Why mathematics?
I have always been fascinated by mathematics, especially the logic, the clear structure and the precision. You start with a few premises and definitions, from which you build up an ever larger, consistent logical construct through reasoning, trying to abstract everything as much as possible in order to be able to apply the theorems in a variety of ways. The high degree of abstraction is challenging at the beginning of the course (for me it felt as if a few synapses had to be rewired) and it takes a while to get used to this way of thinking. Until then, you need a high tolerance for frustration.
In my studies, I am most interested in the field of algebra and representation theory. Despite the high degree of abstraction, or perhaps precisely because of it, there are concrete applications. In the algebra lecture, for example, we were able to prove at the end that an angle cannot be divided into three parts. At first glance, it was not obvious that the theory we had established could be applied or whether this fact could be proven at all.
hen studying, you see proofs that are centuries old, but are still valid. A proven theorem is forever true - provided the proof is flawless. The models developed in most natural sciences often have to be revised after a certain time when new methods and measuring instruments are developed and new experiments provide results that contradict the current model.
Why study mathematics?
Even at school (even if it was mostly just about arithmetic), I was fascinated by the fact that two completely different solutions can lead to the same result. However, I only decided to study mathematics very late, towards the end of my school years. My other great passion is music, especially playing the piano and organ. The works in music have also survived for centuries, some of them have an almost incomprehensible complexity and give you the opportunity to express yourself without words. Even if mathematics with its precise statements and music with its emotionality seem very contradictory at first glance, they have a lot in common. Both open up new worlds. In the end, I chose mathematics as my field of study...
Finally, a word of encouragement to first-year students: Even if studying is sometimes hard, keep at it, it's worth it!
Carolin Dörfer B.Sc.
Award winner for outstanding B.Sc. degree in the Department of Mathematics