Gauß-Vorlesung - Discrete or Continuous?

From Zeno's paradoxes to quantum physics, the question of the continuous nature of our world has been prominent and remains unanswered. From a mathematical point of view, discrete structures or models behave quite differently from continuous ones. The great success story of mathematics from the 18-th century has been the development of analysis. Discrete mathematics had a later start, with a large boost from computers.

However, these worlds are not as far apart as they seem. Computers force us to approximate continuous structures by finite ones; but perhaps more surprisingly, very large finite structures can be very well approximated by continuous structures, often getting rid of inconvenient details. These approaches cross-fertilize each other.