A few years ago I started having an hour most days that I devote to learning and trying new hobbies / habits / whatever, and when I find something interesting I start giving it a 20 minutes slot in that hour until I stop liking it or I feel I've gotten what I want to out of it. I'm nowhere near a professional at any of this stuff but I have a fulfilling level of competence in a ton of interesting things now, and it's brought me a lot of pleasure.
One thing that has helped is signing up for actual university classes as opposed to online courses. Online courses are of course awesome, but taking a few graduate level mathematics courses at a local university really got me back into deep reading, of at least technical material.
Another thing is trying to reduce my anxiety. Instead of worrying about all the books I have that are unread, of which there are hundreds and maybe even over a thousand (yes, I have a problem collecting books), I'm trying to just concentrate on one or two and actually finish before switching or moving on. This is one of the hardest things when your interests change fast, but I am really trying to bolt myself down on this one. I'm not quite there yet.
Right on. That and the constant, never ending polling for information that comes with it leaves you with no downtime and a very worn out feeling. We need downtime throughout the day - pick up a task, do it, put it down and do nothing for a while before switching to another. Without that you can't focus and that leads to irritation which makes things worse.
Somewhat related:
https://news.ycombinator.com/item?id=29739940
Once I started printing things and not reading them with a screen, my reading of real books went up as well. When you're reading on a screen, you don't realize you're competing with physical books. But when you're reading something physical, you do become aware of it.
The best approach will vary based on topic, age, and constraints (e.g. professional with kids).
When I was a teenager, I learned Calc I, II, III and a first course of differential equations. I retained most of it. When I decided to take more advanced math courses later on (just a few years later), I was always saddened by my inability to retain much after the course was over. I kept wondering if I'm in my decline (at the old, old age of 25).
No - I was not. The nature of the material had changed. Whereas stuff you learn in Calc I and Calc II is material you can easily and often apply in engineering, some random theorem in group theory is not. When you study a theorem in Calc II, the frequency with which that theorem is invoked in the same book is high. When you get to higher math, it does become somewhat broader: Most theorems are invoked only a few times in the book.
There's also raw talent vs techniques. Younger me got by with raw talent, but at some point the material you're learning will supersede your talent. You then need to strategize (and different topics may require different strategies). Don't knock raw talent/skills - they can be honed and it may be worth honing them. But broadly: The person who has good systematic study skills will eventually overtake the raw talent person.
Most of the approaches that will work if you have all the time in the world will fail you when time becomes constrained. I started using spaced repetition a few years ago and it has been a game changer. I can study things for a bit, take a break for a few months, and mostly can pick up where I left off despite not practicing that material in those months.
Having said that, most of Becky's advice is good. The one thing I'd disagree with is:
> "Five minutes every day is better than an hour once per week"
This definitely depends on the material. You're not going to get far in math on just 5 minutes a day. Some topics will need a lower bound of minimum time per session.
Last year I taught myself a good deal of category theory, and you're right, five minutes is not really enough to learn most things - but it is enough time to start an exercise - and those five minutes often turn into something longer!
