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Sep 12, 2013 at 5:32 review Reopen votes
Sep 12, 2013 at 14:00
Dec 13, 2011 at 19:07 comment added Ryan Budney Is there a difference between (a) and (b) -- is one meant to indicate a formal proof while the other is not? Or is the difference somehow more subtle?
Dec 13, 2011 at 19:01 comment added Gerhard Paseman The goal of the paper is to provide important and or interesting mathematics for a journal to publish and readers to enjoy or use. Your changes do not provide enough information because it is not clear if the binomial identity exercise is important, or the idea behind the bijection (never mind the proof) or the result itself. You can recast the goal of a paper in terms of your a and b, but that is an author-centric choice, and arbitrary. Reader-centric and publisher-centric views are just as arbitrary. Gerhard "But My Viewpoint Is Important" Paseman, 2011.12.13
Dec 13, 2011 at 18:53 comment added user9072 Meta thread at tea.mathoverflow.net/discussion/1244
Dec 13, 2011 at 17:44 history edited Benjamin Steinberg CC BY-SA 3.0
added 608 characters in body
Dec 10, 2011 at 17:47 comment added JSE The analytic philosophers I know refer to this distinction as "the 'why' of justification versus the 'why' of explanation."
Dec 10, 2011 at 12:43 comment added user9072 @Benjamin Steinberg: I just said 'subjective and argumentative' since this is what the closing reason is called. What I really mean is that this question rather will lead to a discussion (as opposed to answers) and in addition it will be rather subjective one, because as already documented by what is around POVs depend a lot on context and precise interpretation in addition to personal style. Which in general is fine, but just for MO is rather not a good fit.
Dec 10, 2011 at 11:09 comment added Yvan Velenik It also somewhat depends on the field, I guess. As a mathematical physicist, having a correct proof of a statement is far from enough for me (the fact that the statement holds having already been established with reasonable certainty by theoretical physicists). What I very much care about is really understanding why the 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).
Dec 10, 2011 at 8:09 history closed user9072
user3456
Alain Valette
Andrés E. Caicedo
Felipe Voloch
not constructive
Dec 10, 2011 at 7:18 comment added Greg Martin My answer: both (a) and (b). An author who doesn't try to do both has failed. (there, I'm both subjective and argumentative!)
Dec 10, 2011 at 5:45 answer added timur timeline score: 7
Dec 10, 2011 at 4:45 comment added Benjamin Steinberg It may be the answer depends on result A to some extent. Take the odd order theorem in finite group theory. One doesn't need to really understand why it is true in a deep way to apply it and perhaps very few people do understand it. So (b) may be the best route for such a theorem. Other results may be more important because of an insight they provide than because they are useful to prove other results and so (a) would be more important.
Dec 10, 2011 at 4:39 comment added Benjamin Steinberg @darij, of course sometimes one can do both. But have you never had the experience of reading a paper where you understood at each step why line x followed from x+1 but you had not clue how anybody could have thought it up? @quid, I definitely agree it is subjective. I hope it is not argumentative (that wasn't my intention).
Dec 10, 2011 at 1:40 comment added user9072 Vote to close as subjective and argumentative. This is by an large a matter of style/taste. Answers might make a nice/interesting read, but questions like this on MO cause too much direct and indirect difficulties.
Dec 10, 2011 at 1:21 answer added Xander Faber timeline score: 9
Dec 10, 2011 at 1:00 answer added Yemon Choi timeline score: 40
Dec 10, 2011 at 0:56 answer added Dror Bar-Natan timeline score: 56
Dec 10, 2011 at 0:47 comment added darij grinberg Is it really hard to do both at once? In my experience, heuristics that clears up things at the expense of verifiability tends to actually obscure things when read by somebody not already familiar with the subject.
Dec 10, 2011 at 0:43 history asked Benjamin Steinberg CC BY-SA 3.0