  In reconstructing the thought of early Greek philosophers, scholars often turn to Aristotle’s and Plato’s accounts of their predecessors, although Plato’s accounts are embedded in the literary structure of his dialogues and thus do not pretend to historical accuracy, while Aristotle’s apparently more historical presentation masks a considerable amount of reinterpretation of his predecessors’ views in terms of his own thought. In the case of Pythagoras, what is striking is the essential agreement of Plato and Aristotle in their presentation of his significance. Aristotle frequently discusses the philosophy of Pythagoreans, whom he dates to the middle and second half of the fifth century and who posited limiters and unlimiteds as first principles. He sometimes refers to these Pythagoreans as the “so-called Pythagoreans,” suggesting that he had some reservations about the application of the label “Pythagorean” to them. Aristotle strikingly may never refer to Pythagoras himself in his extant writings (Metaph. 986a29 is probably an interpolation; Rh. 1398b14 is a quotation from Alcidamas; MM 1182a11 may not be by Aristotle and, if it is, may well be a case where “Pythagoreans” have been turned into “Pythagoras” in the transmission). In the fragments of his now lost two-book treatise on the Pythagoreans, Aristotle does discuss Pythagoras himself, but the references are all to Pythagoras as a founder of a way of life, who forbade the eating of beans (Fr. 195), and to Pythagoras as a wonder-worker, who had a golden thigh and bit a snake to death (Fr. 191). Zhmud (2012a, 259–260) argues that in one place Aristotle also describes Pythagoras as a mathematician (Fr. 191) and in another as studying nature (Protrepticus Fr. 20) but in neither case are the words likely to belong to Aristotle (see Huffman 2014b, 281, n.7). If Aristotle only found evidence for Pythagoras as a wonder-worker and founder of a way of life, it becomes clear why he never mentions Pythagoras in his account of his philosophical predecessors and why he uses the expression “so-called Pythagoreans” to refer to the Pythagoreanism of the fifth-century. For Aristotle Pythagoras did not belong to the succession of thinkers starting with Thales, who were attempting to explain the basic principles of the natural world, and hence he could not see what sense it made to call a fifth-century thinker like Philolaus, who joined that succession by positing limiters and unlimiteds as first principles, a Pythagorean. Plato is often thought to be heavily indebted to the Pythagoreans, but he is almost as parsimonious in his references to Pythagoras as Aristotle and mentions him only once in his writings. Plato’s one reference to Pythagoras (R. 600a) treats him as the founder of a way of life, just as Aristotle does, and, when Plato traces the history of philosophy prior to his time in the Sophist, (242c-e), there is no allusion to Pythagoras. In the Philebus, Plato does describe the philosophy of limiters and unlimiteds, which Aristotle assigns to the so-called Pythagoreans of the fifth century and which is found in the fragments of Philolaus, but like Aristotle he does not ascribe this philosophy to Pythagoras himself. Scholars, both ancient and modern, under the influence of the later glorification of Pythagoras, have supposed that the Prometheus, whom Plato describes as hurling the system down to men, was Pythagoras (e.g., Kahn 2002: 13–14), but careful reading of the passage shows that Prometheus is just Prometheus and that Plato, like Aristotle, assigns the philosophical system to a group of men (Huffman 1999a, 2001). The fragments of Philolaus show that he was the primary figure of this group. When Plato refers to Philolaus in the Phaedo (61d-e), he does not identify him as a Pythagorean, so that once again Plato agrees with Aristotle in distancing the “so-called Pythagoreans” of the fifth century from Pythagoras himself.  For both Plato and Aristotle, then, Pythagoras is not a part of the cosmological and metaphysical tradition of Presocratic philosophy nor is he closely connected to the metaphysical system presented by fifth-century Pythagoreans like Philolaus; he is instead the founder of a way of life.