[chongli]

No, math is difficult to approach because it's genuinely deep. Trying to verbalize what is going on is extremely difficult, because you end up saying stuff like "and then do that to all of these things, and then do it again to all of the results, and so on ad infinitum, and then take the collection of all of that, and join it with the collection of doing the same procedure as before starting with a different set of objects, and then join those to yet another set of objects and the results of their operations, ad infinitum, ad infinitum..."

People genuinely struggle to think verbally or visually once we extend beyond 3 dimensions and start talking about infinite-dimensional constructs, uncountable sets, and so on...

[sebmellen]

Of course, I understand this, and I hope that my comment didn't come across as saying that math would be easier to "do" if it were all fully verbal. Symbolic reasoning and interpretation are necessary for complex reasoning.

And math is, as you know, a deep but traversable graph. The traversal inherently requires a familiarity with the nodes you pass through when reaching a foreign or more difficult concept.

However, I'll give you an example. If I read through more complex math that I’m not comfortable with in Sage, I can build an intuition for the structure of the problem more easily than if I view the “raw” notation. In that sense, it is easier to for me to “approach” — but approaching something is very different from fluently using it — and I’m under no illusion that approaching a topic is the same as beginning to understand it.

Again, this is definition-dependent. To me, “approaching” something means beginning to glean how I might one day understand it. E.g. watching a 3B1B video feels like “approaching” a topic. Here we reach the limits of language already :)