Mevlüde Alizade, a mathematics student, and Enya Leroy, a high school graduate, are currently completing an internship at the Chair of Algebra and Representation Theory at RWTH Aachen University. We had the opportunity to visit them and take a look behind the scenes of a mathematics institute: What do you actually learn there, and what does such an internship look like in practice?
Why do you want to do an internship at a mathematics institute?
Enya: I wanted to do an internship at a mathematics institute because math has been one of my biggest passions for as long as I can remember. I’ve always been curious to see how this passion translates into actual work life—whether doing math as part of a job would keep the excitement alive or make it feel more like a chore. But from what I’ve experienced so far, if you choose to work on things you’re truly excited about, then work can actually be really enjoyable.
Mevlüde: I have just finished my Undergraduate degree in Mathematics, and even before that, out of all the different subjects, I knew I was drawn to Mathematics the most. An internship at amathematics institute felt like the natural next step to explore mathematics beyond coursework.
Why specifically in the field of algebra?
Mevlüde: I had taken the courses Algebra I and II (mainly about Group and Ring Theories) in my third year, and absolutely loved the structure, abstraction and foundational nature of algebra.
I wanted to learn more about its intersection with other areas of mathematics.
Enya: To be honest, I didn’t choose it just because it was in the field of algebra. What really drew me in was the project on simplicial Surfaces, which I found very interesting—especially because I really enjoy combinatorics. Now that I’ve gotten more familiar with the project, I appreciate how it connects to so many different areas: you can look at it from a geometric, algebraic, group-theoretic, or combinatorial perspective. That variety makes it really exciting to work on.
Do you already have ideas about the direction your Bachelor's/Master's thesis could
take?
Mevlüde: I think my Master’s Thesis will have Algebra in it. That’s the thing about this field, you can integrate it with different fields and build a project from there.
Enya: Not yet, since I just finished school and will only start studying in October, it’s still too early for me to say. I’m open to different areas, and I hope that through my studies—and experiences like this internship—I’ll discover what topics I’m really passionate about and could imagine exploring in a thesis later on.
What do you hope to gain from this internship?
Enya: I hope to gain a first real insight into what research in mathematics is like—what a typical day in the life of a researcher looks like and whether I could see myself doing a PhD later on (which is actually something I’m currently very interested in). Since I’m planning to study at RWTH, I also wanted to get to know the university a bit better in advance. But most of all, I hope to learn new things, deepen my understanding, and discover new areas of mathematics that really excite me.
Mevlüde: I hoped to gain research experience, a skill I believed I severely lacked in. Although, I’ve completed the rigorous coursework, I knew I lacked hands-on experience with mathematical research.
Have you used software tools such as LaTeX, SageMath, Mathematica or GAP?
Mevlüde: Yes, I used LaTeX to write my Bachelor’s Thesis, and I am using it to write about my research here. I have learned to use GAP when I started my internship.
Enya: Yes, I’ve mainly used GAP to work with simplicial surfaces—for example, to compute embeddings or to check certain properties. That’s actually one of the parts of my internship that was completely new to me at first, but I’ve really enjoyed working with it and learning how to use it more effectively.
Thank you very much for the interview!
After the internship, Mevlüde will continue her studies in Italy. Enya will travel to Australia to take part at the IMO- mathematics competition there.
We wish them both continued success - and of course happiness on their future careers!
Are you interested in mathematics comepetition?