I try to quickly learn about every concept I come across to the point that I understand when and why you would want to use it, but not the point that I understand how to implement it. When I encounter a problem that fits the concept, then I can look it up and learn how to do it fully.
I don't know, I feel it has served me well anyway. I like to jump on problems in all kinds of industries, so it is impossible to study everything ahead of time.
I agree with this way of seeing knowledge. Knowledge of subject X shouldn't be represented as a binary field, since everything is fractal and you could spend infinitely long trying to understand it.
Absolutely. I knew there some something with an opposite angle and a hypotenuse, and it only took me a minute or two. If I had never known it, there's no way I could have done that so quickly.
At least in this case you know what things to look up; imagine never having learned those things in the first place.