  The picture of Pythagoras presented above is inevitably based on crucial decisions about sources and has been recently challenged in a searching critique (Zhmud 2012a). Zhmud argues that the consensus view of Pythagoras’ cosmos as presented above is based on the faulty assumption that there was a progression from myth and religion to reason and science in Pythagoreanism. In many cases, he argues, the evidence suggests that early Pythagoreanism was more scientific and that religious and mythic elements only gained in importance in the later tradition. The consensus picture of Pythagoras’ cosmos assigns number symbolism a central role and treats the tetraktys, the first four numbers, which total to the perfect number ten, as a central concept. Zhmud argues that the tetraktys and the importance of the number ten do not go back to Pythagoras but flourish in the Neopythagorean tradition, while having roots in number speculation in the Academy associated with such figures as Plato’s successor Speusippus. One of the central pieces of evidence for this view is that the tetraktys does not first appear until late in the tradition, in Aetius in the first century CE (DK 1.3.8). However, the tetraktys does appear in one of the acusmata in a section (82) of Iamblichus’ On the Pythagorean Life that is commonly regarded as deriving from Aristotle. Zhmud himself agrees that sections 82–86 of On the Pythagorean Life as a whole go back to Aristotle but suggests that the acusma about the tetraktys was a post-Aristotelian addition (2012a, 300–303). Once again source criticism is crucial. If the acusma in question goes back to Aristotle then there is good evidence for the tetraktys in early Pythagoreanism. If we regard it as a later insertion into Aristotelian material, the early Pythagorean credentials of the tetraktys are less clear.  