> This "new math" might be a recombination of things that we already know
If you know anything about the invention of new math (analytic geometry, Calculus, etc.), you'd know how untrue this is. In fact, Calculus was extremely hand-wavy and without rigorous underpinnings until the mid 1800s. Again: more art than science.
And yet nowadays you can restate all of it using just combinations of sets of sets and some logic operators.
Newton and Leibniz were "hand-waving"?
If anything, they were fighting an uphill battle against the perception of hand-waving by their contemporaries.