Claremont Center for the Mathematical Sciences

In this talk we provide evidence for the thesis of the title. We show that techniques from Mathematical Optimization may not only help to solve difficult problems from pure mathematics, but that there are several beneficial side effects for both sides.

We give examples in which modelling a problem as an optimization problem already leads to new views and insights. On the other hand, we show how problems from pure mathematics put special demands on optimization methods. For example, in many cases the exploitation of available structure such as symmetries requires adapted optimization techniques. Another important issue is the verifiability of results when obtained from numerical calculations. As these issues also become more and more important in real world applications, many mathematical problems can well serve as a testbed for future developments in Mathematical Optimization.