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.

**Edit in hope of reopening.** Perhaps if I make things more specific I can get the kind of answer I wanted and things would be less subjective. Suppose I have 2 proofs that finite sets $X$ and $Y$ have the same cardinality. One is proof is a relatively easy computation of the sizes of each set using known identities with binomial coefficients, Stirling numbers, etc. Any decent referee would follow it. The other proof is an involved bijection between $X$ and $Y$ whose details would be involved to check. Space considerations in the journal do not allow for both proofs. Which one should I submit?

reallyunderstandingwhythe statement is true, and that's the main purpose of a proof for me. So, a paper which can only be checked line by line, without ever leading to a full picture is useless, as far as I am concerned (as are proofs relying on long, unenlightening computations). $\endgroup$Meta threadat tea.mathoverflow.net/discussion/1244 $\endgroup$6more comments