From my own perspective, the deeper question concerning sphaerae is to what extent the development of this technology prompted the Greeks and Romans into a new worldview. The technology may have affected not only mathematics, but also the idea that the universe itself is in some sense mechanical — and long before the so-called scientific revolution of the Renaissance. For Samuel Sambursky, the question is
whether these models are only convenient means of illustration, devices adapted to our needs for an ordered description, or whether they represent to a greater or lesser degree some faithful image of a physical reality corresponding to them.
If meant as a faithful image of reality, there are several themes present in such an image. The first would be the realization that gearing, with, where necessary, the addition of pins, slots, and levers, reproduces rather well the celestial properties of determinism, repeatability, regular cyclic motion, and irregular cyclic motion. This set of properties starts to provide a physical explanation for the motions of celestial bodies without ongoing direction or intervention from the gods. This is not to say that the universe is driven by actual gearing, but does suggest that a physical, rather than divine or magical, explanation of its motions is possible, even if the actual details are as yet unknown. Paul Keyser points out that Theodoros, in the fifth century CE, certainly believed in mechanical determinism: the universe moves in a necessary motion like “a machine on wheels and pulleys built by an engineer.” Much earlier, in the fourth century BCE, Eudoxus of Cnidus, Callippus, and Aristotle suggested a universe constructed from nested crystal spheres — some 55 or 56 of them. The spheres could be thought of as a mechanical model even if this construction, they believed, perhaps required divine intervention for the rotations. Turning wheels had been conjectured as cosmic analogies since at least the time of Anaximander, who died around 546 BCE.
The Deeper Question Concerning Sphaerae