Future Proof — Mateusz Michałek

How did you get into math?

Mateusz Michałek: I guess I always knew my calling was to become a mathematician. In remember receiving only a ‘very good’ evaluation in math and ‘exceptional’ in Polish in first grade of elementary school. I couldn’t fathom why, as I was sure that I was way better in math than in Polish. It was only after some years that my parents told me that ‘exceptional’ was not granted in first grade, since there isn’t all that much math to speak of at that stage. It was thanks to my fourth-grade math teacher Mrs. Teresa Lekawska that I dived deeper into the realm of math, as she encouraged me to do extra exercises, take part in competitions and follow additional courses. Another tremendously positive influence was my uncle, Tomasz Michałek. He was a young computer arts student in Cracow when we started our weekly meetings, where he taught me some things that went way beyond my education at school and instead delved into his university education. This sounds extraordinary, however in Poland the university math courses start with more basic things than primary education. Formal introduction of set theory, functions, and induction, it surely takes some time until you learn that 1+1=2. At this point mathematical notation came more natural to me than using the 'standard' language. I was very much disappointed to discover years later that true mathematicians actually write articles in 'standard' language - not just mathematical symbols. My parents also told me later that they were often hesitant to enter the room when Tomasz and I were doing math, as we were actually fighting and shouting pretty regularly in the process. It was a lot of fun!

What would you would like to accomplish?

As most mathematicians, I would like to solve some fundamental problem. The one I am currently working on is related to finding optimal ways of computing the determinant or multiplying matrices. This is very much related to the question that people were studying for millennia: how to solve a system of linear equations?

Why did you choose to become a scientist at MiS?

It was a combination of quite a few factors. I already spent a year at the MPI in Bonn, so I knew that MPIs offer the highest possible research standards. At the same time my wife was offered a postdoc at the UFZ in Leipzig and Bernd Sturmfels, with whom I had worked before, became MiS director. I was offered an absolutely great position; probably one of the best in the world a young mathematician may hope for. Thus, the choice was very clear for me.

What advice would you give young researchers starting out at the institute?

In many games, like chess or go, we start by learning the rules. Then we learn some tricks that allow us to outperform people who merely know the rules. The next, extremely powerful, step is usually to start planning a few moves ahead. While this is not a universal advice to solve mathematical problems, I think it’s a wise choice to somewhat plan out your mathematical career. You don’t have to follow these plans to a T, which is usually impossible anyways, but it is good to have them - even if it’s just to have the option to ignore them later.

Which scientist would you love to work with?

To be honest, I simply contact anyone that I’d like to cooperate with. To the surprise of my fellow students I could get acquainted with senior professors at the university by simply knocking on their doors and had no problems contacting a Fields medalist even as a bachelor student. The main reason for the ease of these approaches was that I always felt very welcome: thus, maybe one more advice for young researchers is to not be afraid to discuss math with anyone you like!

Honored with the Kazimierz Kuratowski Award in 2015 by the Institute of Mathematics of the Polish Academy of Sciences and the Polish Mathematical Society.

• M. Michałek and Y. Shitov, Quantum Version of Wielandt’s Inequality Revisited, IEEE Transactions on Information Theory, vol. 65, no. 8, pp. 5239–5242, Aug. 2019.
• J. Buczyński, T. Januszkiewicz, J. Jelisiejew, M. Michałek, Constructions of \(k\)-regular maps using finite local schemes, J. Eur. Math. Soc. 21 (2019), 1775–1808.
• J. Landsberg, M. Michałek, On the geometry of border rank algorithms for matrix multiplication and other tensors with symmetry, SIAM Journal on Applied Algebra and Geometry 1 no. 1 (2017), 2–19.
• M. Michałek, B. Sturmfels, C. Uhler, P. Zwiernik, Exponential varieties, Proceedings of London Mathematical Society 112 no. 1 (2016), 27–56.
• M. Lason, M. Michałek, On the toric ideal of a matroid, Advances in Mathematics 259 (2014), 1–12.