I sometimes think math notation is a conspiracy against the clever but lazy.
Being able to pronounce the greek alphabet is a start, as you can use your ear and literary mind once you have that, but when you encounter <...>, as in an unpronouncable symbol, the meaningless abstraction becomes a black box and destroys information for you.

Smart people often don't know the difference between an elegant abstraction that conveys a concept and a black box shorthand for signalling pre-shared knowledge to others. It's the difference between compressing ideas into essential relationships, and using an exclusive code word.

This fellow does a brilliant job at explaining the origin of a constant by taking you along the path of discovery with him, whereas many "teachers" would start with a definition like "Feigenbaum means 4.669," which is the least meaningful aspect to someone who doesn't know why. https://www.veritasium.com/videos/2020/1/29/this-equation-wi...

It wasn't until decades after school that it clicked for me that a lot of concepts in math aren't numbers at all, but refer to relationships and relative proporitons and the interactions of different types of things, which are in effect just shapes, but ones we can't draw simply, and so we can only specify them using notations with numbers. I think most brains have some low level of natural synesthesia, and the way we approach math in high school has been by imposing a three legged race on anyone who tries it instead.

Pi is a great example, as it's a proportion in a relationship between a regular line you can imagine, and the circle made from it. There isn't much else important about it othat than it applies to everything, and it's the first irrational number we found. You can speculate that a line is just a stick some ancients found on the ground and so its unit is "1 stick" long, which makes it an integer, but when you rotate the stick around one end, the circular path it traces has a constant proportion to its length, because it's the stick and there is nothing else acting on it, but amazingly that proportion that describes that relationship pops out of the single integer dimension and yields a whole new type of unique number that is no longer an integer. The least interesting or meaningful thing about pi is that it is 3.141 etc. High school math teaching conflates computation and reasoning, and invents gumption traps by going depth first into ideas that make much more sense in their breadth-first contexts and relationships to other things, which also seems like a conspiracy to keep people ignorant.

Just yesterday I floated the idea of a book club salon idea for "Content, Methods, and Meaning," where starting from any level, each session 2-3 participants pick and learn the same chapter separately and do their best to give a 15 minute explanation of it to the rest of the group. It's on the first year syllabus of a few universities, and it's a breadth-first approach to a lot of the important foundational ideas.

The intent is I think we only know anything as well as we can teach it, so the challenge is to learn by teaching, and you have to teach it to someone smart but without the background. Long comment, but keep at it, dumber people than you have got further with mere persistance.