Even math geniuses can't know what an equation means without telling what its variables stand for.

When reading math makes sense, it cannot be put into words truly.
But when writing proofs in symbols, it cannot take place of language either.
However, without combining symbology and language, I won't be able to comprehend.

Sometimes the clarity of a geometry is only appreciated by learning symbology which skates around such form.

Just prove everything with the chain rule or by making it equal to zero.
Sure it seems to work?!
What ignorance will I find myself in next month?

Solutions in differential topology simply must include one or two definitions which are building blocks to the given solution.
In other words, they don't have to reinvent the wheel of mathematics.
Note to self: I was doing it "right" all along.

In fact, not answering a math question exactly like pedagogy is just using common sense.
It seems like such an easy statement from induction, but so profound from deduction.

The self-math brain leaves me with only a space in my head, even without a tongue.
Ready to reflect only "numbers" back at myself.
It is rather humiliating actually not to have a narrative in my brain besides "math", "math", and again "math".

The idea is to learn math without losing ingenuity, curiosity, questions, and doubt.

The multiplication of complexity in math can only occur if there are simple agreements made of previous complexity.
So it is not so much a "web" but a house of cards.

The difficulty of visualization comes from 3-ness which gives rise, as Lao Tzu said, to everything-ness.

More depth of understanding of math could come from breadth of sources.

Like reading among other things, problem solving starts from a child, so not until every small problem is solved on the way to the big one, will there be a real answer.
That's why some children keep asking "why?"