Why do this rather then define an abstract, human-evaluatable, programming language? Give it some S-expr syntax and make more things implicit and you're golden.

Making strange squigles on a page doesn't help. Making strange greek symbols on the page doesn't help. Writing functions, "unit tests", building on abstractions, and creating "libraries" do help. We all know this because it works well in CS. Why would this not work well in physics?

Ditch the alphabet soup (and yes, even the 5th centry Greek alphabet soupe). Abstract common ideas into "functions". Write human-provable "test-cases". Add documentation. Use logically derived variable names (even if they're 5-10 characters). Formalize the definitions and syntax of this language and it's abilities. You'd be golden.

Phi shouldn't mean 30 things depending on the field you're in.

Am I wrong? Is this not possible? Is there a reason as to why math and logic can't be expressed as an abstract programing language? Is there a reason why it wouldn't be better to have a completely standard way as to how to define all of your algorithms and logical assertions?

I could be wrong but no one has provided information as to why what we do is better. Nor does this look much better (what kmill has linked).

yes, it's happening: https://ncatlab.org/nlab/show/Globular

> Use logically derived variable names

I agree. It just becomes a pain in the ass to write this stuff. The greek is math-asm for the hand.

> completely standard way as to how to define all of your algorithms and logical assertions?

people are working on it, for example: https://github.com/UniMath/UniMath "This coq library aims to formalize a substantial body of mathematics using the univalent point of view."

One thing to note however is that the mathematics in the OP is inherently two (and higher) dimensional, and so it makes much more sense to adopt a language that is two (or higher) dimensional. Squashing it down into one dimensions (like with a usual language) creates a big mess.