  There is more controversy about the fourth-century evidence. Zhmud argues that Isocrates regards Pythagoras as a philosopher and mathematician (2012a, 50). However, it is hard to see how the passage in question (Busiris 28–29) supports this view. Nowhere in it does Isocrates ascribe mathematical work or a rational cosmology to Pythagoras. He reports in general terms that Pythagoras brought “ other philosophy” to Greece from Egypt but what he emphasizes is that Pythagoras was “more clearly interested than others in sacrificial rites and temple rituals.” It is true that earlier, in a passage that does not mention Pythagoras (Busiris 22–23), Isocrates had said that some of the Egyptian priests studied mathematics but if Isocrates thought Pythagoras also brought mathematical learning from Egypt he has chosen not to say so explicitly. What Isocrates emphasizes about Pythagoras is what the rest of the early tradition emphasizes, his interest in religious rites. Fr. 191 from Aristotle’s lost work on the Pythagoreans reports that Pythagoras “dedicated himself to the study of mathematical sciences, especially numbers” and Fragment 20 from Aristotle’s Proptrepticus says that Pythagoras said that human beings were born to contemplate the heavens and described himself as an observor of nature (Zhmud 2012a, 56 and 259–260). Unfortunately, in neither case are the words in question likely to be Aristotle’s. Fr. 191 comes from a book on marvels by Apollonius (2nd BCE?). The words in question come before Apollonius mentions Aristotle and, as Burkert pointed out (1972a, 412), are overwhelming likely to be by Apollonius himself, since they serve as the transition sentence between Apollonius’ account of Pherecydes and his account of Pythagoras. In the face of the huge extant corpus of Aristotle’s works in which he never ascribes any mathematical work to Pythagoras, a single sentence that is not ascribed directly to Aristotle and that, in terms of function, appears to be the work of Apollonius and not Aristotle cannot with any confidence be used as evidence that Aristotle regarded Pythagoras as a mathematician. The same situation arises with Fr. 20 of the Protrepticus. If the words in question were by Aristotle they would be his sole statement that Pythagoras was a natural philosopher. The case of Fr. 20 is even more tenuous than that of Fr. 191. Fr. 20 comes from Iamblichus’ Protrepticus, large parts of which are likely to derive from Aristotle’s lost Protrepticus but, as is his practice, Iamblichus does not make any explicit reference to Aristotle. The further problem with Fr. 20, as Burkert noted (1960, 166–168), is that the same story is told first about Pythagoras and then immediately afterwards about Anaxagoras: both are asked why human beings were born and both answer “to contemplate the heavens” (Iamblichus, Protrepticus 51.8–15). This awkward repetition of the same story about two different people immediately suggests that only one story was in the original and the other was added in the later tradition. This suggestion is strikingly confirmed by the fact that Aristotle does tell this story about Anaxagoras in his extant works (Eudemian Ethics 1216a11–16) but not about Pythagoras. Thus, if the passage in Iamblichus’ Protrepticus is, in fact, from Aristotle, it is very likely that only Anaxagoras appeared in Aristotle’s version and that Pythagoras was added in the later tradition, perhaps by Iamblichus himself. Since these two passages are unlikely to be from Aristotle, there are no references to Pythagoras as a mathematician or as a natural philosopher either in Aristotle’s extant works or in the fragments of his works. Aristotle only knows Pythagoras as a wonder working sage and teacher of a way of life (Fr. 191). Aristotle’s attitude is similar to his predecessors in the earlier fourth century: Plato’s sole reference to Pythagoras is as the founder of a way of life and Isocrates emphasizes both the way of life and the interest in religious ritual.