Suppose I read a(n undergrad) textbook, and get to a theorem in the text. Should I force myself to prove it without looking at the proof, only referring to theorems previously encountered?

Apparently this is beneficial. But most of the time I'll just get stuck, as with most problems, and it tends to burn time and patience. I feel it may be better to just read the proof and try to absorb the technique and insight, rather than stubbornly insisting on proving it by myself. It's also discouraging to eventually give up, since there's still the rest of the book to cover. (Furthermore, "hands-on opportunities" are always available in the problem section.) Would just reading the proof (after giving the theorem just a few moments of thought) help me learn faster, since I can then cover more content? Or is this a bad habit that I shouldn't develop?

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    $\begingroup$ That's the ideal way to learn maths; of course, none of us lives in an ideal world. $\endgroup$ – Lord Shark the Unknown May 2 '18 at 7:52
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    $\begingroup$ I'd say at least give it $30$ seconds and see if you get any idea as to how to start. If yes, it will be more exciting to try that idea even if it fails than it would have been to just read the proof. $\endgroup$ – Arnaud Mortier May 2 '18 at 7:53
  • $\begingroup$ After reading the theorem, I'll make sure I completely understand the statement and then go onto the proof. Supposing it doesn't work out nicely (i.e. stuck on a line for 5 or more minutes) I'll continue onward and come back to at the end of the section. Hopefully at that point I'll some more maturity with the topic and It'll be easy to see. $\endgroup$ – TrostAft May 2 '18 at 8:12

That's a very high expectation to set for yourself and if it were possible then I would say go for it, but it'll almost certainly be too hard. Most textbook authors already leave out some details of proofs for the reader to fill in. I would definitely do that for every proof you encounter as authors are usually thoughtful about giving you enough to get going but leaving you enough to do on your own and fortify your skill set.


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