# Mr. Kußmaul, why do you study mathematics?

March 25, 2024

Graduate award winner for outstanding M.Sc. degree at the Department of Mathematics
Portraits in the Department of Mathematics at the University of Stuttgart - Valentin Kußmaul M. Sc.

I think for me it's because I want to understand things precisely. In mathematics, everything is based on simple axioms. With the laws of logic, new and unforeseen statements arise from these, which are written down in theorems. In the proof, the theorem is broken down into understandable and verifiable steps of reasoning, so that even the most complicated things become comprehensible.

The second reason is my interest in physics. All physical theories are written in the language of mathematics. We should consider ourselves lucky because our current theories (theory of relativity, quantum physics) deviate greatly from our intuitive understanding. Only with the help of mathematical formalisms is it possible for us to understand nature at all.

Why should you study mathematics at the University of Stuttgart?

The University of Stuttgart has committed and competent lecturers who offer a wide range of lectures. Early on in your studies, you have the opportunity to take elective modules and develop your skills according to your own interests. In addition, the university offers the flexibility to attend lectures from other departments. In this way, for example, I was able to attend various lectures on theoretical physics.

What are you researching as a doctoral student in mathematics?

Together with my supervisor, I am working on the theory of quantum electrodynamics, which describes the interaction between radiation and matter. As mathematicians, we take the equations established in physics and try to derive physically relevant properties from them. If we consider more than two interacting particles, the equations cannot be solved explicitly. In physics, it is common to use approximation methods to simplify the calculations in order to arrive at a result.

The task of mathematics can be to investigate the extent to which the approximation corresponds to the actual solution. Instead, we try to obtain information about the full model directly. In this case, however, we have to restrict ourselves somewhat in the questions we ask; for example, it will not be possible to calculate the dynamics of the system for every point in time, but the problem could become manageable for long periods of time.

The techniques learned during the course are applied in research. Much is based on functional analysis (the theory of infinite-dimensional spaces) and, building on this, spectral theory, which together form the mathematical foundation of quantum physics and were developed in the 20th century.This is one of the strengths of mathematics: it is designed in such a way that you can learn the achievements of previous generations without having to go the hard way again.I like the idea that with every mathematical work, the collective knowledge grows and seemingly unattainable theorems can be proven bit by bit. Who knows, maybe one day we will be able to make a modest contribution to this.

Valentin Kußmaul M.Sc.
Award winner for outstanding M.Sc. degree in the Department of Mathematics