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The discrepancy couldn’t be greater: when mathematics professor Thorsten Theobald gives exercises or exams, he thinks, for example, “A square can be divided into two triangles in two ways using a ‘diagonal’. There are five ways to break down a pentagon into triangles using diagonals. How many possibilities are there with the 7-corner and the 20-corner? What law is behind it?” In his own research, he even deals with very general or abstract questions such as: “Does a given system of equations and inequalities only have a finite number of solutions with certain properties, and if so, how many such solutions are there es?” – With his specialty “discrete mathematics” Theobald often encounters surprised faces at first. “Discrete mathematics deals with discrete objects, that is, with objects that are separate from one another and thus distinguishable,” he defines, emphasizing in particular that the word “discrete” here does not mean the opposite of “indiscreet”, i.e. the opposite from “chatty” or “clumsy-confidential”, but that “discrete” rather means the opposite of “continuously”.
However, when Theobald explains how much discrete mathematics is in the application programs (“apps”) of a smartphone or tablet, it becomes clear: Discrete mathematics has its place in our everyday life – for example, when a smartphone is in the mountains, far away from mobile phone networks determines its own location and uses the Global Positioning System (GPS) evaluates the signals from typically eight to ten satellites. “Or look at QR codes,” Theobald continues, “they contain all kinds of information in a square matrix of black and white pixels, for example a certificate of a COVID-19 vaccination, a public transport timetable, an Internet Link or a plane ticket.”
everyday challenges
Airline tickets or vaccination certificates should still be legible if the paper with the QR code printed on it is crumpled or missing a piece, or if the code is scanned by a camera with a dirty lens. Therefore, QR codes must be generated in such a way that the entire information can be reconstructed from only a part of the pixels. “In order to generate error-tolerant QR codes, you have to use discrete mathematics,” says Theobald, “and that’s what fascinates me about this research subject: you’re dealing with comparatively simple, concrete questions that are often raised by problems of everyday life . However, their solutions are anything but clear; on the contrary, they are associated with great challenges and they can only be determined with the help of algorithms or computers.”
It becomes particularly interesting for him when different mathematical sub-areas come together. “That’s often the case in my own research,” emphasizes Theobald, “I can’t always sort questions into separate drawers, I’m often dealing with a continuum of terms that play a role again and again, ‘geometry’ or ‘optimization’, for example, or ‘computer algebra’.” Assignments, i.e. recognizing and investigating structures, had fascinated him as a fifth or sixth grader, reports Theobald and describes how he, back in the early 1980s, fiddling around with the popular Rubik’s Cube rotating puzzle. “Getting to the bottom of things has always appealed to me, and I had my first programming experiences at an early age. So it was actually quite natural that towards the end of my school days I decided to study mathematics and computer science,” says Theobald.
duty and privilege
The university teacher Theobald regards passing on his knowledge and skills to students in courses not only as an obligation, but also as a privilege. “In this way, I can act as a source of ideas for the students and can pass on my mathematical approaches and perspectives to prospective mathematicians,” he emphasizes, adding: “At the same time, I hope that I will do my training job justice in an appropriate way” – by it should benefit students who only take the compulsory courses in discrete and computational mathematics, as well as top students who attend further special courses and have the potential to advance mathematical research a little.
Mathematical research had taken him all over Germany and later also to the USA, including to the elite universities of Yale and Berkeley. But when he was offered a professorship at Goethe University in 2006, “that was an extremely attractive biographical turn for me,” Theobald recalls. This was not only due to the academic reputation of Goethe University, but also because it brought him back to his roots in two ways: “To my professional roots, because I studied here, and to my family roots, because I live in Frankfurt -Höchs born, so to a certain extent I was baptized with Ebbelwoi.”
Stefanie Hense
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