[PandaRider]

I appreciated the article for emphasising memorising definitions and statement of theorems... But not for proofs. For proofs, a general outline would be sufficient.

[xanderlewis]

For proofs, I find it a good idea to memorise (or at least implicitly retain) the reason a result is true. So, yes, an outline, but minus any of the implementation details of the proof. I kind of think every book in the definition-theorem-proof style should really be definition-theorem-reason-proof.

The reason part being essentially a one or two line natural language summary of ‘why the proof works’ — something that is almost always possible and is enlightening and conducive to efficient memorisation, but that for some reason is very rarely written down explicitly.

[gowld]

I think a better word is "motivation" -- why we chose this option at this juncture instead of many other options. Yes, it's a "reason", but "reason" already means something else.

The "Reason" as result is true is that it follows from the previously established axioms via logical reasoning.

[jll29]

> definition-theorem-reason-proof

Along the lines of your own argument: even better would be

reason0-definition-reason1-theorem-reason2-proof

[youoy]

It depends if you want to be able to prove new things by yourself or not. If you want to do it, then you definitely need to understand /recall all of the whys of every section of the proof. They are all there for a reason. If you don't, you just want the intuition of why the whole theorem is true.

[abdullahkhalids]

You should definitely memorize most of the "basic" (and short) proofs in some field you are super interested in. The intermediate and advanced proofs, only the outline is sufficient.