I don’t remember where I got this: it was in my memories from a few years ago: but it shows a relationship between these various things and a chemical reactor.
You can read it as all of these things describe what happens in a chemical reactor or you can read it as these things come from chemical reactions ultimately.
None of these are “abstract theoretical mathematics”. Or is it?
Allow me to share something about theoretical chemistry:
The Table of the Elements is an exercise in Theoretical Chemistry. Lining things up just so in a spreadsheet basically, allowing for gaps where some elements may theoretically belong. Then you search for those elements.
It’s a generalization, which is what abstractions are. Patterns.
Theoretical physics describes what’s not there but perhaps something _should_ be there. The subatomic particles, the various string theories, all of which are abstract and theoretical. Maybe concrete existence can be shown one day, maybe not.
Now to theoretical mathematics. There’s a LOT that gets used in current mathematics. It actually is a world full of weird shortcuts and slight-of-hand tricks that work and not at all a logician’s dream.
Much of current mathematics can be applied to concrete systems which is great but it doesn’t have to. Nothing about mathematics MUST apply to reality as it’s abstract by nature being axiom (rule) based. It’s more akin to lawbooks. What’s legal? Is there a law for that? If you break a law maybe there’s a hidden law that should be put in that belongs there?
There may be many laws that haven’t been discovered/invented yet in mathematics. They’re theoretical and abstract. But all of mathematics really is.
Yet oddly it can be grounded to the human motor system which would make sense as it’s used for and by humans and how we think about things and how we think is guided by what guides us internally. But from that foundation it goes up from there.
One excellent use of theoretical mathematics for me has been computing. Alonzo Church’s lambda calculus is the foundation for all computer programming ultimately, as is the work of Alan Turing. Shannon’s information theory in the late 1940s is a VERY abstract generalization of communication into things called ‘bits’ – ‘ datum’ / ‘data’ and all sorts of abstractions from there that BECAME insanely useful far beyond anyone’s imagination