I'm in a group chat but it's the identity group

The order-6 hexagonal tiling is a regular tiling of the hyperbolic plane, with 6 hexagons joining at each vertex. Its Schläfli symbol is {6,6}. It can be created through alternation of the order-6 square tiling. It is self-dual.

“That’s funny” said the child “because 2+4=6 and two pounds and four pounds is six pounds. It’s like the same as math!”

“What happens if you add 6+1?”

“SEVEN”

“What if we put one pound of mangos on the scale?” <mangos added>

“IT’S THE SAME!!”

“OK, what’s 7-4?”

“Three?”

“What if we take the four pound watermelon off the scale?” <watermelon removed>

Point the First: This is true of almost every skill that you can acquire. You don't ever get good at cooking, you just get bad at more technical dishes. You never get good at guitar, you just get bad at more intricate songs. You never get good at art, you just get bad at more ambitious pieces. The nature of improving is such that in order to grow past your limit you must first be at your limit. This is called the intermediate value theorem. To improve is to struggle, and that is as true of math as it is of anything else.

Point the Second: My first point basically just says "this happens to everyone" which, while true, is not the most comforting message. When I'm actually experiencing these feelings, what makes me feel better is a certain metaphor that I do think applies uniquely well to mathematics:

Learning mathematics is climbing a mountain which is vertical in front of you and horizontal behind you.

Now, for the actual proper metaphor I need more setup (and I could talk at length about why I love this as a metaphor not only for learning math but more importantly for teaching it) but the basic idea is what's in the sentence. In mathematics, even more so than in other subjects, the stuff you learned last year seems trivial and the stuff you're learning this year seems impossible.

This is of course hyperbole, but it's a very real effect which has lead some of the most brilliant mathematicians I know to devalue and degrade their own skills. "I've only learned the easy stuff," they moan, "the hard stuff is beyond me!" Like no, girl, you're just assuming that the topography you see is actually what's there.

Keeping this metaphor in mind is what really makes me feel better about struggling in math, both in that it justifies the "now I'm bad at harder math" feeling (Of course I am! The mountain is so steep here! But I've climbed it before and can do it again!) and the "everything I've learned is trivial" feeling (Of course it is! The mountain is flat there, as a direct result of my efforts! This is something to be proud of!)