 In The Refutation of all Heresies, the Christian bishop Hippolytus (died ca. 235 CE) adopts the strategy of showing that Christian heresies are in fact based on the mistaken views of pagan philosophers. Hippolytus spends considerable time describing Pythagoreanism, since he regards it as the primary source for gnostic heresy (see Mansfeld 1992 for this and what follows). Hippolytus’ presentation of Pythagoreanism, which groups together Pythagoras, Plato, Empedocles and Heraclitus into a Pythagorean succession, belongs to a family of Neopythagorean interpretations of Pythagoreanism developed in the first century BCE and the first two centuries CE and which also appear in later commentators such as Syrianus and Philoponus. Hippolytus’ interpretation shows similarities to material in Eudorus, Philo Judaeus, Plutarch and Numenius among others, although he adapts the material to fit his own purposes. He regards Platonism and Pythagoreanism as the same philosophy, which ultimately derives from Egypt. Empedocles is regarded as a Pythagorean and is quoted, sometimes without attribution, as evidence for Pythagorean views. According to Hippolytus the Monad and the Dyad are the two Pythagorean principles, although the Dyad is derived from the Monad. The Pythagoreans recognize two worlds, the intelligible, which has the Monad as its principle, and the sensible, whose principle is the tetraktys, the first four numbers, which correspond to the point, line, surface and solid. The tetraktys contains the decad, since the sum of 1, 2, 3 and 4 is 10, and this is embodied in the ten Aristotelian categories, which describe the sensible world. The pseudo-Archytan treatise,  The Whole System of Categories, had already claimed this Aristotelian doctrine for the Pythagoreans (see 4.2 above). Finally, the intelligible world is equated with Empedocles’ sphere controlled by the uniting power of Love in contrast to the world of sense perception in which the dividing power of Strife plays the role of the demiurge (Refutation of all Heresies 6, 23–25).