“Believe in yourself.”
Kathryn Hess Bellwald is an American-born mathematician, known for her work on algebraic topology both pure and applied. She is Associate Vice President for Student Affairs and Outreach and a full professor in the School of Life Sciences at the Ecole Polytechnique Fédérale de Lausanne (EPFL), where she leads the Laboratory of Topology and Neuroscience.
She graduated with a Ph.D. in Mathematics from MIT at the age of 21 and held positions at the universities of Stockholm, Nice, and Toronto before moving to EPFL, where she became an adjunct professor in 1999 and associate professor of mathematics and life sciences in 2015.
Her research focuses on algebraic topology and its applications, primarily in the life sciences, neuroscience in particular, but also in materials science. She has published extensively on topics in pure algebraic topology including homotopy theory, operad theory, and algebraic K-theory. On the applied side, she has elaborated methods based on topological data analysis for high-throughput screening of nanoporous crystalline materials, classification and synthesis of neuron morphologies, and classification of neuronal network dynamics. She has also developed and applied innovative topological approaches to network theory, leading to a parameter-free mathematical framework relating the activity of a neural network to its underlying structure, both locally and globally.
In 2016 she was elected to the Swiss Academy of Engineering Sciences and was named a fellow of the American Mathematical Society for her "contributions to homotopy theory, applications of topology to the analysis of biological data, and service to the mathematical community" and a distinguished speaker of the European Mathematical Society in 2017. In 2021 she gave an invited Public Lecture at the European Congress of Mathematicians. In addition to her strong publication record, she has won several teaching prizes at EPFL, including the Crédit Suisse teaching prize, the Polysphère d’Or, and the best teacher prize in the Faculty of Life Sciences in 2018. In 2008, she created the Euler course, an accelerated mathematics program, unique in Europe, for highly gifted children. She has four sons. Adapted from: Kathryn Hess - EPFL
Keywords: mathematics, algebraic topology, homotopy theory, operad theory, network theory, neuroscience.
Lausanne – October 12th, 2022.
How did you (decide to) become a scientist? When I was ten years old, I was lucky enough to participate in an astronomy course that was set up by my parents. My parents, in the US, created what they called the Association for High Potential Children because they saw that my sisters and I were all very bright and interested in a lot of things and they wanted to set up some activities for us. First of all, they set up a course in astronomy. They found a local astronomy professor who was willing to teach astronomy to a group of kids and it was absolutely fantastic. We were sitting in the planetarium looking at the stars and we went to the observatory once which seemed extremely late at night to me at the time, taking pictures of the moon and Saturn. And I was thinking: this is what I want to do. What really struck me was the evolution of a star, from when it starts to develop until it turns into either a brown dwarf or a black hole or whatever depending on the mass of the star. I was just “Ahh, this is fantastic”.
So, I decided when I was ten to be an astrophysicist because I just wanted to understand the life cycle of stars and the universe and everything. It was clear for quite a while that this was what I wanted to do and when I started university I thought, well, I’ll study physics to become an astrophysicist. When I went to university, I decided to study both math and physics, since I knew physicists needed a lot of math. When I was in my third year of university studies, during this double major in math and physics, the only women professor I had in math or physics, was teaching me electromagnetism for a semester. She asked to see me in her office and when I went there, she said: “look, you’re doing very well in my course but you’ve no physical intuition as far as I can tell. The reason why you’re doing so well is that you are a very good mathematician. You should study math”. I realized that she was right; till then I’ve been sort of trying to force myself as a square peg into a round hole and it was working ok but it was not going to work as a researcher. So, I dropped the physics part and just continued with math and I was very happy. While I was still an undergraduate studying math I took a graduate-level course in analysis, which I loved - I thought “this is what I want to do”. What I didn’t realize until I started graduate school the following year was that I really loved it because the teacher was amazing - he was one of the best-known pedagogues in that field. When I started taking courses in that area, I realized that the subject itself was not something that fitted my brain - it was that professor who was just magical. At the same time, I took some other courses to try and there was one that sort of resonated with my brain, and I said: ah yes, this is the way my brain works. That’s how I ended up in the field of mathematics in which I work now [algebraic topology].
What is your drive and excitement in science and in doing what you do now? Over the years I evolved from being simply a pure mathematician to working on various applications as well. I continue doing mathematics and at the same time, I work on applications in a wide range of fields, particularly within the life sciences. My heart still thrills to understand the big picture and deep structure in mathematics, but I’m also highly motivated by meaningful applications.
People talk about how mathematicians are of two types, that Freeman Dyson talked about: birds and frogs. The frogs dive into the mud and they solve very hard and very deep problems and then the birds once they are up there in the sky, they see the big picture. What really makes me excited is seeing these analogies between two very different parts of mathematics. You see the same kind of structures showing up in two different parts of mathematics. Why am I seeing two same structures in different places? That is what I find absolutely thrilling and satisfying. And on the other hand, taking this very pure mathematics and seeing how it can be applied in very concrete situations to understand the complexity of biology is mind-boggling. To start to understand what’s going on, being able to use mathematics to describe the patterns, to discover the patterns, is also really exciting. I feel very lucky to be able to do both.
Would you have one word to give as a gift to other women and more in general to young aspiring scientists, women or men? Believe in yourself. There’s a story behind that as well. When I started working on my thesis problem, my thesis advisor gave me a paper to read and said to me “I think you'll find this interesting”. At the end of this paper, there was a list of 10-15 open questions. I started with question 1. As I read the question, I started thinking about it and how this [question] looks relatively simple to state - and this is an advantage - but it had been open for quite a while. I really liked the problem. Shortly after I started working on it, I went to what was probably my first math conference. There I met one of the very well-known people in the field – an older man – and I told him that I was working on this problem. He said: “Uhm that conjecture is false and you'll find the obstruction at this point”. He said it couldn't work.
But I was naive and young enough to think, “I don't think he is right, “so I just continued trying. I was willing to look for counter-examples but at the same time, I really believed it should be true. I kept working on it and in the end, I proved it! He was wrong. That was a real lesson, and I tell my Ph.D. students: “if I tell you that something is not going to work, don't believe me. I could be wrong. Thus, believe in yourself”.
