1. Bernhard Riemann or Albert Einstein?
Riemann. His ideas on the geometry of curved spaces were revolutionary and are the foundation of my entire research. Without Riemann, Einstein might not have been able to formulate his general theory of relativity at all.
2. Where does your passion for mathematics come from?
During my school time, I was particularly fascinated by mathematics, computer science, physics, and other natural sciences. The fact that I ended up choosing mathematics was perhaps an organizational coincidence: At the University of Vienna, I had the opportunity to start studying mathematics directly in the summer semester after completing my civil service. I simply stuck with it and have never regretted it.
3. What are you currently researching?
My research focuses on scalar curvature, a subtle measure of how strongly space is curved. I’m developing new comparison theorems: What are the geometric consequences if we know that the curvature exceeds a certain value everywhere? Is the geometry already completely determined by the curvature boundaries in some situations?
4. How would you describe your field of scalar curvature to nonspecialists in a way they can understand?
That’s difficult, since scalar curvature only becomes truly relevant in higher dimensions. In short: The Gaussian curvature of a surface measures how much the geometry of a surface deviates from the Euclidean plane. In higher-dimensional spaces, there are many “surface directions” at every point, each with its own Gaussian curvature. Scalar curvature summarizes all of these into a single number.
5. Speaking of geometry. It’s only when you leave the plane that things get really interesting. What’s so fascinating about curved space?
On curved surfaces, geometry behaves unexpectedly: A triangle can have an interior angle sum other than 180 degrees, and two lines that are initially parallel may later meet or diverge exponentially. This forces us to develop a more general theory.
6. Differential geometry describes complex structures with six or ten dimensions. How does the human mind deal with spaces that go beyond imagination?
It is often enough to gain a two- or three-dimensional, albeit vague, understanding that can be transferred to higher dimensions. This is mathematically underpinned by abstract definitions and formulas, whereby it makes no difference whether these are three, six, or 10,000 dimensions. This interplay of low-dimensional intuition and general formalism is surprisingly powerful.
7. What other mysteries does geometry still hold in store for us?
What forms can a space take if we demand that the curvature does not become negative anywhere? Differential geometry of the 19th and 20th centuries has comprehensive answers to this question for strong curvature concepts. For the scalar curvature – the weakest – we often understand only fragments.
8. When does a mathematician go hopping mad with despair?
When a proof hasn’t worked for months, even though you think you have a clear picture of what should happen. But in mathematics, intuition alone isn’t enough. Occasionally, you’re completely off the mark and only realize it later.
9. What would you say in hindsight to your high school math teachers?
Thank you to my teacher for the exciting topics in the advanced elective course. That gave me an early insight into what mathematics really is beyond school math.
10. We stand on the shoulders of giants: Which prominent figure in your field would you like to visit using a time machine, and why?
Bernhard Riemann during his habilitation lecture in 1854. I would like to know whether he realized how far-reaching his ideas were. And perhaps to bring him modern antibiotics.
11. If you weren’t a mathematician, you’d probably …
...have ended up in IT.
12. Many STEM fields complain about a lack of young talent. How would you get young people excited about mathematics today?
By showing how relevant mathematics has become. Financial markets, artificial intelligence, digitalization… our world is becoming increasingly mathematized. Society needs people who understand these connections; otherwise, it will be left behind.
13. You have been Professor of Geometry at the University of Potsdam since 2025. Have you been able to settle in at the institute and in your new home in Brandenburg?
Yes, really very well! My colleagues at the institute gave me a warm welcome, and Potsdam is a wonderful city. On the one hand, there are plenty of opportunities to get out into nature and rest one’s mind. On the other hand, after many years in Münster, I enjoy being closer to a metropolis like Berlin.
14. Was there an aha moment during your studies that had a lasting impact on you?
The realization that in mathematics, you can truly understand everything from scratch. No black box, no “that’s just the way it is.” Every statement can fundamentally be traced back to axioms. That clarity inspired me.
15. What opportunities do you see for mathematicians in the job market beyond academia?
Much of what used to require specialized expertise is increasingly being automated. However, mathematicians are well-positioned to understand and plan the big picture: We learn early on to think abstractly and to penetrate complex structures. Tech companies, consulting firms, banks, public institutions, and many other organizations are looking for such people. This is confirmed by many colleagues who have successfully transitioned into the business world.
16. Do you dream about formulas and curved spaces at night?
When I can’t fall asleep, my thoughts sometimes circle around a problem, and occasionally I wake up with an idea. But whether it’s any good only becomes clear the next day at my desk. Unfortunately, most of the time it is not completely right.
17. When you’re not solving differential equations, what do you like to do most?
Go for a run to clear my head. And read about topics that have nothing to do with mathematics. The contrast helps me rest my mind.
18. Which comes more naturally to you: research or teaching?
Research. But teaching helps me find a balance through contact with students and structure my own understanding.
19. Studies show a decline in math performance among ninth graders over the years. What would you suggest for improving the general public’s understanding of mathematics?
It shouldn’t be socially acceptable to boast about not understanding math. When it comes to reading, writing, or understanding history and politics, no one would think of doing that. Math is just as essential a skill and should be treated as such.
20. How do you measure the “beauty” of a formula or a proof?
When a surprising result follows from just a few premises. The most beautiful proof arises when, through the choice of the right term and a creative twist, a deeper truth is revealed by a short argument.
21. Parallelization and superposition: Will mathematics make faster progress with the use of quantum computers?
Quantum computers accelerate certain algorithmic tasks and also raise fascinating theoretical questions in their own right. However, as far as the practice of mathematics as I know it is concerned, I don’t see any direct connection in the short term. Perhaps machine learning and computer-aided formalization on classical systems have much more immediate potential to transform mathematical research.
22. Speaking of practical applications: How can geometry and graph theory contribute to the development of new materials, building materials, or molecules?
Classical differential geometry and geometric analysis certainly play a role here, but that’s not really my area of expertise.
23. You’ve studied, researched, and taught in various places. If you had to choose: Vienna, Göttingen, Münster – or perhaps Potsdam?
All of these places have their own academic merits. From a purely personal perspective, Potsdam and Vienna are at the top of my list.
24. Math influencers: Which social media channels would you particularly recommend?
3Blue1Brown on YouTube.
25. Which major mathematical problem would you like to see solved in your lifetime?
What interests me most are new, general methods for studying scalar curvature that do not rely on existing spinorial or minimal-surface methods. Something else, though more widely known: the Penrose inequality in its full generality. It connects the geometry of scalar curvature with the physics of black holes and has so far only been partially proven.
26. And what about a non-mathematical one?
How consciousness develops.
27. What is the most difficult part of your job?
The moments when you don’t know whether you’ll ever find a solution with your current approach, and you have to stay focused despite all the distractions.
28. And what is the best part?
When you understand something that no one else has understood before.
29. The laws of mathematics: invented or discovered?
We invent the language and notation. But the underlying structures and relationships seem to exist independently of us.
30. If something does not fall into place: How do you deal with dead ends in thinking and research?
I switch to another project for a while and hope that, with some distance, I’ll make progress later on.
31. What role do teams and networks play in mathematical research?
A very important one. The best mathematics often emerges in small groups of two to four people – large enough for different perspectives but still small enough for deep discussions where everyone involved can see the entire project. You meet in a place with few distractions, discuss various ideas, and suddenly things come together to form a new piece of research.
32. Which researchers do you admire?
Misha Gromov, the great surveyor. His ideas have created entire fields of research, including the most important aspects of my own.
33. Research projects, collaborations, events: What’s coming up at the Institute of Mathematics?
On May 22, 2026, as every year, we will organize the traditional “Euler Lecture in Sanssouci” together with Berlin’s mathematical institutes.
This article appeared in the university magazine Portal - Eins 2026 „Inklusion“.