Archimedes. Mathematics in turbulent times (Q2842522)

The author, a mathematician, aims to explain Archimedes' thoughts to a broader audience. After a biographical introduction, the book focuses on 72 central theorems of Archimedes' works. It does neither intend to give a complete description of them nor a mere translation of the demonstrations. It concentrates on a clear explanation of his proof methods. What matters here is Archimedes' mathematical thinking and mathematical achievements with regard to the parabola, the cylinder, the cone, the sphere, spirals, paraboloids, floating bodies and regular bodies. In other words, Aumann prefers a mathematical instead of a historical approach and makes every effort to support the reader's understanding. For that reason he added an appendix that contains nineteen theorems of school mathematics that he often needs in his explanations. Special emphasis was laid on the exactness and clearness of the nine tables and 174 maps, photos, and geometrical figures. From the mathematical point of view this is a very fine, instructive book. Historical details are not always reliable because old mistakes are repeated: Archimedes did not use infinitesimals but indivisibles (p. 70). The famous letter to Eratosthenes is not a ``methodology'' (p. 70) but an ``approach (ephodos) related to mechanical theorems''. The title of Kepler's ``World harmony'' is not ``Harmonices mundi'' (p. 218) but ``Harmonice mundi'' etc.