The problem with math books. Succinctness. There you have it. This is the single most annoying problem with succinctness. When you go over a line of text someti

The problem with math books. Succinctness. There you have it. This is the single most annoying problem with succinctness. When you go over a line of text sometimes it is justified to spend 3 hours with it. But sometimes its not, its just something that you are not seeing. The thing with math books is you cant tell if it needs 3 hours or 2 minutes because all the lines look the same and the succinct ones kinda jump at you without warning. Succinctness is Power, but if you are facing a powerful person in combat you wont be singing the glories of origins of your foes power. The way I go about these books is to work the theorems myself. It will take a loooong time to get through the first few chapters because that is where you are getting oriented towards that kind of thinking. The second chapter is usually the hardest! Stick with it. Do not try to calculate how long it is going to take to complete this book at this rate. Because the thing gets faster as you read it. Some kinda exponential function at work, the more you read the faster you can read since you have an intuition for the succinct parts and you can sense them from far. Many times you don't have to complete the book since the later chapters are on a need to know basis and the fundamentals are covered in the first half of the book. Also the thing gets faster once you cross the second chapter since you know the language now. Why you should work the theorems yourself: When you read them you feel like you know them, but this is a bias. ( I use that word as an umbrella term to refer to all unintentional consequences of the way our mind works ). Once you try to reconstruct the theorem, that is when you get to understand all the gaps, holes and whole craters in your knowledge with such clarity. Clearly knowing what you don't know is the last but one step before you know it. This is like finding the exact line in which the bug occurs, 95% of the times when I have done this the fix is immediately obvious to me. The remaining 5% of the times the bug is a consequence of the architecture (fondly referred to as a feature). To think of a parallel to this in learning: these are the times when you feel an Ah ha moment where whole areas of darkness come to light. You need a guru by all means to guide you. Not all the information about the difficulty of a topic is captured by a book. You wont understand the consequences of a particular way of thinking unless you have spent a few years doing it wrong. So find a person who has been down that path to guide you. Also a buddy group makes the whole experience much more manageable and fun.