Although Pythagorean philosophy dealt with subjects as wide ranging as politics and religion, mathematics formed the basis of the Pythagorean conception of the universe. Aristotle records that "in numbers they thought they observed many resemblances to things that are and that come to be" (Curd, 28). The Pythagoreans recognized the numerical principles underlying many observable phenomena. Because mathematical principles correspond to so many physical properties of the world, it makes sense for the Pythagoreans to pursue mathematics in their cosmology.
Indeed, Aristotle says that "they supposed the elements of numbers to be the elements of all things that are" (Curd, 28). Unlike the Milesians, the Pythagoreans held the first principle to be mathematical, a non-material source. Anaximander may have come closest to this sort of view when he posited the boundless as the first principle. However, the boundless was unlimited matter. The Pythagoreans differ insofar as their first principle is non-material. In this regard, they may have been closer to Xenophanes, who believed in a prime, eternal, and immutable god. Yet it is unclear whether or not Xenophanes held this god to be material. He certainly did not attribute anthropomorphic traits to it, but it is not clear that he held this god to be immaterial.
Consequently, the Pythagoreans contribute a unique conception of the cosmos to Greek philosophy. They maintain that the underlying stuff of the universe is mathematical. Additionally, their first principle is uniquely non-material. Mathematical principles are more intelligible than tangible, so this provides a more abstract cosmology than had been presented by Xenophanes or the Milesians.