  In the Pythagorean Memoirs, Pythagoras is said to have adopted the Monad and the Indefinite Dyad as incorporeal principles, from which arise first the numbers, then plane and solid figures and finally the bodies of the sensible world (Diogenes Laertius VIII. 25). This is the philosophical system that is most commonly ascribed to Pythagoras in the post-Aristotelian tradition, and it is found in Sextus Empiricus’ (2nd century CE) detailed accounts of Pythagoreanism (e.g., M. X. 261) and most significantly in the influential handbook of the differing opinions of the Greek philosophers, which was compiled by Aetius in the first century CE and is based on the Tenets of the Natural Philosophers of Aristotle’s pupil Theophrastus (e.g., H. Diels, Doxographi Graeci I. 3.8). The testimony of Aristotle makes completely clear, however, that this was the philosophical system of Plato in his later years and not that of Pythagoras or even the later Pythagoreans. Aristotle is explicit that, although Plato’s system has similarities to the earlier Pythagorean philosophy of limiters and unlimiteds, the indefinite dyad is unique to Plato (Metaphysics 987b26 ff.) and the Pythagoreans recognized only the sensible world and hence did not derive it from immaterial principles. In the Philebus, Plato himself tells a story that is very much in agreement with Aristotle’s report. While acknowledging a debt to the philosophy of limiters and unlimiteds, which is found in Aristotle’s accounts of Pythagoreanism and in the fragments of the fifth-century Pythagorean Philolaus, Plato makes clear that this is a considerably earlier philosophy, which he is completely reworking for his own purposes (16c ff.; see Huffman 1999a and 2001). How are we to explain the later tradition’s divergence from this testimony of Aristotle and Plato? The most convincing suggestion points to evidence that, for reasons which are not entirely clear, Plato’s successors in the Academy, Speusippus, Xenocrates and Heraclides, chose to present Pythagoreanism not just as a precursor of late Platonic metaphysics but as having anticipated its central theses.  Thus the tradition which falsely ascribes Plato’s late metaphysics to Pythagoras begins not with the Neopythagoreans in the first centuries BCE and CE but already in the fourth century BCE among Plato’s own pupils (Burkert 1972a, 53–83; Dillon 2003, 61–62 and 153–154). This view of Pythagoreanism finds its way into the doxography of Aetius either because Theophrastus followed the early Academy rather than his teacher Aristotle (Burkert 1972a, 66) or because the Theophrastan doxography on Pythagoras was rewritten in the first century BCE under the influence of Neopythagoreanism (Diels 1958, 181; Zhmud 2012a, 455). Aristotle’s careful distinctions between Plato and fifth-century Pythagoreanism, which make excellent sense in terms of the general development of Greek philosophy, are largely ignored in the later tradition in favor of the more sensational ascription of mature Platonism to Pythagoras. The evidence for the early Academy is, however, very limited and some reject the thesis that its members assigned late Platonic metaphysics to Pythagoras (Zhmud 2012, 415–432). The key text is found in Proclus’ Commentary on the Parmenides (pp. 38.32–40.7 Klibansky). Proclus quotes a passage in which Speusippus assigns to the ancients, who in this context are the Pythagoreans, the One and the Indefinite Dyad. Some scholars argue that this is not a genuine fragment of Speusippus but rather a later fabrication (see Zhmud 2012a, 424–425 and for a response Dillon 2014, 251). If the Academy did not assign the One and the Dyad to Pythagoras, however, it becomes less clear how these principles came to be assigned to him. Theophrastus assigns them to the Pythagoreans (Metaphysics 11a27), but since Aristotle distinguishes the Pythagoreans from Plato on this point, Zhmud’s suggestion (2012a, 455) that he is following his teacher and just taking “the next step” does not work. Theophrastus’ evidence makes best sense if we accept the traditional view and suppose that it is on the authority of Plato’s successors in the Academy that he bases his departure from his teacher’s, Aristotle’s, view.