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Excuse me if this question is better fitted for another SE, as it is somewhat more of a meta question, but still on-topic.

As a background, I'm an undergraduate Mathematics major in my final semester, currently planning to take a gap year and apply to Math PhD programs.

Since my 3rd year, I've been typing up all my homework assignments in TeX even when not collected, and that has gained me lots of useful knowledge of the language. However, when perusing published papers and stuff like that (or even just TeX.SE threads!) I am consistently mind-boggled by the level of detail and variety of structures that can be created in TeX, much beyond my current ability.

So my question is, besides just using TeX to type up standard homework problems, and reading the various manuals and Tex.SE, are there any practical approaches for improving general TeX fluency and capabilities, for instance, to the approximate level needed for professional academic mathematics writing?

As a corollary, is this even something that people intentionally practice, or is it basically always 'learn as you go' as you encounter specific problems?

pyridoxal_trigeminus
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    For me, it was learn as you go. But I read up on good typography and a little bit on graphics design. When I then tackled a document, I sometimes had ambitious output in mind and then looked up how to achieve it in LaTeX. Many patterns for things I regularly wanted, I now remember. – TeXnician Mar 20 '22 at 08:34
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    To learn, teach. Directed learning will gain wider understanding. See if you can start answering questions, or, if you don't know, find out by researching, what the answer will be. Try emulating equations and layouts in papers you have seen. Find the limits of what is possible. Learn more of "deep" packages, like unicode-math and tikz. Are there specialist packages for your area? (e.g. knots). If not, should you write some? There will be half a dozen ways of implementing any one solution - what are their differences and benefits? Play. Etc. Answer: "Yes", to both limbs of your corollary. – Cicada Mar 20 '22 at 10:39
  • Perhaps https://tex.stackexchange.com/questions/1319/showcase-of-beautiful-typography-done-in-tex-friends may lead to ideas. – Cicada Mar 20 '22 at 10:43

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