unknown into realms that lie beyond the limits of human perception.
Without mathematics, it would be impossible, in Goethe’s words, “to
know what holds the world together from the inside.”
I would like to thank Dr. Lossau for allowing me for two years to
present mathematical topics to readers of Die Welt. I retain wonderful
memories of our collaboration.
I wish also to thank Elke Behrends for many photographs, par-
ticularly the photomontages appearing in Chapters 6, 10, and 15. I
am also grateful to colleagues Vagn Hansen (Copenhagen) and Robin
Wilson (Oxford) for the images that they provided (Chapters 53 and
89). Finally, I would like to thank Tina Scherer and Albrecht Weis for
their extirpation of so many typographical errors during proofreading
so that you, dear reader, will not have to be annoyed by them.