Wendelin Werner does research in the area of probability theory, with a special focus on self-avoiding random walks and Brownian motion. He is Professor of Mathematics at the Swiss Federal Institute of Technology in Zurich (ETHZ).
»There are about 30 people in the world who thoroughly understand my work«
Mathematicians often want to revisit an emotional world from their childhood through their work. For me, it's what I felt sitting with my brother and father in the garden at night watching the stars. It fascinated me that their size was a matter of perspective and that everything we were seeing had happened a very, very long time ago. That knowledge felt intoxicating and it drove me to investigate and master similar questions. I think it still remains one of the biggest motivators for my work.
One thing that interests me is the relationship between randomness and continuity. On an intuitive level, we know that time and space build a continuum. In very broad terms, my work looks at how randomness can be scattered and retrieved along a continuum of randomness. This question is relevant, for example, for phase transitions in physics. If a water glass has a temperature of zero degrees Celsius, it can contain water or ice. But how exactly are the states of water or ice determined at the various points in the medium? Which microscopic features trigger macroscopic features?
I could describe the specific topics I work on with similar brushstrokes, but it would be nothing more than propaganda. There are about 30 people worldwide who thoroughly understand my work. It's a pleasant situation, actually, because many of those colleagues are wonderful people. Mathematics draws a host of great people. At the same time, it is a very abstract world into which we can retreat and feel very secure and at ease.
"Mathematics draws a host of great people"
As a probability theorist, I often hear a number of pseudo-philosophical questions: Is there such a thing as coincidence? What is the meaning of randomness? Does our world have deterministic traits? But one of the beautiful things about mathematics is that we do not have to answer those types of questions. It's not in our job description. Our work takes place within the abstract world of maths. The same applies to certain geometries: you can work with them without knowing whether they even exist in the real world. In our abstract world, it is possible to prove the properties of seven-dimensional spaces, even though we will never be able to see those spaces with our own eyes.
I do not believe that my research will be useful for everyday applications in 20 or 50 years. Nor is that my goal. Like most pure mathematicians, my motivation comes from being able to create an elegant mathematical structure with elegant proofs.
Video: Mirco Lomoth
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