically that they called me and asked me to apply - which I did, and got the job as amanuensis, a sort of professor’s assistant (not to be interpreted as assistant professor!). This was August 1969. I worked for Professor Fabricius-Bjerre, who was a kind and thoughtful employer.
There was among the faculty at the time a range of attitudes towards what the professor’s assistants should do. Some regarded assistants as simply graders. Fabricius-Bjerre, fortunately for me, strongly encouraged us to continue our research. Along with teaching, of course. It was enlightening for me to teach, for instance, classes in differential geometry; in addition to the formal and very abstract differential geometry that I knew, here was also the geometry of the engineers, with details of curve geometry, curvature and torsion, kinematical relations and so forth. My own research, as a consequence, turned a bit from algebraic topology towards differential geometry.
What came as a real surprise to me was the attitude towards women as staff that some of the senior faculty members had. I had come from a department in Aarhus with a pioneering spirit and a very informal and collegial atmosphere. At the Technical University, the tone was much more formal and conservative. It was a very male environment. Not till some time into the 1970s was the old system of the ‘Professor dictatorship’ abolished. About this time, I got tenure.
Q - Where and when did your interest for holomorphic dynamical systems arise?
A - In the late 1970s, I was supervisor for a Master’s student who wanted to write about new developments in geometry and dynamical systems. Talking to Peter Leth Christiansen about the subject, I was pointed to very recent work of Robert May, and others, about iterative systems, period doubling and these things, just emerging at the time. I read some of the papers. There was a remark in one about how it ‘would be interesting’ to look at cubic polynomials. I decided to give that a try. At the time, computers were punch-card fed! We found some structures, a cusp catastrophe. The student graduated. I read more. I wrote a paper about some special cases of cubic polynomials, the associated kneading sequences. I started going to conferences about iterative systems. The first person to show me a picture (crude at the time, in the early 1980s) was Predrag Cvitanovic, then at the Niels Bohr Institute. In June 1983, Cvitanovic organised an international conference on the new science of chaos. The conference was attended by physicists, biologists, chemists and some mathematicians. Among them were Adrian Douady and John Hubbard. I was in a bit of a hurry because I was also going to “Dynamic Days” in Twente, Holland. I organised Douady to give a lecture at my department. We had discussions. They asked what I was doing and when I told them: cubic real polynomials, they immediately pointed out that this made much more sense to study in the complex plane.
My background in holomorphic functions was limited but I was convinced that this would be a fruitful direction. Looking back at those days, I feel lucky and privileged to have been at the right place, with the right questions, and then on top of this have people who encouraged me and believed in me. I said to Hubbard, I have heard that you have generalised the concept of kneading sequences to the complex domain - can you explain to me how this is done? And he did. He explained about what is now called the ‘Hubbard-tree’. Then he said: now it is your turn to work the same thing out in another example. To this day I wonder how I managed to do it, but I did. He was suitably impressed. Douady and Hubbard suggested that after Twente, I should come to Paris and we could collaborate on this. In addition to this, they suggested that I attend an upcoming Summer School where Thurston was to lecture and that I should then visit Cornell University. I did, and we managed to formulate and convince ourselves of a new theorem in just a week. We uncovered the classical Cantor set in the parameter space for cubic polynomials.
Q - Eventually, you spent a year at Cornell?
A - Hubbard invited me to spend a year as visiting professor, September 1984-September 1985. This I had to negotiate with my family and the department at DTU. My children were hesitant; in the end, we managed to all go. Sven’s company negotiated with him and he found a position as a visiting scientist at Cornell. Our son Kim had just graduated from high school and could attend classes at Cornell, and our daughter Eva got into a local high school. My department at DTU gave me leave without pay. We all travelled to Ithaca. I taught three courses, one of them a course in dynamical systems, based on Hubbard’s notes, that later became a textbook.
Hubbard and I worked on two papers (or, more precisely, a paper in two parts), the second of which was only finished three years later. Both were published in “Acta Mathematicae”.
We returned to Denmark after a year and a half.
Back in Denmark I began to supervise more students in holomorphic dynamics, among them Carsten Lunde Petersen. He was a graduate from the University of Aarhus but he wanted to work further on holomorphic dynamical systems. I advised him on his PhD thesis. I also supervised projects by DTU students and one semester I gave a course in holomorphic dynamics at the University of Copenhagen. I travelled a lot and made contacts with a large international group of people. The field was in rapid expansion. Yoccoz found in the Mandelbrot set combinatorial structures very similar to the ones that Hubbard and I had worked with in the cubic polynomials. This was further developed in a paper by Douady and me from 1987.
Q - The international group of people, the ‘crowd’, working on holomorphic dynamics, is known to be a very close-knit group of mathematicians, with famously good relations and a strong sense of community and collegiality. What do you see as the reason for that?
A - There are actually several schools, some centered on topics and some centered on people. My own background in topology fitted naturally with the approaches taken by Douady and Hubbard. We asked topological questions and used techniques from topology. Other people came from a more measure-theoretical direction. Around me, we were much influenced by Douady’s attitude of openness, sharing of ideas and support for young researchers.
Q - In 1993, there was a fairly large international conference that you organised?
A – Yes. Eventually, the field had begun to grow so much that we felt it was natural to conduct an international conference. I applied for money from various sources and, in June 1993, we had the meeting in Hillerød, Denmark. It was a “NATO Advanced Study Institute”. It was a seminal event, more perhaps than we realised at the time. We had 110 registered participants and about 70% were PhD students or postdocs, so it was very much a meeting of young researchers. Many young researchers came together here for the first time, met informally with senior people and also made contacts between themselves that are still in place. In the Scientific Committee we had, among others, Sebastian van Strien and I believe it was he who suggested the ‘free-for-all’ sessions where people could ask any questions about any topic and whoever knew about it would get up and explain at a blackboard. Everyone took notes. Many stood up for the first time then and there and spoke in an international setting. In among that we had of course more formal, prepared lectures. It was a magical two weeks.
Q - Another topic that you have been affiliated with is “European Women in Mathematics”. How did this begin?
A - It began when I attended the ICM conference in Berkeley in 1986. I was invited to a panel discussion organised by the “Association for Women in Mathematics” (AWM). This was partly because during my year at Cornell, Hubbard had introduced me to a female colleague Linda Keen. Linda and I became friends and she was involved with AWM, in 1986 as president. I was asked to bring a Scandinavian perspective to the discussion and I did as best I could. We were four women from Europe and we decided to form as a subset of, or sister organisation to, AWM, a “European Women in Mathematics” committee. We were Caroline Series, Franceois Roi, Gudmund Kalmbach and me. Meeting Caroline Series then was also a wonderful new connection within holomorphic dynamics. But it began with “European Women in Mathematics”.
Q - How did your work with the European Mathematical Society begin and what do you remember from the period?
A - I was an individual member of the EMS almost from the beginning and very early on became a delegate of individual members to council meetings. I was inspired to be a candidate for that through the network of European Women in Mathematics and later also for the executive committee of the EMS. I served for eight years on the executive committee, from 1997 to 2004, the last four years as one of the vice-presidents. In 1997 the EMS was still a very young society but it developed rapidly. I remember especially the cluster of activities preparing for 2000 as a "World Mathematical Year", expanding the interfaces of the EMS to society and also the many activities to make it a broader mathematical organisation, including the different mathematical branches. The EMS Publishing House was established during that period, due to an initiative of Rolf Jelstch.
Q - You remained during your EMS period and are still active with European Women in Mathematics?
A - It was not possible to continue being active in "European Women in Mathematics" during that time. Since 2010 I have been a member of the EMS committee "Women in Mathematics". We see our task to be an umbrella organisation for the various national initiatives around women in mathematics. We work closely together with "European Women in Mathematics". For the upcoming ECM in Krakow in 2012, our committee is organising a panel discussion, chaired by Caroline Series, who has been the chair of the committee since 2012.
Q - You have also worked with the history of mathematics, in particular the Danish-Norwegian surveyor and mathematician Caspar Wessel, who described the geometry of complex numbers in the late 1700s?
A - In 1995 Douady had a 60th birthday conference at the Poincare Institute and I wanted to find a unique present. Douady, being multi-talented, had taught himself quite a bit of Danish. I thought Wessel’s original paper on complex numbers, written in Danish, would make a nice present. I contacted the Royal Danish Academy of Science and Letters to obtain a copy of the original article. This turned out to be quite involved. In the end, they decided to give me one of the original folios from 1797. Suddenly I stood with one of these original, unbound stacks and Douady’s birthday was approaching. At the very least I had to have it hardbound. I contacted the book binder at DTU, who was immediately interested in this unique assignment. He made a beautiful bound volume. I read, in the weeks before the conference, a lot about the history of Wessel and his work and I realised that I couldn’t just hand Douady the book without saying at least a few words about the significance and the history behind. At the conference, there was quite a stir. Not very many people had heard about Wessel; most people believed that Argand had been the first to describe the geometry of complex numbers. When I came home, I wrote a letter of thanks to the Danish Academy and reminded them of the significance and that we were actually near a bi-centennial of its first publication. They ought to have a complete English translation made. They then arranged, with Professor Jesper Lützen at the University of Copenhagen as chairman, a Wessel Symposium. Discussing with Lützen, I said that there ought to be a Wessel biography and that perhaps I would like to write it. He agreed. I began to dig further into historical sources and was surprised to find so much help and enthusiasm from various sources. Wessel is quite known in the land surveying business, and people there were so forthcoming. Also from mathematical colleagues in Norway, I received help and support. I met Niels Voje Johanson, who was also at work on a biography and we decided to join forces. He supplied much valuable material from the national archives. The biography was published in time for the Academy Symposium, which lasted a full week.
Q - You were elected Chair of the Danish Mathematical Society and greatly boosted the activities of the society. What do you see as your biggest accomplishment?
A - The work as a member of the executive committee of the EMS strengthened my views on the important role played by the national mathematical societies. I had earlier been a member of the board of the Danish Mathematical Society, in fact during a period where several initiatives were taken that involved mathematicians from the different mathematics departments in Denmark, both in so-called pure and applied mathematics. Originally mathematics at university level was concentrated around the Copenhagen area. In the late 1950s the mathematics department at Aarhus University was founded and since then several other mathematics departments have been established at newer universities. The Danish Mathematical Society needed, in my mind, to reflect this change in diversity more directly. Having expressed that, I was asked if I was willing to become president of the society. During my presidency, we started a newsletter, Matilde. The second editor was Martin Raussen, who later became editor of the EMS Newsletter and is now one of the vice-presidents of the EMS. I am grateful for the support from many individual mathematicians and also from the different mathematics departments during my presidency.
Q - You are now retired but seem as busy as ever. You even have time for beekeeping?
A - Four years ago I retired. In the beginning it mainly meant that I stopped teaching mathematics courses but otherwise continued as before. But gradually I am changing priorities. I still enjoy being involved with mathematics, although it is not as intensive as before. I have taken up other interests, such as singing in a choir. However, beekeeping is the main activity. Ten years ago Sven decided to become a beekeeper. The life of the bees immediately fascinated me too, although I did not have the time to be much involved. To retire earlier than I had to was partly motivated by obtaining more time for beekeeping. I enjoy the outdoor activity. Bees in cities are popular these days. It is a way to get closer to nature. It is a gift to have a background in natural science, since mathematics, physics, chemistry and biology need to come together when one tries to understand how the bees function as social insects.
Interview by Poul G. Hjorth
Technical University of Denmark
Email: p [dot] g [dot] hjorthmat [dot] dtu [dot] dk
Published in the Newsletter of the European Mathematical Society
No. 84, June 2012