In my discrete math course, I am often finding myself spending way too much time attempting a single math proof.

I am starting to think that reading as many proof solutions as possible is a better approach to practice. I guess this would help me recognize more proof patterns on the exam.

Did anyone get significantly better at writing eloquent proofs by simply reading and absorbing as many proofs? Or did the process of thinking from ground up in new proof situations help you develop your proof writing skills?

• It doesn't strike me as an either-or situation. Sometimes we get stuck on attempting a proof, and later an idea will occur to us that opens the way to a successful attack. Of course reading proofs may "seed" our mind with ideas (perhaps of what to avoid!), and reading proofs is a useful skill in its own right. But just reading proofs will not likely get you ready to write them. Dec 20, 2015 at 15:09
• @hardmath Yes, I see what you mean. How long should I be trying to prove something before I move on? Sometimes a proof is just so frustrating and I want to peek at the answer. Are you suggesting that I should just skip it and come back at a later time? Because I feel like so much time is wasted just starting at the problem, when I can just use that time to read multiple other proof solutions. Dec 20, 2015 at 15:17
• Of course I'm no longer in school, so I have the luxury of waiting until I have an idea before attempting to write up a proof! As advice in taking an exam in mathematics, particularly ones that ask for proofs, I would say read over all the problems, assuming a reasonable amount of time is given, and do triage on them: which ones are clearly doable, which ones seem hopeless at first glance, and which ones is there a bit of an idea that needs more time to puzzle out. All your efforts and tactics will pay off in the long run, so keep trying proofs and reading those "model" proofs. Dec 20, 2015 at 15:28

The problem with reading a proof before attempting them yourself, is you have no muscle-memory to help you remember them. It's like learning to swim from a book.

The ideal process is something along the lines of. . .

1. Attempt the proof on your own. If the proof is an exercise from a textbook, you can be fairly certain you already have the tools to complete the proof at your disposal -- there is no 'flash of inspiration' required. How long to do this depends on how much progress you seem to be making. If you are making absolutely no progress and the problem completely stumps you, a good idea is to go back to the logic of earlier proofs, and see if anything might apply to your current problem.