The title of this book on mathematics is borrowed from Stefan Zweig's "Sternstunden der Menschheit" (Starry Hours of Humanity). While it deals with world history, it does not primarily focus on the well-known historical events, but rather on more obscure ones that nonetheless concentrated the course of world events. The field of science, and particularly mathematics, has many such events to offer. The stories in this book aim to trace the history of mathematical ideas through a very personally motivated selection of events, highlighting their context and consequences, from Pythagoras to Perelman. The journey from surface understanding to deeper comprehension is the essence of mathematics, and particularly spectacular breakthroughs of this kind are "Starry Hours." To truly understand them, it is beneficial to go back to the source and travel to the time when the breakthrough occurred.