Introduction
I sit with my coffee and wonder, can I explain the general pattern of Mathematics on a single page?
My gut says yes, my brain says maybe, and so I shall give it a go.
Mathematics, the written language
I aim to explain the essential concepts of the Mathematics humans write on rectangular surfaces. In order words, I'm limiting my scope to talk about 2D written mathematics only. Even written math is out of scope, as I've already shown that in earlier work.
My claims are limited to that scope, though you may find these concepts useful beyond this.
Cheating, a bit
I need to admit that although this essay shall not exceed a page (including illustrations), I am undercounting the length of my explanation of Mathematics because I am ignoring the considerable requirements the reader must have developed to be able to parse English.
Ok. No more caveats. Time for the essential concepts in Mathematics.
Pixel Surface
Mathematics requires a 2D contiguous grid of Pixels whose color can be altered.
Cells
Mathematics requires the ability to draw or envision membranes around contiguous groups of pixels to form Cells.
Atoms
Mathematics requires Atoms, which are single indivisible cells with colored pixels.
Particles
Mathematics requires Particles, which are contiguous regions that can contain atoms and other particles recursively (called subparticles).
Holes
Holes are Particles that contain an identification atom and a list of atoms that fit that hole.
Parsers ★
Parsers are a type of particle who's atoms and subparticles define holes. Parsers are pressed against other particles and bind to particles who's subparticles and atoms fit a parser's holes. I put a ★ next to Parsers to indicate that these are the thing you should study to understand this system.
Transforms
Parsers can contain Transform definitions, which are Mathematics that transform one particle into another.
These meta concepts are enough to define all of Mathematics.
These concepts apply not just to formulae, but to geometry, et al as well.