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Interview with Dylan Müller recipient of the 2022 Edouard Gans Prize
Express Bio
Place of birth: Geneva
Bachelor: Geneva
Master’s & PhD supervisor: Anders Karlsson, UNIGE
Dylan's primary area of interest is number theory, but he is also interested in many other areas. He received the 2022 Edouard Gans Prize awarded by the Faculty of Science on the recommendation of the Mathematics Section's College of Professors for his master's thesis: Équations de la chaleur p-adiques, fonctions zeta associées et fonctions zeta spectrales sur graphes. The Prize is awarded for the best Master's thesis in mathematics of the year at the University of Geneva.
The mysterious ingredient
Although Dylan enjoyed playing with numbers from a very early age and enjoyed mathematics at school, he did not always anticipate studying mathematics. During his journey into mathematics, he encountered many challenges and surprises and was inspired in unexpected ways.
Following his father's footsteps and being attracted by the idea of finding and solving problems, he completed an apprenticeship in mechanics. Still, he was disenchanted when confronted by the limitations of the working process way. Determined later to pursue his education in engineering school, he took up the passerelle, a bridging exam to gain admission to higher education.
To his surprise, while preparing for the exam, he rediscovered mathematics and fell back in love with it. His maths teachers at the time Mr. Courtebras and later Ms Chaves, identified his talent and encouraged him to pursue his studies in mathematics. They also introduced him to the ingredient that later became Dylan's source of inspiration.
The teachers’ approach was much more than "I'll do the proof, then you'll learn it". They introduced subjects with a substantial element of mystery, and for Dylan the mysterious aspect was an excellent motivational tool. Dylan's first encounter with this mysterious aspect was the Taylor expansion of trigonometric functions. He later reencountered this "mystery" as an undergraduate at UNIGE while studying geometry with Christophe Pittet.
His fascination with this mysterious side of mathematics could probably explain why he is interested in many subjects.
Were you surprised to receive the Edouard Gans Prize? Yes. I was not expecting it at all, but I am very honoured!
How did Number Theory come in the mix?
Even though we didn't have many courses on number theory during my bachelor's, reading books and talking to people like Anders Karlsson led me to discover that number theory has a mysterious and intriguing side.
The central part of my work is studying spectral zeta functions. In general, they are hard to define. If we were to start from the beginning, prime numbers have fascinated people since the time of the Greeks, as we know, mainly because they are the building blocks of numbers in the multiplication way. A central importance is to understand the distribution of prime numbers. People like Euler and Riemann observed that studying prime numbers is related to studying a special kind of function: the Riemann zeta function. and studying these functions is essential to understanding prime numbers in general.
However, I am not really working on the Riemann zeta function directly, as I am not trying to solve the Riemann hypothesis. There are a lot of mysterious aspects in this theory. In contrast to other challenging problems where mathematicians know which parts to address and know that it might take ten or twenty years to get there, but it will eventually work, for the Riemann hypothesis, to my knowledge, no one knows the path to solve it.
Around 1950, there was a significant advancement with Tate's Thesis, which provided a scheme to understand some of the fundamental properties of zeta functions. It was a real breakthrough as it initiated much work.
I am studying a problem related to the Riemann zeta function in different settings to understand maybe not a pattern but something that could help find a roadmap to this problem without being sure it will work.
What do you most like about it?
The fact that there are many unsolved mysteries. Even though much work has already been done on the subject, it is still hard to get a clear picture of what is happening in this hypothesis. However, I feel uncomfortable when I don't fully understand something. And even if it takes a long time, I always try to build something to gain an understanding. My favourite moments are when I suddenly understand something and can come up with a satisfactory explanation.
What are the challenges?
Doing maths is excellent, but most of the time, you are alone with the hope that what you are doing will help someone someday. So, it is imperative to discuss with other people, or at least have them look at what you are doing, even though they might be from different fields. As in my case, I am currently exchanging with someone who is in category theory, and it does not only help me to talk and structure my ideas, but now I am also trying to incorporate some of his work into what I am doing.
What helps you to cope with the ups and downs?
It is not something I am very good at, but my family and friends help me. I try to practice sports that are very physically and technically demanding and can absorb you completely. For me, this total immersion is essential. The benefit of stepping back from my work, particularly when I am completely absorbed by it, allows me to then come back to the problem with a fresh mind.
What is your favourite part about being a mathematician?
One of the things I like is the creative part. During my bachelor's, I wasn't exposed to this creative aspect. I discovered it mainly towards the end of my Master's when I started to see why some ideas are beautiful in maths. The way I see it is that the bachelor's provided me with the tools, but the openly creative part came after.
I guess this could be a problem as sometimes people who have the potential to be very good mathematicians get crushed by the bachelor's approach, where you must learn abstract things with limited explanations. But when you continue and genuinely like maths, you find your own way of doing maths.
