Mine is probably more specific than most,
I need a sophisticated way to create mathematics notes but non-linearly.
The very basic problem is that mathematics is very definitions driven and sometimes it’s easy to forget what the definition of something is. So backlinking/transcluding/ability to open panes is very help.
The second issue is that there are multiple ways to view the same mathematical object: e.g. the definition of a continuous function in high school math to college. But the college view has multiple ways to look at it, a sequence definition, a topological definition, a geometric definition.
All of these definitions are very precise (where back-linking to definitions helps). But directly having it in the text can get cumbersome. Sometimes I don’t need to see all those different definitions.
Finally, the other main issue is unifying mathematics. For example calculus and linear algebra at the undergraduate level are separate topics but higher level mathematics can unify these with differential forms. Somehow I need to be able to connect these topics together and understand how they interact.
At a very high level, Terrence Tao (very famous mathematician) says he’s able to evaluate whether he thinks a theorem is true or not just based on the implications it would have on the rest of mathematics.
He describes it as a “strain” on his mental web of mathematics. It would be very cool to approach that level, or somehow manage to get his mental web out of his head and onto “paper”.
This relates to a topic I’ve been thinking about for awhile which is “implicit/institutional” knowledge and how to get it out of key people onto paper.