Pretty much all our theories we have–be they in physics, chemistry, biology or astronomy–are formulated in mathematical language. So mathematics seems to be the universal language that applies when it comes to natural phenomena. And mathematics is not at all a closed subject like many outsiders think: it’s something that they’ve learned in school and that’s it. No, mathematics is a science like all the others, and constantly new things are being developed and being explored. And the kind of mathematics I would like to develop or explore is one that might be particularly useful for applications in physics.

I can only truly understand the physics if I can actually understand the mathematics behind the theory.  So, my motivation is on the physics side–I would consider myself a physicist–but the way I work is more like the work of a mathematician. 

Concretely, what I do is called quantum statistic mechanics or quantum many-body problems.  So we try to understand how the microscopic laws of nature that govern the motion of atoms and molecules how they lead to the many different phenomena that we observe in macroscopic systems.

So a simple example is water and ice. The main constituents are the same.  It’s just–it’s just the water molecules but, depending on external parameters like the pressure or the temperature, they might look very different in practice, right?  Not only that, the mathematical theory describing them is exactly the same. One big challenge is to understand how this is–how can the same equations on the microscopic level lead to such drastically different effects on the macroscopic level. And that’s the basic question I’m trying to understand using modern mathematical tools. 

The better we understand nature, the better we understand the structure of materials and so on, and the better we will be able to manipulate them. If one looks back in history, the people who invented our modern theory of quantum mechanics almost 100 years ago, they certainly didn’t have in mind the fact that nowadays we would be using computers and cellular telephones and all this technology, which as a basic input needed our understanding of quantum mechanics which, came much, much earlier.