Since I have been studying AI & machine learning at a high age a few years ago, I have been faced again with refreshing my math and statistics comprehension since I studied economics. Math was never my forte, but I love it! It is a very fascinating abstract and logical science very much to my liking!
I think one of the major obstacles to learn math more quickly and better is the lack of a rigorous, international, and universal standardization of notation and symbols used in representing mathematical concepts etc..
I would also postulate that the current language/notation of mathematics is more suitable for rote learners than for non rote learners (e.g. meaningful or associative learners). Thus, the latter are disadvantaged in the field of mathematics or they may not even bother. Thus, if my postulate has some relevance, then the progress or advance of mathematics is seriously impeded.
I also noticed there are only a few websites out there dedicated to explain mathematics in a straight forward way: e.g. Encyclopedia of Math (quite abstract and verbose) and Wolfram Mathworld (a better website for my purposes)
I also think the current traditional and mostly used notation with a centuries old history is not of great help. Greek or Latin letters is all very nice and a compliment of those great mathematicians that came before. Single symbol notation is surely parsimonious, but perhaps also ambiguous and constraining! Why e.g. not use acronyms that most people can associate much better? The immense strive for compactness and abstractness of notation is an obsession!
This practice of notation requires probably most people to do extreme mental acrobatics to follow the whims of mathematicians! This is unnecessary! It is still almost like the language of witchcraft, mystics, or alchemists! A more universal and better developed language would possibly serve better to advance mathematics! When only a few people can really understand what mathematicians or other scientists are expressing than this is a problem! The effort to learn this arcane language are a serious obstacle!
Too many times long mathematical expressions are very repetitive and you have to look very close what term has actually changed from one line to the next. This is totally unnecessary and causes clutter! Instead of using e.g more acronyms or other short forms to replace repetitive terms.
Authors of research studies, book chapters, and books frequently and quite often dramatically change the meaning of notation within a few pages or from chapter to chapter. Often these changes look quite arbitrary and ad hoc. Inconsistency of these changes is another serious issue. Very often you also find the reuse of the same math symbols within pages of each other for very different purposes.
Some authors also like to excuse or admit these change by saying something like with a little abuse of notation.
There is also a strange dichotomy: In mostly theoretical papers, adequate, brief numerical examples are left out almost by default as if it was a plague or too demeaning for a theoretician to be bothered with! Occasionally hints or references to textbooks or tutorials are provided.
It would be highly recommendable that every paper, chapter etc. is preceded with a section summarizing the notation/nomenclature etc. being used with some explanations! Instead, usually scholars seem to make up the notation in their papers as they go.
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