This book invites you to marvel: discover how, for example, Archimedes was able to determine the area of a parabolic segment 1,800 years before the invention of "classical" integral calculus, derive a summation formula for square numbers with Ibn al-Haitham, or explore quaternions with Hamilton.The 21 selected ideas are vividly developed with the help of numerous colour illustrations - you will be astonished by the thought processes of mathematicians long since passed!Many ingenious approaches have been almost entirely forgotten by posterity - for instance, the polymaths from the Islamic cultural sphere are scarcely known in Europe today, despite their significant contributions to the development of mathematics. Each chapter therefore also provides information about the lives of these individuals and the eras in which they lived, notes and explanations on further questions they addressed, as well as extensive references to additional literature that is generally accessible.The chapters can be read independently of one another - where appropriate, connections to other chapters are indicated. Most topics can be followed with a solid background in upper or middle school mathematics, making the book suitable for anyone with an interest in mathematics - but also for school study groups and as inspiration for extended essays.This book is a translation of the original German 2nd edition Mathematik - einfach genial! by Heinz Klaus Strick, published by Springer-Verlag GmbH, DE, part of Springer Nature in 2025. The translation was done with the help of artificial intelligence. In the subsequent editing, the author, with the friendly support of John O'Connor, St Andrews University, Scotland, tried to make it closer to a conventional translation. Still, the book may read stylistically differently from a conventional translation.