Ian Stewart leads the reader to the power of mathematics in the study of the Universe. Already the Babylonians explained the motions of the Sun, the Moon, and the major planets by using arithmetic, and in doing so made advances in mathematics. The Greeks in later centuries used geometry to provide a mental image, a first model, for observed celestial motions. Many consequences, such as predictions of lunar and solar eclipses, reached an advanced state. The restriction of using only the simplest geometrical figures, such as circles, as the foundation, however, hampered the progress for many centuries until Johannes Kepler discovered his famous mathematical laws of planetary motion. He ended up using ellipses instead of circles to describe the planetary orbits.