 What seems clear is that the early Pythagoreans conceived of nature as a structured system ordered by number (see the entry on   Pythagoras), and that such  post-Parmenidean Pythagoreans as Philolaus (last half of the 5th century, more than a generation after Pythagoras’ death) and Archytas (late 5th to early 4th century) held more complicated views about the relation between mathematics and cosmology than it is reasonable to suppose Pythagoras himself could have advanced. The Pythagorean tradition thus includes two strains. There are reports of a split in the period after Pythagoras’ death between what we would term the more philosophically inclined Pythagoreans and others who primarily adopted the Pythagorean ethical, religious and political attitudes. The latter, called the acusmatici, followed the Pythagorean precepts, or acusmata (which means “things heard”). The former, the philosophical Pythagoreans (including Philolaus and Archytas), were the so-called mathematici, and while they recognized that the acusmatici were indeed Pythagoreans by virtue of accepting Pythagorean precepts, they claimed that they themselves were the true followers of Pythagoras.