Abstract
This introductory chapter focuses on the Pythagorean question, which remains one of the most intricate in the history of early Greek science, philosophy, and religion, and has every chance of being consigned to the category of insoluble problems. It suggests that like any other complex scientific problem, it can be broken down into a number of smaller, particular ones, which may prove amenable to solution. There are many facts on which agreement may be reached; there is also an undoubted hierarchy of interpretations, ranging from those admittedly impossible or unverifiable to those which are more probable and internally consistent.