Our institute is one of two mathematically oriented institutes of the Max Planck Society. Approximately 130 scientists and PhD students are working on a diverse array of research problems.

The mission of the Institute is to carry out research in pure and applied mathematics and to promote the mutual exchange of ideas between mathematics and the natural sciences. History shows that the fundamental problems of physics, chemistry, biology and other sciences have led to important new developments in mathematics, while mathematics has had a profound impact on these fields of knowledge. For example, Fourier's studies of the equations of heat conduction led to the development of the theory of Fourier series and, more generally, to the creation of harmonic analysis. In addition, his practical work as a surveyor inspired Gauss, one of the greatest mathematicians of all time, to develop his theory of surfaces and differential geometry. This, in turn, forms the basis of Einstein's theory of general relativity and the standard model of particle physics. Heisenberg's formulation of quantum mechanics also accelerated the development of functional analysis, especially the spectral theory of operators. Finally, the Standard Model of particle physics is formulated in the context of gauge field theories based on a profound synthesis of physics, geometry (topology) and analysis.

The main areas of mathematical research at the Max Planck Institute for Mathematics in the Sciences are analysis, geometry, mathematical physics and scientific computing. A major research topic is the theory of nonlinear partial differential equations. Its particular foci include:

- Riemannian, Kählerian and algebraic geometry including their interrelation with modern theoretical physics
- Mathematical models in material sciences (microstructures, micro magnetism, homogenization, phase transitions, refraction phenomena, interfaces and thin films)
- Continuum mechanics (the theory of elasticity and hydro- and gas dynamics)
- Many-particle systems in statistical physics and neural networks
- General relativity theory and quantum field theory
- Problems of mathematical biology
- Scientific computing

Most of these mathematical models typically give rise to partial differential equations with strong nonlinearities, whose solutions have singularities or describe complicated vibrational and concentration effects. In practice, these mathematical effects correspond to shock waves, turbulence, material defects or microstructures seen under a microscope. To understand these phenomena, it is necessary to develop analytical tools to identify all the significant mathematical objects. The collaboration between mathematics and modern sciences covers a wide range of topics, including areas with strong interaction with mathematics, such as statistical physics, elementary particle physics, cosmology, celestial mechanics or continuum mechanics, as well as research areas that are only beginning to be mathematized, such as a variety of questions in materials science or biology.

The Institute has *few permanent research posts*. As with other international mathematical research institutes, there is a *strong visitor program* open to mathematicians from all over the world. *Guests* can come to the Institute for a maximum of two years to work on different areas of research. Periodically, leading scientists are invited to assume a prominent position at the Institute as *Sophus Lie Visiting Research Professor*.

On March 1, 1996, our institute officially opened its doors at Inselstraße 22. Today we are very proud to be one of the most renowned mathematical research institutions in the world. We owe this to the numerous scientists who have accompanied us through the last 25 years with groundbreaking research projects, successful doctorates, significant research results and, last but not least, a creative and familiar cooperation. Warmest thanks also go to all employees in administration, library, IT and scientific service, who make our institute a perfectly functioning scientific institution.