About the Institute

Fundamental questions in the natural, engineering, and economic sciences have long inspired mathematicians to seek new mathematical structures and methods. The interaction between mathematics and the natural sciences is at the core of the research conducted at the Max Planck Institute for Mathematics in the Sciences (MiS).

Institute Profile

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.

Institute History

The Max Planck Institute for Mathematics in the Sciences (Max Planck Institute for Mathematics in the Sciences, abbreviated as MPI MiS) was founded in 1996 as part of the Max Planck Society for the Advancement of Science (MPG). On March 1 of that year, it opened its doors at Inselstraße 22 in Leipzig.

The choice of Leipzig as the location for the new institute was influenced by the outstanding scientific and personal reputation of Eberhard Zeidler, who was active at the University of Leipzig and played a leading role in its renewal after the fall of the Berlin Wall. Although Zeidler passed away in 2016, his vision of a deep connection between mathematics and theoretical physics, which guided his scientific life, had a lasting impact on the institute. In 2017, on what would have been his 77th birthday, the institute held a commemorative conference in his honor and renamed its library the “Eberhard Zeidler Library.”

At the institute's founding, in addition to Eberhard Zeidler, Jürgen Jost from Ruhr University Bochum and Stefan Müller from ETH Zurich were also appointed. Jürgen Jost, with his background in Riemannian and Kählerian geometry as well as geometric analysis, later expanded his research perspective to include mathematical biology and neurobiology, developing new methods from geometry and topology to study complex systems. Stefan Müller, who left the institute in 2008, established a new research field at the intersection of phase transitions in materials science, non-convex variation calculus, and geometric analysis.

In 1999, the institute expanded to include a fourth department with the appointment of Wolfgang Hackbusch, who brought scientific computing and numerical analysis to the institute, covering another important aspect of mathematics in the natural sciences. Hackbusch retired in 2013.

The close cooperation with the University of Leipzig allowed the institute to accompany young and promising early-career scientists on their path to a doctorate from the very beginning. Many of them became successful representatives of their field and shaped the development of mathematics in the natural sciences. This collaboration reached a new level with the establishment of the joint graduate school "International Max Planck Research School Mathematics in the Sciences" (IMPRS) in 2005. Since then, the University of Leipzig and MPI MiS have jointly educated doctoral students.

After Eberhard Zeidler's retirement, Felix Otto was appointed in 2010. Known for his work on the connection between optimal transport, diffusion, and gradient flows, Otto dedicated himself to mastering randomness in continuum models. In 2017, the institute welcomed Bernd Sturmfels from Berkeley as a director. Sturmfels, an expert in commutative algebra, combinatorics, and algebraic geometry, opened up a completely new direction at MPI MiS by developing algebraic tools for new approaches in statistics and data analysis. Recently, he has also embraced the institute's tradition of applying geometric methods and principles to physics.

In 2022, the generational change at the institute was completed with the appointment of László Székelyhidi and Anna Wienhard, the latter as the successor to Jürgen Jost. Székelyhidi, a former doctoral student of Stefan Müller, is known for his successful application of partial differential equations and variation calculus, particularly convex integration, to problems in fluid dynamics. Anna Wienhard, as Jürgen Jost's successor, is recognized for her expertise in understanding the deformation of geometric structures, known as higher Teichmüller theory. She applies differential geometric insights and methods to problems in data analysis. With Anna Wienhard's appointment, the Max Planck Society achieved a milestone by appointing a female mathematician as director of a Max Planck Institute for the first time.

In addition to the directors' research groups, the institute's scientific profile is also shaped by our Max Planck Research Groups. These groups serve to promote early-career scientists and offer promising young researchers the opportunity to take their first steps in leading a group. The goal is to accompany mathematical talents on their path to a professorship and support them in the best possible way.

Today, MPI MiS ranks among the most renowned mathematical research institutions worldwide. This success is due to the commitment and innovations of numerous scientists who have accompanied the institute since its founding with groundbreaking research projects, successful doctorates, and significant research results. Our special thanks go to all employees in administration, the library, IT, and scientific services, who, with their dedication and expertise, contribute to making our institute a perfectly functioning scientific institution. With our outstanding scientists, dedicated employees, and innovative research projects, we are well-positioned to continue advancing mathematics in the natural sciences in the future.