>>11564531I have the same feeling. It's also worth noting that there are several things at the intersection of CS, math, and even physics, philosophy, and logic that are very interesting and closely related.
Some of the deeper developments in cryptography and arithmetic geometry are closely connected to both (1) work in algebraic geometry, number theory, and Langlands program, and (2) model theory, logic, and what might loosely be called "structure theory" in algebra. Basically, this is a deep connection between information processing/representation in cryptography/computer science, the relationship between geometry and algebra in mathematical physics, algebraic geometry, and group theory, and finally the concepts of structure, composition, homomorphism, etc. that the logicians and cat theory types work with.
There is something really deep going on here, but I don't think any human being has ever even gotten close to seeing the big picture. All I can say, as someone with very little authority on the matter, is that it appears to be deeply connected to traditional philosophical notions surrounding representation, Platonism, scientific realism, and the very concept of a "scientific" model. It seems like in mathematics, there can't be any notion of an ontologically "fundamental" or "primitive" structure. Everything is determined by relationships and functions within larger structures. One cannot postulate a circle or shape on its own, in isolation. Along with a shape, comes incidence geometry, and from that one finds a doorway into a world of all sorts of universes, affine and projective, Euclidean and otherwise. And as soon as one has presupposed a geometric space, they already have everything they need to do algebra. Reversing the process, we begin with Peano arithmetic (in fact, Pressburger will sufice for many purposes), and within this little system for natural number arithmetic, we already have everything we need to do real analysis.
