My question, motivated by idle curiosity while sitting in LaGuardia airport, is the following. You've just proved nice result A and it is time to write the paper. What is the real goal of the paper?

(a) to get the reader understand why result A is true.

(b) to convince the reader result A is true.

In some cases it may be feasible to do both. But often there is some tension between (a) and (b). To understand a result one needs global understanding. One may need to do some ugly computations in coordinates or deal with pictures that LaTex doesn't handle.

On the other hand to check the truth of a paper it is often easier to have local understanding because humans can only keep so much info in their brain at once. So if (b) is your goal you will work hard to break things up into smaller certifiable statements. That way once the reader has been convinced that Lemma X is true they can work with the statement and forget why it is true. To make it easier to check a proof one is often led to invent new formalisms or language and find coordinate free arguments. This can affect negatively (a) because you may not see the forest because of the trees.

I'd like to get the community's opinion. Usual Community Wiki rules are applicable.