### Invited Presentation: **Discrete Mathematics and Theoretical Computer Science
**

**Martin Grötschel**

*Konrad-Zuse-Zentrum and TU Berlin, Berlin, Germany*

The meaning of the term Discrete Mathematics (DM) has evolved over
the last decades. Today it includes (roughly) classical combinatorics,
graph theory, combinatorial optimization, integer programming,
matroid theory, coding theory, and even some branches of geometry,
algebra, and number theory. Discrete Mathematics overlaps
significantly with Theoretical Computer Science (TCS), in particular
in the theory of algorithms.
Driven by the explosive growth of computing power and by numerous
applications, DM & TCS have experienced tremendous progress in
the last 50 years - both in theory and in their use in practice.
There is no way to cover all the areas and all success stories.
I will focus on a few highlights (of my choice) and will try to
show the advances that have been achieved along these examples.
Success in theory is typically marked by the proof of important
theorems. The max flow-min cut theorem, the characterization of
totally unimodular matrices, the matroid intersection theorem,
the 4-color theorem, and the perfect graph theorem
are five of many examples of a rich harvest of this kind that
I will mention.
Progress is often fueled by new notions and theories providing
suitable tools and concepts for the understanding of unexplained
phenomena. Prime examples here are the concept of NP- and other
types of completeness, general complexity theory, and the theory
of random graphs, all developed in the last 50 years.
Our daily life is full of (usually unnoticed) contacts with DM & TCS.
Whether we ride a city bus, fly in an airplane, find a route with
a car navigation system, order a book, use a phone, or withdraw
money from an ATM, DM & TCS are involved in some fundamental way.
I will present some breakthroughs in the algorithmic solution
technology focussing on large-scale real-world examples
of this kind.