Michael Joswig is an international renowned scientist in the field of polyhedral and geometric combinatorics. Since 2013 he is Einstein Professor for Discrete Mathematics/Geometry at the Technische Universität Berlin. With help of his dual expertise Michael Joswig actively supported the development of the software “polymake“, a worldwide used software in the field of discrete geometry.
»Numbers are our friends«
I became interested in programming at an early age. As a teenager, I programmed physical formulas and games on pocket calculators. One of my creations was called “Lunar Lander“; the player's task was to land a space capsule safely on the moon. There were two parameters: height and the landing engines. The number in the display stood for the height above the moon's surface. I ended up programming that game in several different versions. Today, computers play an important role in my research. I am involved in basic research in geometry that I combine with linear optimisation problems in both engineering and biological applications.
Together with colleagues, I programmed the software “polymake“. The program provides a flexible research platform for geometric combinatorics that is used around the world. In a nutshell, polymake gives you geometric information for optimisation tasks. We used it to analyse an engine control problem, for instance, which was dependent on six parameters. Standard methods proved useless in that case, but with polymake, we were able to find other methods that could be employed for modelling.
Precisely because I use computers often, I am always pondering how we can harness their computational power to create valid mathematical proofs. These questions currently make up a highly specialised niche, but I think that we will devote more attention to them in the future, because computers are being used more and more for mathematical problems.
There are quite a few mathematical problems that have hounded me for days, weeks, or even years. They remain in my thoughts when I go home in the evening and well into the night. Then I wake up in the morning and there is a glimmer of a light that can develop into a real idea while I'm in the shower. Puzzling over a problem like that helps me find answers.
Numbers are foreign to so many people. They are not part of their everyday lives and they don't have a very easy relationship with them. As a mathematician, I have absolutely no qualms about approaching numbers; I think we see them differently: numbers are our friends.
Geometric forms are a big part of how I think. I am an avid photographer and when I am taking pictures, I look for geometric forms in my environment. But even when I'm just walking through the city and I see a certain shape or form, it can have an impact on my thought process. It's a form of visual inspiration that takes my thoughts in a new, unexpected direction.