Digging into the foundations of science with Sebastian Krapp
Sebastian Krapp likes to dig deep into the foundations of science. Now a newly appointed lecturer in the Mathematical Foundations of Language at the University of Zurich, and a member of the NCCR Evolving Language, his work provides NCCR research projects with sturdy proof-of-concepts. His career illustrates the importance of interdisciplinarity in science, to have a full picture.
From fundamental mathematics…
Sebastian Krapp always had a knack for mathematics. As he was finishing high school, a teacher convinced him to go and study the topic at Oxford University. There, he discovered algebra and pure mathematics. “I didn’t want to stop digging for the reasons behind things, and that’s how I ended up in mathematical foundation and logic,” he explains. “The only thing that may be deeper would be philosophy,” he adds half-jokingly.
After completing his Master’s degree, he came back to Germany, in Konstanz, for a PhD in model theory. The German academic system allowed him to teach at a university level immediately, which he liked.
Opportunities in fundamental mathematics are scarce, but luckily his supervisor opened a post-doctoral position he was able to get, right after his PhD. For 4 years, he worked on logic and explored other science fields to broaden his view. One of the big projects he conducted was on the foundations of artificial intelligence. “This was just before the topic was cool!” says Sebastian. “Though of course it was already on the rise in the scientific community.”
He worked on concepts like definability, meaning the ability to express a mathematical concept, like a set of numbers, in simple language. Though some sets appear to be very simple, they are actually impossible to describe, like intervals of infinites, for example.
Lecturer Sebastian Krapp © University of Zurich
…To language
But what does fundamental mathematics have to do with language? “Considering my background in pure mathematics, it’s a bit strange where I ended up,” laughs Sebastian Krapp. But generally, mathematical logic deals with the formalization of abstract language, which involves syntax and semantics.
“Around 2021/2022, I was introduced to the topic of formal language theory by a student, who would later become my doctoral student,” he remembers when asked what led him down this path. She asked him for advice on a master’s thesis topic at the intersection of mathematical logic, algebra and theoretical computer science. “It was a good example of a surprising connection between two relatively distant areas – formal language theory and algebra, both dealing with formal abstract objects.”
He joined the NCCR Evolving Language as a lecturer in the Mathematical Foundations of Language at the University of Zurich, in the Institute for the Interdisciplinary Study of Language Evolution (ISLE). It is not so common that people from other fields, especially applied sciences, understand the importance of these foundations. “I’m lucky to be part of the ISLE, an avant-garde institution that is interested in explaining the foundations of language, and that is building new models,” notes Krapp.
In the NCCR Evolving Language
The lecturer’s first project in this new position in language was with Prof John Mansfield’s work. The latter had come up with a computer model that could explain how word order is determined in a noun phrase. It was a possible explanation as the simulations backed up the reality, but he was missing a proof-of-concept, i.e. a demonstration showing that a specific idea, method, or product is soundly based on theoretical mechanisms. “This is where I stepped in,” says Krapp. “You start from the first principle, and you run the algorithm on a sheet of paper, with the goal of proving that the observations made in simulations are mathematically correct.”
Sebastian Krapp is now involved in many NCCR projects, including the WP Hierarchy. A hierarchy is an abstract construct; it doesn’t have a common definition. “We want to mathematically define what a hierarchy is, which could be used to level the playing field and figure out disagreements among scientists,” he explains.
He also accompanies a lot of PhD students, to have proof-of-concepts on their project. He recently started his own group and welcomed his first PhD students! “I also like the managerial aspect of research, like writing grants; I think it’s rewarding to see that people get to have their own project, thanks to my work, Sebastian Krapp comments.
Mathematician vs the world
In the NCCR Evolving Language, Sebastian Krapp interacts with people from various backgrounds.
“Usually, pure mathematics is an isolated field: it is common that mathematicians evolve in their own convoluted bubble and do not interact with the outside world,” says Sebastian Krapp. “I think there is a lot of lost potential.” The people in fundamental mathematics are often not aware that they can be useful in interdisciplinary research. Usually, it’s because mathematicians think working with other fields doesn’t benefit their work as much as other’s. “But there is a way to benefit both, I want to show that it’s not a one-way street,” states Krapp. In the next few years, Sebastian Krapp would love to bring mathematics closer to the ISLE.
Of course, working interdisciplinarily comes with its difficulties, as each field has its culture. For example, Sebastian Krapp dislikes the publication culture of some other fields. Fundamental mathematics follows the lead of the classical humanities for this, where the publication process for a paper may take years, giving enough time for proper reviewing and revision. “ In some disciplines that are represented here, there are external pressures to publish quickly,” says the researcher. “It’s not my point of view of science.”
Sebastian Krapp also likes to confront himself with the real world, outside the doors of the university. “One of the main reasons why I enjoy what I do is because I am involved in science communication,” he says. “And when I’m passionate about something, I like to talk to people about it!” For example, he self-organized outreach events in schools. Many people questioned the choice, he recalls – but for him, outreach is rewarding, especially because so many people carry negative experiences with mathematics and he gets to share his enthusiasm with others.
