aau/MüllerDaniel Brosch, postdoctoral researcher at the Department of Mathematics at the University of Klagenfurt, is looking into some of the toughest open questions in discrete mathematics. For his research, he recently received a prestigious Marie Skłodowska-Curie Postdoctoral Fellowship, which will take him to the world’s northernmost university in Norway for two years.
“My passion is mathematical problems that are so vast that solutions have not yet been found,” explains Daniel Brosch, postdoctoral researcher at the Department of Mathematics at the University of Klagenfurt. He goes on to say: “At first, I have no idea how to tackle the problem. When I’m faced with a problem like this, I know what I need is new ideas! That’s what I enjoy.” There are still many such major unresolved problems in mathematics, he explains. Wherever the number of variables is high or even infinite, it becomes difficult to arrive at a clear result, even with the help of computers. It is often the case that the solution found is ‘good enough’, but at the same time it is not clear whether it is actually the best solution. Daniel Brosch illustrates this with an example: “When designing a computer chip, various components have to be connected to each other. This requires connections that are routed past each other and over each other. These crossed connections make production more expensive, so you want to keep their number to a minimum. Once you have found a solution for this, I want to prove that the solution cannot be improved upon, i.e. that you have found the optimal solution.”
The way he searches for solutions can be described as follows: “I examine the symmetry of problems together with other hidden structures, then I try to exploit them as far as possible, formulate the problem as an optimisation problem and implement it practically for the computer.” The computer then calculates, sometimes for only a second, but sometimes for a month. “If we’re lucky, the result will be correct.” Or, as in the case of a recent calculation on a large cluster server in California, even though the wrong result is returned, the researchers gain clues to the actual proof: “The giant server calculated for a month, and then the result was 26. But we had assumed that the solution would be 24. This gave us clues to adjust our construction accordingly. ” Ninety percent of Daniel Brosch’s attempts go wrong, but 10 percent work if he is lucky. He is used to sometimes working on a problem for a few years without making much progress.
Research like this requires a special kind of person, as Daniel Brosch’s CV shows. He never had it easy, even though he always had a keen interest in mathematics. His enthusiasm was so great that he began studying mathematics at the University of Cologne at the age of 15, alongside his school studies. At first, it was difficult for him to get to grips with university-level mathematics, but he invested a lot of his free time in learning to understand the structures. After graduating from high school, he only needed two semesters each for his Bachelor’s and Master’s degrees. This was followed by four years at Tilburg University in the Netherlands, where he completed his doctoral studies. There, he was involved in a European network of young researchers and became aware of the postdoctoral position at the University of Klagenfurt. Since 2022, he has been conducting research in the working group led by Angelika Wiegele, Professor of Applied Mathematics, on ‘Discrete Optimisation’.
“I am currently working on two major unsolved problems that no one else has ever been able to solve. Many have already tried and failed. I don’t think I will succeed either, but I want to give it a try,” says Daniel Brosch. His latest success – outside of mathematics – also demonstrates that he enjoys tackling major challenges. Only 9.6 per cent of all applications for scholarships in the Marie Skłodowska-Curie Action ‘Postdoctoral Fellowships’ (European Commission, Horizon Europe) were recently approved. Daniel Brosch’s application was one of them: he will now spend two years conducting research at the world’s northernmost university, UiT Norges arktiske universitet in Tromsø, Norway, under Cordian Riener, Professor of Mathematics.
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A few words with … Daniel Brosch
What is the first thing you do in the office each morning?
Grab a coffee and see who’s around for a chat.
What makes you furious?
I think I have more patience than I should have! It’s not easy to ruffle my feathers.
And what calms you down?
I enjoy reading and crafting, and I make puzzles with my 3D printer.
Do you take proper holidays? Without thinking about your work?
Every weekend is a holiday here! You’ll often find me on the slopes skiing in winter, and otherwise out on Lake Wörthersee or on my gravel bike.
What are you afraid of?
Deadlines! There’s always another one on the horizon.
Der Beitrag The more symmetries, the better: Mathematician Daniel Brosch seeks solutions to seemingly unsolvable problems erschien zuerst auf University of Klagenfurt.