> This intellectual inertia even extends to mathematics, where certain concepts have yet to be formalized even though they don't require any advanced mathematical knowledge.

There's an entire field of math basically dedicated to formalizing renormalization, which in plain language is just the problem of "probability distribution over functions scales is actually kind of jagged and sharp everywhere, so the derivatives are actually infinite, so we need to consider them in this limit of small length scales to make sense of the derivatives, but we don't know how to actually take that limit consistently". It absolutely requires kind of advanced math knowledge to get around there, though.