 It is difficult to be sure of Hippasus’ dates, but he is typically regarded as active in the first half of the fifth century and perhaps early in that period (Burkert 1972a, 206; Zhmud 2012a, 124–125). The split in Pythagoreanism may have occurred after the main period of his work and was perhaps connected to the attacks on the Pythagorean societies by outsiders around 450 BCE (Burkert 1972a, 207), but certainty is not possible. Zhmud (2012a, 169–192) has argued that the split is an invention of the later tradition, appearing first in Clement of Alexandria and disappearing after Iamblichus. He also notes that the term  acusmata appears first in Iamblichus (On the Pythagorean Life 82–86) and suggests that it also is a creation of the later tradition. He admits that the Pythagorean maxims did exist earlier, as the testimony of Aristotle shows, but they were known as symbola, were originally very few in number and were mainly a literary phenomenon rather than being tied to people who actually practiced them (Zhmud 2012a, 192–195). The consensus view, which accepts the split, is based on Burkert’s argument that Iamblichus’account of the split between the acusmatici and mathêmatici can be shown to be derived from Aristotle (1972a, 196). Burkert later reaffirmed this position, although with a little less confidence, asserting that the Aristotelian provenance of the text is “as obvious as it is unprovable” (1998, 315). Indeed the description of the split in what is likely to be the original version (Iamblichus, On General Mathematical Science 76.16–77.18) uses language in describing the Pythagoreans that is almost an Aristotelian signature, “There are two forms of the Italian philosophy which is called Pythagorean” (76.16). Aristotle famously describes the Pythagoreans as “those called Pythagoreans” and also as “the Italians” (e.g., Mete. 342b30, Cael. 293a20). Thus, Aristotle remains the most likely source. Zhmud also argues against the split on the grounds that there are no individuals in the historical record that can be confidently identified as acusmatici. Since the acusmatici were neither original nor full-time philosophers, however, and simply preserved the oral taboos handed down by Pythagoras, it is not surprising that they are not singled out for attention in the sources. Only a relatively small number of the names in Iamblichus’ catalogue can certainly be identified as mathêmatici and most of the others, particularly the 145 individuals whose names are only known from the catalogue, are likely to be acusmatici, who to a greater or lesser degree followed the Pythagorean acusmata, but left no other trace of their activity. In addition, a number of other Pythagoreans of the fifth and fourth century, who figure in anecdotes about the Pythagorean life are likely to be acusmatici (see below). 