Our institute is one of two mathematically oriented institutes within the Max Planck Society, where approximately 150 scientists and doctoral students work on a variety of research problems. The institute conducts research in both pure and applied mathematics and fosters the exchange of ideas between mathematics and the natural sciences in both directions. Historical experiences show that fundamental problems in physics, chemistry, biology, and other sciences have led to significant developments in mathematics, while mathematics has had a profound impact on these fields. For example, Fourier's studies on heat conduction equations led to the development of Fourier series and harmonic analysis. Additionally, Gauss's practical work as a surveying engineer inspired his theory of surfaces and differential geometry, which in turn laid the foundation for Einstein's general relativity and the Standard Model in particle physics. Heisenberg's formulation of quantum mechanics also accelerated the development of functional analysis, particularly spectral theory for operators. Finally, the Standard Model of elementary particles is formulated within gauge theories, which are based on a profound synthesis of physics, geometry (topology), and analysis.
Mathematics has a unique property: while mathematical insights have a different degree of truth compared to empirical findings and thus are enduring, mathematics as a science is always evolving and adaptable to new requirements. This adaptability is something that a research institute dedicated to mathematics in the natural sciences must also embody.
In terms of research focus, the institute concentrates on selected topics, prioritizing those that are fundamentally important for applications and have the potential for deep and exciting mathematics. It is not bound to specific subfields but seeks what is scientifically fruitful and sustainable. Ultimately, what matters is mathematical depth and scientific creativity.