With the exception of gravity, the physical universe behaves so far as we know, in line with mathematical structures such as groups, fields, and specifically invariant fields.
Of course nobody knows why the universe exists or is as it is - that's more in the realms of philosophy and perhaps religion. As an extreme, the universe could be Terry Pratchett's disk on 4 elephants on a space turtle, a digital simulation, or created picoseconds ago with all past data created at that time too, and if that was how it is, there wouldn't be much point in arguing. So I don't mean to ask stuff about how or why the universe exists and is as it is, in a broad sense. That's off topic here anyway.
But in a narrow sense, as physicists and scientists, is there a reason we might nonetheless tentatively feel that the universe should be well described by essentially, abstract mathematical structures such as groups and fields? With every last familiar entity, all objects and forces, being mere epiphenomena and emergent things arising from those fields?
Or might we, from looking around us and thinking about what we see, somehow expect or anticipate it to be that way?
People immersed in a field often have very refined intuitions and gut senses about it. It wouldn't surprise me if there were reasons to. If we looked around us with 21st century eyes, would these kinds of abstract mathematical structures be what we'd expect to underpin forces and particles, or to parallel the physical world at a subatomic scale, or would it totally surprise us?
