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• CommentAuthorquid
• CommentTimeDec 13th 2011

What is the main goal of a paper really?

Quick facts: closed couple days ago. Now edited with the idea of reopening. 3 votes to reopen.

Personal opinion: I voted to close the original version; my opinion stays essentially unchanged by the edit.

1.

Are options (a) and (b) different? They look to be essentially the same.

• CommentAuthorbsteinberg
• CommentTimeDec 13th 2011

I saw a few votes to reopen so I decided to try an edit to see if I could convey what was intended as the point of the question. In part I am torn between two arguments I have for a theorem and I am hoping people's opinion on this will help me. I really think that (a) and (b) can be quite different, but if I am alone I am happy to find out and have the question closed. I only tried to revive it when I saw the reopen votes (I myself don't want to vote to reopen because I don't think I should be involved).

As an example I have in mind from my own work, I have two ways to prove a certain finite dimensional basic algebra is hereditary. One is by counting the number of paths in its quiver and showing it is the dimension of the algebra. The proof is combinatorial but not even bijective. Anyone who reads the proof will agree it is correct, but nobody will have any feeling why this algebra is hereditary. The other proof goes through a long, circuitous homological path by which it is shown that yes Ext between simple modules vanishes after degree one. This proof requires much more effort on the reader to decipher than the short counting proof, but it is more informative and this is not an isolated case.

In fact, I claim it is possible to write a correct proof without understanding the result yourself. I have even seen authors admitting that they proved something via a "mindless" computation and they don't really understand why it is true. So I do not believe (a) and (b) are the same. The question is that in cases when they are different, what is preferable. A good answer of course maybe Qiaochu's idea of writing a blog! But I am happy to keep it closed if people really think it is not an MO-suitable question. Note it was CW from the beginning. I strongly believe all such questions with no right answer should be such.