Will I learn most from reading proofs, proof outlines, or solving problems? I have been self studying some topics in theoretical statistics for a bit over a year but still do not have a good balance between reading proofs in detail, reading proofs to get a general idea and solving exercises. Solving exercises definitely feels the most productive, but I'd expect that reading proofs closely has a lot of value for growing my mathematical maturity. As a note, I'm mostly talking about proofs from literature, not textbook proofs.

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*If a proof is hard enough that I need to spend hours going through it, am I just wasting my time? Do you have any tips for making this time more productive? (I usually try to follow each step and justify each claim.)

*Is there much value in skimming a proof? I still don't have enough experience that I can think "post-rigorously". Skimming proofs usually does not feel productive to me.

 A: The advice will be different for everyone. If you are looking to learn the contents of a paper,  I think what works for me is to concentrate on the parts where I am maximally confused.  If you read a theorem and think "hmm, seems reasonable, I can sorta see how to prove that" then maybe you can get away with just skimming over the proof if it's not too important.  On the other hand, if the theorem makes you say "WTF?" then maybe you need a much closer look.  Of course, if you're new to the field, most theorems are going to be in the second category.
On the other hand, if you're looking to practice your skills or test your understanding you should read a paper in a very different way.  Try taking the statements of the theorems and proving them yourself first before reading the proofs. The theorems in the first category above are especially good candidates for this.  And of course if it is a textbook with exercises, do those.
I've also found it useful to read papers multiple times at different levels of detail.  First time skimming, then reading, then verifying most details, then verifying 99% of the details.  It's also often useful to read a paper out of order. Skip to the important stuff first, the main theorems.  Then go back and see how the lemmas are useful towards that goal.
