Traditionally, the natural sciences form the main focus of the Max Planck Society. The main objective of the natural sciences is to progress towards or contribute to a better understanding of natural processes. Engineering science makes use of this knowledge and develops methods and techniques that allow specific or particular technical systems to be constructed. However, the engineering sciences can no longer be regarded as a field of pure application. Even in this field there is the need for basic research, i.e. long-term fundamental studies. Chemical industries, for example, are trying to meet the increasing requirements of safety, pollution control, and efficiency with greater integration of the plant sections. Production processes, therefore, become increasingly complex. The utilization of biological processes by biotechnology also involves complex dynamic behavior – a topic hardly comprehensible. Micro- and nanoelectronics and -technology encounter similar issues. In order to understand and develop such complex systems, the engineering sciences must take into consideration the natural scientific and mathematical fundamentals of the related processes. Strategies for safe handling and optimal operation of complex systems can only be developed by making use of new methods of systems and information theory. Because of this basic research, engineering sciences must be interdisciplinary. It is compelled to consider both natural sciences and industrial application, and their combination. The requirements for this mediator role cannot be satisfactorily met within the traditional setting for research in engineering science, i.e. universities and industry. For this reason, in 1996 the Max Planck Society decided to establish the Max Planck Institute for Dynamics of Complex Technical Systems, which is the first Max Planck Institute for the engineering sciences. Over time, it has become clear that mathematical descriptions of the processes are indispensable. With the help of mathematics, analysis and optimization of the processes can be prepared for computer simulation. Subsequently, in addition to the three engineering departments, a department of numerical mathematics was established, succeeding the expired department of the founding director.