My two cents (as someone a bit more familiar with this stuff):
I don't think there is a single universal skill at play. Much like reading code, I think it depends on your familiarity with the specific 'programming language' in which the code/argument is written: show, say, Lisp to a Javascript-only programmer, and they would likely get stuck as well.
In this particular case, I happen to be familiar with this particular dialect of mathematical physics (and its style of argumentation), so I was able to follow along. But show me, say, some crazy algebraic number theory stuff, and I would be totally lost.
Going back to your question, then, I suggest getting familiar with the particular mathematical 'dialect' (and, I cannot emphasize more, style of argumentation) you are interested in.
For example, in this particular case, I would read up on --and, ideally, develop some 'muscle memory' for-- (some) differential equations and multivariate differential calculus using, say, Khan Academy.
(A bit of familiarity with the somewhat non-constructive style of argument of 'modern' classical mechanics wouldn't hurt either.)
I don't think there is a single universal skill at play. Much like reading code, I think it depends on your familiarity with the specific 'programming language' in which the code/argument is written: show, say, Lisp to a Javascript-only programmer, and they would likely get stuck as well.
In this particular case, I happen to be familiar with this particular dialect of mathematical physics (and its style of argumentation), so I was able to follow along. But show me, say, some crazy algebraic number theory stuff, and I would be totally lost.
Going back to your question, then, I suggest getting familiar with the particular mathematical 'dialect' (and, I cannot emphasize more, style of argumentation) you are interested in.
For example, in this particular case, I would read up on --and, ideally, develop some 'muscle memory' for-- (some) differential equations and multivariate differential calculus using, say, Khan Academy.
(A bit of familiarity with the somewhat non-constructive style of argument of 'modern' classical mechanics wouldn't hurt either.)