most recent 30 from http://mathoverflow.net 2013-05-22T22:35:19Z http://mathoverflow.net/feeds/question/83092 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/83092/what-is-the-main-goal-of-a-paper-really Benjamin Steinberg 2011-12-10T00:43:04Z 2011-12-13T17:44:34Z

<p>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?</p> <p>(a) to get the reader understand why result A is true. </p> <p>(b) to convince the reader result A is true. </p> <p>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. </p> <p>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. </p> <p>I'd like to get the community's opinion. Usual Community Wiki rules are applicable. </p> <p><b>Edit in hope of reopening.</b> 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?</p>

http://mathoverflow.net/questions/83092/what-is-the-main-goal-of-a-paper-really/83093#83093 Dror Bar-Natan 2011-12-10T00:56:51Z 2011-12-10T00:56:51Z

<p>Papers are written so that their author(s) can forget their content and move on to other things. Therefore when you write you should be very careful to put in enough of the big picture and enough of the details so you'd be able to reconstruct your thoughts 10 years later if you'll need to, assuming you'll forget everything but retain some familiarity with some basic principles of mathematics.</p>

http://mathoverflow.net/questions/83092/what-is-the-main-goal-of-a-paper-really/83094#83094 Yemon Choi 2011-12-10T01:00:59Z 2011-12-10T01:00:59Z

<p>I would add</p> <p>(c) To convince the reader that I had a good reason for caring that A is true.</p> <p>This has seemed sadly lacking in many of the papers I've refereed (sample bias, probably). Of course this goal is not easy to achieve, but I do sometimes wish authors would make more effort.</p>

http://mathoverflow.net/questions/83092/what-is-the-main-goal-of-a-paper-really/83095#83095 Xander Faber 2011-12-10T01:21:33Z 2011-12-10T01:21:33Z

<p>As you say, one goal of a paper is to certify that something is true. But the author should be more concerned with the result's certifiability than any reader. The author, being human, also requires the result to be broken up into smaller and more easily verified pieces. I can't count the number of times that I have proved a statement modulo certain details, and upon writing them up carefully I discovered that a new case emerged or the statement of the theorem needed to be altered in some (perhaps material) way. </p> <p>The introduction of a paper is a great place to sketch an overview or give heuristics ... most readers will not venture beyond it anyway. </p>

http://mathoverflow.net/questions/83092/what-is-the-main-goal-of-a-paper-really/83112#83112 timur 2011-12-10T05:45:11Z 2011-12-10T05:45:11Z

<p>Put (a) in the introduction, and explanations between theorems and lemmas. Then use proofs to achieve (b).</p>