Are there any theorems that can only be explained by analogies requiring knowledge of quantum mechanics?

Question

The theorems I’ve seen in analysis can be explained by analogies that invoke the macroscopic visible world, areas, volumes, life sized physical things in sets. Are there any theorems in math that if dumbed down into an analogy, can only be an analogy understandable with knowledge of quantum mechanics which deals with the smaller of the smaller? Or is it true that all intuition and analogies for explaining any theorems can be explained in both quantum and microscopic terms and macroscopic terms? The many theorems in geometry or topology can be explained using visual observable analogies. Are there any geometric or topological theorems that only make sense if you’re visualizing or understand the relativistic wave equations of the quantum mechanical world? I suppose not because not every mathematician understands QM and no one can see QM. The answer seems to also be no because Schrödinger managed to explain QM using macroscopic cats. And Einstein explained relativism using the touching a hot stove and woman example. But I’ve noticed that those trite analogies abstract way too much info from the real nature of QM.