[godelski]

  > behind every hard formula lies an intuitive explanation

Probably a good thing to teach people when starting out. Especially since I think one thing people have is converting the symbols to the abstract ideas they communicate.

I agree you're definitely right that a lot of math (if not most) is really unintuitive. But I think I still like the sentiment behind that idea. Maybe it changes with translation, but I feel like that equations make a lot more sense when I break them down and think about what the symbols are doing and looking at their relationships with one another compared to when just looking at them as symbols to manipulate. Like seeing the form F=ma as more than mass and acceleration and but how in structure it is similar to F=-kx. Getting there isn't easy but once you do it is much more intuitive than it was before.