 Kepler has been described “as the last exponent of a form of mathematical cosmology that can be traced back to the shadowy figure of Pythagoras” (Field 1988, 170). It is true that Kepler’s work led the way to Newton’s mechanics, which cannot be described in terms of ancient geometry and number theory but relies on the calculus and which relies on a theory of physical forces that is alien to ancient thought. On the other hand, many modern scientists accept the basic tenet that knowledge of the natural world is to be expressed in mathematical formulae, which is rightly regarded as a central Pythagorean thesis, since it was first rigorously formulated by the Pythagoreans Philolaus ( Fr. 4) and Archytas and may, in a rudimentary form, go back to Pythagoras himself.