There is a major confusion embedded in your mind, a term that is trying to mean too much.

That term is “Mathematics”.

If you ask the average layperson what they think of mathematics, their reaction will range from mild distaste to pure hatred. The word “mathematics” evokes boring theorems and arduously memorized proofs. It brings to mind the strange and archaic symbols used to express obvious-in-retrospect ideas.

$\sum\limits_{n=0}^\infty x_n$

If you ask someone who has studied engineering or the sciences what they think of mathematics, they will tell you that math is not something which can be loved or hated, for math is simply The Rules. It is any pattern, any symmetry, any abstraction. You can no more hate math than you can hate the fact that reality is ordered. Sure, the language of math is a bit old, but symbols are not symbolism. Math is not the language, it’s what the language says.

Blue Flower

If you ask a mathematician what they think of mathematics, they will answer that math is the exploration of the rules. Given any axioms, math is about plumbing the logical depths that those axioms imply. It’s about listening to what the rules say and discovering new true things. It requires incredible creativity and the rewards are boundless, but it’s not for everyone.

Julia

These are three wildly different definitions for “mathematics”. Which is true?

Is math $\Sigma$ and $+$ and $\frac{1}{4}$ and the other cumbersome notation?

Is it the underlying truths of any system, regardless of the notation used?

Or is it the exploration of underlying rules, the pursuit of truth?

Mathematics is all of these things. It is a word that means too much.

Simplifience discards the term “Mathematics”. We shatter it into its component parts and use those instead.

The underlying rules of any system don’t need a special name. It’s enough to say that we have a model or a system. Anything that works has Rules which flow from Axioms.

The language and notation used to describe such rules will be referred to as the “formalization”. Models and systems have formalizations. If they work, you can figure out how they work and write it down. The specific squiggles that you use are inconsequential.

The exploration of rules in pursuit of new truths is not within our scope. Exploration of underlying rules is among the noblest of pursuits. It leads to deep and unexpected revelations which greatly expand our knowledge of the universe. It is the realm of those who wish to step beyond simplifience and discover new laws of reality.

Math is not a single word: it is one label trying to mean too many things. It is a contrive. We choose to discard the word. We shatter it and move on.