Even more interesting is that when Mathematics does provide something that is useful to physics, when Physics runs with this development, it can be seen as an adaptive trait that has benefits in the current "environment", that necessarily continues to propagate itself throughout the field of study.
What's really interesting here is the viewing of this evolutionary tension in the context of predator and prey. The assumption of one of these two roles by Mathematics and Physics could be fixed, which would be disturbing, though it's more likely to be fluid.
What are the conditions for the switch, and when in history has it taken place?
The first step in this process was taken by Newton, wherein the picture was evolved from one of two dimensional symmetry, to three dimensional symmetry.
What Dirac is referring to here must be about the effect of the laws of motion and the conception of gravity, but I'm not certain about the two dimensional nature of the pre-Newton conception of the number of fundamental symmetries in nature.
The second step was taken by Einstein, who included time as a dimension, to give us a four dimensional symmetrical picture of nature, though this symmetry is not entirely perfect.
There is a bit of extra work to do to integrate the concept of a four dimensional world, when to the consciousness, the world seems to be fundamentally three dimensional. Really, we just experience a three dimensional section of what is effectively a four dimensional reality.
One of the main issues here has to do with the nature of the perception of the passage of time, which, as Kant put it, we perceive based on changes in our internal state, making our experience of it largely interoceptive, though there is certainly exteroception at play, in terms of watching an object move, the motion of the object is analogous to the passage of time.
Interestingly enough, this is the truth of Einstein laid bare, with the connection between space and time as degrees of freedoms being necessary for exteroceptive perception of the passage of time via the observation of motion.
Another giant step forward via Einstein was that the space constituted by the three non-temporal dimensions is curved, via general relativity, which tells us that gravity is the result of that curvature, which is the effect of mass on that space.
One of the issues resulting from this, is that taking the sectional view of things, while applying relativity theory, leads to a removal of a number of degrees of freedom.
The introduction of the quantum was spearheaded by Planck, who realized the energy of electromagnetic waves was always a multiple of a certain unit, which depended on the frequency of the waves, and Einstein noticed this very same unit in his photoelectric effect.
At first, there was no physical understanding of this, until Bohr developed his conception of the atom, which allowed for electrons to move discontinuously between certain orbits, or energy levels of the atom.
This conception however, was only capable of being applied in special situations, particularly when there was only a single electron being analyzed.
 Quantum theory took a large jump forward, via Heisenberg and Schrodinger, whose matrix mechanics and wave equation respectively, allowed for experimental spectroscopy data to be treated properly.