As a mathematician one is accustomed to many things. Hardly any other academics encounter as much prejudice as we do. To most people, mathematics is the most colourless of all school subjects – incomprehensible, boring, or just terribly dry. And presumably, we mathematicians must be the same, or at least somewhat strange. We deal with a subject that (as everyone knows) is actually complete. Can there still be anything left to find out? And if yes, then surely it must be totally uninteresting, or even superfluous.

Thus it is for us quite unaccustomed that our work should so suddenly be confronted with so much public interest. In a way, a star has risen on the horizon of scientific knowledge, that everyone sees in their path.

Experimental mathematics, a child of our ‘Computer Age’, allows us glimpses into the world of numbers that are breathtaking, not just to mathematicians. Abstract concepts, until recently known only to specialists – for example Feigenbaum diagrams or Julia sets – are becoming vivid objects, which even renew the motivation of students. Beauty and mathematics: they belong together visibly, and not just in the eyes of mathematicians.

Experimental mathematics: that sounds almost like a self-contradiction! Mathematics is supposed to be founded on purely abstract, logically provable relationships. Experiments seem to have no place here. But in reality, mathematicians, by nature, have always experimented: with pencil and paper, or whatever equivalent was available. Even the relationship, well-known to all school pupils, for the sides of a right-angled triangle, didn't just fall into Pythagoras' lap out of the blue. The proof of this equation came after knowledge of many examples.