The neural network counterpoint feels odd, but with respect to summations and integrals as leaky abstractions I think the author's point is that deploying them

The neural network counterpoint feels odd, but with respect to summations and integrals as leaky abstractions I think the author's point is that deploying them effectively as tools typically depends on a mountain of hierarchical knowledge on top of which elementary calculus is built. I don't know that this is necessarily a requirement -- one could conceive of a world where integrals are taught purely in terms of methods for moving in and out of that concept domain (analogous to the train/predict interface common in ML), and where people are simply taught algebraic rules for manipulating integrals entirely in the realm of integrals without relying on their pedagogical grounding in limits (sort of like how we have high-level descriptions of layers, drop-out, and other concepts that are at the same level of abstraction as neural networks themselves). I think the author claims that this latter approach is rare in mathematics, and it seems they make the stronger claim that mathematical concepts aren't generally amenable to that kind of strategy with integrals and summations as specific examples of where it's impossible. FWIW, I disagree with that assertion, but nevertheless it seems to be what the author is trying to say.