Still struggling to understand. You're saying that most coding has no high level ideas and is just boilerplate, and the ones that aren't are the ones LLM's struggle with? This could be true I can see it.
WRT the understanding not being shown on the page in math, I guess I tend to agree(?). But I think good mathematical papers show understanding of the ideas too more than just the proofs which result from the understanding. The problem (probably you know this but just for the benefit of whoever is reading) is that "understanding" in mathematics, at least with respect to producing proofs, often rely on mental models and analogies which are WRONG. Not like vague but often straight up incorrect. And you understand also the limitations of where the model goes wrong. And it's kind of embarrassing (I assume) for most people to write wrong statements into papers even with caveats. For simple examples there's a meme right where to visualize n-dimensional space, you visualize R^3 and say (n-dimensional) in your head. In this sense I think it's possibly straight-up unhelpful for the authors to impose their mental models on the reader as well (for example if the reader can actually visualize R^n without this crutch it would be unhelpful).
But I'm not sure if this is what distinguishes math and programming. There's also the alternative hypothesis that the mental work to generate each additional line of proof is just order of magnitude higher than the average for code. Just meaning that it usually requires more thought to produce a line of math proof. In this possibility, we would expect it to be solved by scaling alone. One thing it reminds of, which is quite different admittedly, is the training of leela-zero on go. There was a period of time where it would struggle on long ladders. And eventually it was overcome with training along (despite people not believing it would be resolved at first). I think in that situation, people summarized afterwards the situation as, in particular situations, humans can search much deeper than other places, and therefore requiring more training for the machine to match the humans' ability.