# Gabriel Dill – Magician of an abstract universe

Prix Schläfli 2021 Mathematics

For the Matura, he wrote a satire on Berlusconi – in Latin. And for his dissertation, which was awarded the Prix Schläfli, he chose a field that is rather exotic even for insiders: Diophantine geometry. Gabriel Dill likes it a little complicated.

Astrid Tomczak-Plewka

Anyone, who devours Ulysses in his or her spare time, raves about the "magic" of mathematical equations, and spends years solving problems that 99.9% of the population is not even aware exist – yes, such a person must face the question: "Are you a nerd?" Gabriel Dill takes his time to respond, searching for words to respond seriously and adequately. "I can get very excited about abstract questions, get into topics that are far removed from reality," he says finally. However, the term "nerd" is somewhat clichéd.

### Mathematics is something social

On the contrary, "Mathematics is something very social," Dill points out. "You are constantly exchanging ideas with other people." For example, in the "Bernoulli's Round Table", which he co-organised: a platform for doctoral students to give talks to each other about their areas of expertise. "It makes you think outside the box," Dill says. Even though this round table naturally constitutes like-minded people, who, like Dill, like to puzzle, "brainstorm", pose and solve problems that do not tend to arise in real life.

Gabriel Dill also addressed such a problem in his dissertation at the University of Basel. It is about a subfield of number theory called "Diophantine geometry". Diophantus of Alexandria was a mathematician of ancient times and is considered one of the founders of algebra and number theory. The "Diophantine equations", for which one searches for special (for example, integer) solutions, are named after him. One question might be: which integers are areas of right triangles with rational side lengths? In turn, "Diophantine geometry" uses the geometry of objects defined by Diophantine equations to solve the equations. A famous supposition that has so far been only partially proved establishes a connection between geometry and arithmetic. Dill proved this supposition in certain special cases in his dissertation.

### "Ambitious, technically versatile, original ideas"

For the uninitiated, it is hard to understand the world. For the initiated, on the other hand, it is clear: Dill's dissertation is "ambitious, technically versatile and contains original ideas," writes the jury. "The award is a great joy for me," says the 27-year-old. "I am proud of my dissertation and felt I did a good job." To others, this might sound arrogant and smug. Not so with Gabriel Dill: In conversation, it becomes clear that he is not driven by a desire for recognition or competition. He is, so to speak, the prototype of an intrinsically motivated person.

Growing up in Basel with a brother 6 years younger, he discovered his penchant for intellectual challenges at an early age. In grammar school, he took Latin and Greek, following the footsteps of his parents. His matriculation project thesis was based on the model of Seneca's lampoon on Emperor Claudius. It was the time when Berlusconi made headlines with his "bunga bunga" excesses. A good opportunity for the high school graduate, who wrote his satire on the would-be Roman emperor bilingually in German and Latin. When he recalls it today, something flashes in Dill's eyes, and one senses what thieving pleasure this work must have given him.

Although it may seem today that Gabriel Dill lives only for the mathematical universe, there is also a world outside for him. He played the violin intensively until moving to Oxford, where he is doing postdoctoral research until next spring. He is a member of the Juso Basel, enjoys hiking and loves creative writing.

One may think of Gabriel Dill as a happy person. A kind of philosopher who has not forgotten childlike wonder. "Actually, mathematics is a language that understands and explains many natural phenomena," he explains, echoing the definition of mathematics as an "auxiliary science." But he goes on: "You can also just explore this language as a universe unto itself."

### Related topics

Gregor Weiss has two passions: mountain sports and biology. What connects the two? You can only reach your goal with perseverance and team spirit. This also applies to his work on the body's own defence against urinary tract infections, which earned him the Prix Schläfli award in biology.

Image: Miki FeldmüllerHer work could pave the way for new forms of cancer screening: Claudia Aloisi researched a new method for quantifying and determining DNA damage at ETH Zurich. She got the Prix Schläfli award in chemistry for this.

Image: ETH Zürich / Nicola PitaroThe body's own defence against urinary tract infections, a new method for quantifying and determining genetic damage, evidence in so-called Diophantine geometry and the question of how soot from combustion processes influences the formation of clouds and thus, the climate – the Swiss Academy of Sciences (SCNAT) is awarding the Prix Schläfli 2021 to the four most important insights of young researchers at Swiss universities. Claudia Aloisi (Chemistry), Gabriel Dill (Mathematics), Fabian Mahrt (Geosciences) and Gregor Weiss (Biology) receive the prize for findings in their dissertations. The Prix Schläfli is awarded annually to the four best dissertations in the natural sciences. This prize was first awarded as early as 1866.

Image: M. Feldmüller, G. J. Crescenzo, ETH Zürich / N. Pitaro, M. BosshardHis field of research is the smallest particles with a large effect: Prix Schlaefli award winner Fabian Mahrt has investigated the conditions under which carbon black (soot) forms ice particles. He first had to build the apparatus for the innovative experiments.

Image: Giuseppe J. Crescenzo