Classically, one could imagine a completely static space, thus without time. As is known, this picture is unconceivable in quantum physics due to vacuum uctuations. The fundamental difference between the two frameworks is that classical physics is commutative (simultaneous observables) while quantum physics is intrinsically noncommutative (Heisen-berg uncertainty). In this sense, we may say that time is generated by noncommutativity; if this statement is correct, we should be able to derive time out of a noncommutative space.
The interplay between Mathematics and Physics has been constant over the centuries, with a sort of discontinuity soon after the Quantum revolution. Physics always provided a direct, or indirect, source of inspiration for Mathematics. On the other hand, Physics theories were established on mathematical grounds.