The fun of brainteasers
Eva Viehmann was fascinated by mathematics while she was still at school. At home she was motivated by her father, who is also a mathematician, and together they looked beyond the confines of school mathematics. “It’s a subject which contains so much more than just calculations,” she says. “It makes you think about how numbers and geometrical objects are related, or about how to solve mathematical brainteasers. Even then, it was fun for me – and it still is today,” says Viehmann, 43, who has been researching and teaching at the University of Münster since February 2022. Talking to her about her work, or watching her in her lectures and seminars, you can feel her enthusiasm for her subject. And it was this passion, as well as her skills, which convinced the German Research Foundation to award her the Gottfried Wilhelm Leibniz Prize in December.
Over the past few years, Eva Viehmann has been doing research primarily on arithmetic algebraic geometry as part of the Langlands Program. This was set up by Robert Langlands, a Canadian, in 1967 and it consists of a series of far-reaching conjectures which connect number theory and representation theory with each other. “This project belongs to one of the most fascinating fields of theoretical mathematics, and research on it is nowhere near completion,” she explains. It comprises what appear to be enigmatic connections between on the one hand number theory – i.e. the theory of integers – and on the other hand representation theory, which deals – roughly speaking – with symmetries.
Numerous prizes and awards – including two ERC Grants from the European Research Council – bear witness to the fact that Eva Viehmann is an expert in her subject. But what means more to her is the recognition shown by other colleagues in her field. “It makes me happy when other researchers who understand what my work is about can appreciate the results of my research and continue work on them,” she says. After all, she comments, research is all about working together to push projects forward, increase knowledge, carry out verifications and extend the findings we already have. In addition, she also talks about her work outside specialist groups – for example, in podcasts, videos or interviews. For her, it is important that the image of mathematics, and access to the subject, should change. Patience and perseverance are decisive factors for any success in mathematics. “We don’t use just one single method or process for making calculations. Rather, we try to understand what is behind things, and how we can tackle the actual problem,” is how she explains her work. This can certainly take months, or even years, she says. Sometimes you even have to break off a research project, she adds, and admit to yourself that you’re stuck at a dead end – which makes it all the more gratifying when you achieve a breakthrough in your research after a long time and can share it with others in the worldwide community of specialists.
After her academic career had taken her to Bonn and Munich, Eva Viehmann came to Münster about two years ago. “Among mathematicians there is a basic community spirit marked by solidarity and tolerance,” she says, “and I experience this feeling of community particularly strongly in Münster. This openness and collegiality is not something that can be taken for granted. Moreover, she says, Münster provides an ideal research environment in her particular field of pure mathematics, which includes for example algebra, topology, functional analysis and number theory. At the Institute her immediate neighbours are colleagues who are working in closely related fields. Eva Viehmann can now use the 2.5 million euros which the Leibniz prize is worth to expand her working group in accordance with her wishes. “It’s great that I can now offer excellent researchers from all over the world the opportunity to come to Münster and join in our research. That will give me the freedom to do what I really want to do,” she adds – because she still has plenty of aims for her research. “What drives me is the urge to make new insights and to understand unsolved problems. I never get tired of brainteasers.” Whether with colleagues at work or with her children at home – just as she experienced it during her school days.
Kathrin Kottke
This article is from the brochure "Twelve months, twelve people", published in February 2024.
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