Memory skills and the ability to do quick arithmetic in your head (the two go hand in hand). I would suggest reading some of Dominic O’Brian’s books, and then visit the various mnemotechnic forums. Most of the techniques you will find are geared towards memorizing for competitions, but with slight adjustments they can be used anywhere.
It seems a little silly at first, but it has probably been the biggest return on investment I have ever made. I started practicing these techniques last summer, and when school started I used them (Method of Loci especially—basically you just imagine a spatial location you know well and place images representing the things you want to memorize at unique points in your spatial journey) to memorize as much as I could, using spaced repetition software (mentioned somewhere else on this thread) to lock the most important things in.
Now, instead of writing down copious amounts of notes in class and not understanding a single thing, I just sit, listen, and memorize. I’ll also write down broad labels for things I need to make sure I remember (i.e if we are talking about “normal subgroups”, I will write down “normal subgroups”, but memorize the rest. This is just to have a hook to the topic so I can look it up later if I don’t remember something). By focusing on the images I am creating in my head, I’ve noticed that it even helps me focus more intensely on the topic that the images are referencing. By the time class is over, I can run through the entire lecture as if I was reading a book. This is the best part, really; it’s completely flipped my idea of studying on its head. Now I can just sit in the park and think, and it will qualify as studying because I have an entire book in my head with images to play around with.
I’ve also used it to memorize entire textbooks (not word for word, more like “page for page”). Again, it seems silly and pointless at first, but it really works wonders when you get the hang of it. Instead of belaboring over a topic that you don’t understand and then an hour later looking back 10 pages to see the illuminating point, all you have to do is rewind a “walk through your friend’s house” or “a drive to the beach”. At first it will take 10 times longer to do this than it would to just read the book. Currently, it only takes me about twice as long. I just have to make sure I go back through it in my head later on so I can plant it in my long term memory (spaced repetition is amazing for this).
It takes a hell of a lot of work though, if you want it to be more than a gimmick. And there doesn’t seem to be much information for people who want to use it for scholarship rather than for their shopping lists. Even posts I’ve seen here about the method of loci seem pretty dismissive of its utility, that it doesn’t help you understand. I think these claims are somewhat valid, but it’s like using Mathematica to solve integrals and then claiming that it doesn’t help you understand them. Well, yeah. But you could construct a 3d plot of an integral, and even make it interactive to see how it changes when you change some of the variables. Surely that will help you understand more. It’s the same thing for mnemonics. I could memorize a book word for word using these techniques and not understand a single thing; or I could take concepts and ideas from a page, mold a visual representation of them in my head, and make sure that my notion of how the representation acts and looks is congruent with these concepts and ideas. Then as I learn more, I go back and adjust this image for any discrepancies, and also use the image in later scenes when the concept/idea comes up again. Kind of like OOP in your imagination. They don’t have to be valid physical models for your concept, only approximations of the idea as you understand it in visual form. It surprised me how illuminating these approximations can be—more than once I have attempted to create a visual image only to get stuck and realize “Ah, that’s what I don’t understand!”.
Even if creating images doesn’t help you understand, using this method is still an amazing way to create hooks for stumbling points in your reasoning. It’s like having a jumper cable for your mind at all times. For any topic or concept you know you understand but have trouble at certain points, just make an image reminding you of the key elements and place it in your chosen spatial journey. When you need your reasoning, moving through your spatial journey and seeing these images will trigger a domino effect and you’ll slide right through with no trouble.
Anyway, sorry for the jumbled wall of text. I’m trying to communicate how fucking useful this has been for me, but it’s a little difficult with this kind of personal topic. So even if you find my reasons too subjective, I implore you to really try it. Not with the mindset that it’s a stupid little parlor trick, but that it has the possibility to be a huge improvement in how you assimilate knowledge.
Also, learn to differentiate between genuine curiosity and what I like to call pseudo-curiosity—basically, being satisfied by conclusions rather than concepts. Don’t let the two overlap. This is especially hard when conclusions are most of the time readily available and often the first item in a google search. In terms of genuine curiosity, google has been the bane of my existence—I will start off moderately curious, but instead of moving to that higher stage of curiosity, I will be sated by facts and conclusions without actually learning anything (similar to a guessing the teacher’s password situation). After a couple hours of doing this, I feel very scholarly and proud of my ability to parse so much information, when in reality all I did was collect a bunch of meaningless symbols.
To combat this, I started keeping a “notebook of curiosities”. The moment I get curious, I write whatever it is I’m curious about, and then write everything I know about it. At this point, I determine whether or not anything I know is a useful springboard; otherwise, I start from scratch. Then I circle my starting node and start the real work, with the following rules:
Every fact or concept I write must follow directly from a previous node (never more than two or three reasoning steps away). Most of the time, this results in a very large diagram referencing multiple pages. I use pen and paper only because I like to use it outside.
Wikipedia is a last resort—I don’t want to be tempted by easy facts. I use textbooks → arxiv → jstor → google scholar in order of preference. It’s a lot of work.
If I skip some reasoning or concept because I think it is trivial, I write the reason why it is trivial. Most of the time, this results in something interesting.
Doing this has revealed many gaps in my knowledge. I’ve become increasingly aware of a lack of internalization of basic concepts and modes of thinking that are necessary for certain concepts. It also forces me to confront my actual interest in the subject, rather than my perceived interest.
The majority of what I use it for is math related, so it’s more tailored to that use case.