TITLE: Do you prove all theorems whilst studying?
QUESTION [81 upvotes]: When you come across a new theorem, do you always try to prove it first before reading the proof within the text? I'm a CS undergrad with a bit of an interest in maths. I've not gone very far in my studies -- sequence two of Calculus -- but what I'm trying to understand right now, though, is how one actually goes about studying so that when finished with a good text, there's more of an intuitive understanding than superficial.
After reading "The Art Of Problem Solving" from the Final Perspectives section of part eight in 'The Princeton Companion to Mathematics', it seems to hint at approaching studying in that very way. A quote in particular, from  Eisenstein, that caught my attention was the following -- I'm not going to paraphrase much:

The method used by the director was as follows: each student had to
  prove the theorems consecutively. No lecture took place at all. No one
  was allowed to tell his solutions to anybody else and each student
  received the next theorem to prove, independent of the other students,
  as soon as he had proved the preceding one correctly, and as long as
  he had understood the reasoning. This was a completely new activity
  for me, and one which I grasped with incredible enthusiasm and an
  eagerness for knowledge. Already, with the first theorem, I was far
  ahead of the others, and while my peers were still struggling with the
  eleventh or twelfth, I had already proved the hundredth. There was
  only one young fellow, now a medicine student, who could come close to
  me. While this method is very good, strengthening, as it does, the
  powers of deduction and encouraging autonomous thinking and
  competition among students, generally speaking, it can probably not be
  adapted. For as much as I can see its advantages, one must admit that
  it isolates a certain strength, and one does not obtain an overview of
  the whole subject, which can only be achieved by a good lecture. Once
  one has acquired a great variety of material through [...] For
  students, this method is practicable only if it deals with small
  fields of easily, understandable knowledge, especially geometric
  theorems, which do not require new insights and ideas.

I feel that this type of environment is something you don't often see, especially in the US -- perhaps that's why so many of our greats are foreign born. As I understand it, he does go on to say that he wouldn't particularly recommend that method of study for higher mathematics, though.
A similar question was posed to mathoverflow where Tim Gowers (Fields Medal) went on to say that he recommended similar methods to study: link
I'm not quite certain that I understood the context of it all, though. Upon asking a few people whose opinion mattered to me, I was told that it if time were precious to me, it would be a waste going about studying mathematics in that way, so I'd like to get some perspective from you math.stackexchange. How do you go about studying your texts?
Edit: Broken link added fixed.

REPLY [7 votes]: I did try to prove propositions in my textbooks before reading proofs when I was studying subjects like linear algebra, real analysis... But later on when things becoming more and more difficult, I had to give it up, and today I am still wondering if that was worthwhile...Because on one hand, there are many benefits of doing so: you may gain better understanding of the statement, improve you skill of proving things (), and you get great joy when you work something out! On the other hand, you will process very slowly (if not then congratulation!), but there is tons more to explore. 
However, I do have some little suggestions: 

if you develop the hobby of proving everything on you own, do not forget to zoom out from your proof of a specific statement and review the big picture of a lecture, a section or even a subject once for a while. 
if you don't want to prove it, read others' proof, don't skip it. 
maybe you can pick one or two subjects which are most important or interesting for you.