It's an interesting question. Others will be better able to answer, but I would note that the proper evolutionary model here may be punctuated equilibrium or, more pertinently, Kuhn's "Structure of Scientific Revolutions," with its near-random paradigm shifts.
A truly authoritative work, such as Aristotle's logic or Euclid's geometry will hold sway for centuries, until it accumulates too many failures or complications, in the manner of Ptolemy's astronomy. Then some opening will bring cascading change.
Because of its very formalism, I suspect, mathematics may be unusually dependent on taboos. The Pythagoreans felt the the irrationals menaced the cosmic order, or so the story goes. The Greek mathematicians were constrained by their superstitious rejection of "nothing" or "zero" or negative numbers.
Which is not so unreasonable. Imaginary numbers were resisted for similar reasons and many mathematicians, notably Kronecker, had an almost visceral dread of Cantor's set theory, which seemed to be turning math in pure fantasy. The boundary line between "proper math" and wild conjuring is viewed by many as a slippery slope with almost cosmic implications. And concepts like infinity always raised theological shudders.
So, as I say, strong taboos with punctuated equilibria. Someone dares an idea at the very moment some controversy allows an opening and the field can no longer shut that barn door. Sometimes it seems overdue. It is hard to see why Euclid's fifth postulate lasted so long on a spherical planet. Similarly, Descartes' merging of algebra and the grid seems like it could have come at any time, with practical applications.
After Newton, of course, mathematics was developing alongside physics, so practical possibilities drove things on. My favorite "math taboo" was Berkeley's complaint about the infinitesimals or limit in Newton's calculus, which he described as "the ghosts of departed quantities." In this case, the calculus was just too useful to be derailed by metaphysical niceties.