Timeline for Explaining the main ideas of proof before giving details
Current License: CC BY-SA 4.0
27 events
| when toggle format | what | by | license | comment | |
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| Jul 3, 2020 at 20:18 | history | edited | YCor | CC BY-SA 4.0 |
removed capitals from title (the question was bumped anyway)
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| Jul 3, 2020 at 18:47 | answer | added | Steven Landsburg | timeline score: 0 | |
| Mar 10, 2019 at 12:40 | review | Close votes | |||
| Mar 10, 2019 at 13:50 | |||||
| Jan 28, 2019 at 16:35 | review | Close votes | |||
| Jan 29, 2019 at 2:21 | |||||
| May 27, 2018 at 4:28 | comment | added | Abhimanyu Pallavi Sudhir | Because good proofs are just a formalisation of the intuitive understanding -- rather than wasting space explaining the insights, you can just give them the proof, and an even somewhat experienced reader can re-create the details. | |
| May 26, 2018 at 17:08 | answer | added | Per Alexandersson | timeline score: 4 | |
| May 26, 2018 at 0:53 | comment | added | Gro-Tsen | I think the difficult question is really "how to decide at what level of detail to give the main ideas" (too sketchy and it becomes a kind of how to draw an owl joke; too detailed and it becomes a slightly less readable version of the proof itself; so the problem is to find the right balance). | |
| May 25, 2018 at 23:23 | comment | added | Greg Martin | Since nobody seems to have mentioned it, I will say that there are (still) a lot of badly written math papers being created and published. Our discipline doesn't seem to sanction poor writing particularly much (indeed, there might still be a few who see "hard to read" as correlated positively with "important math"). Same with giving talks, for that matter. | |
| May 25, 2018 at 23:06 | answer | added | fedja | timeline score: 12 | |
| May 25, 2018 at 15:11 | comment | added | LSpice | @KConrad, or one can link to the specific answer: mathoverflow.net/a/7342/2383 . (I assume this is the one you meant.) | |
| May 25, 2018 at 15:07 | comment | added | Praphulla Koushik | @KConrad Hello Sir :D I just did not wanted to make them feel bad :D :D | |
| May 25, 2018 at 14:12 | comment | added | Francesco Polizzi | Well, sometimes journal editors and referee also complain because "the paper is too technical" :-) | |
| May 25, 2018 at 14:08 | comment | added | Timothy Chow | In practice, "taking up space" seems to be a major reason, even though it arguably shouldn't be a major reason. Journal editors and referees still complain about paper length even in today's electronic age, and so there is pressure to eliminate "redundant" material. You're much more likely to feel pressure to eliminate informal explanation than to feel pressure to eliminate formal proofs. | |
| May 25, 2018 at 13:01 | comment | added | Francesco Polizzi | I mean, it seems to me that the fact that many authors do not do so or that sometimes it is done in a bad way is not a good reason to say that it should not be done. | |
| May 25, 2018 at 12:52 | comment | added | Francesco Polizzi | Is it good to try to explain the main ideas of a complicated proof before giving the details? How can the answer be no? | |
| May 25, 2018 at 8:52 | comment | added | Mikhail Skopenkov | One more common reason is that the authors do not really understand their own proofs (this is applicaple to the author of this comment as well:) | |
| May 25, 2018 at 7:25 | comment | added | KConrad | For those who want to see the other half of the joke/quote Praphulla refers to, search for Szpiro on the MO page mathoverflow.net/questions/7155/famous-mathematical-quotes. | |
| May 25, 2018 at 7:07 | comment | added | Joce | Breaking up the proof into preparatory lemmas is a way of explanation. If they are appropriately chosen, stating the lemmas actually gives the outline of a long proof better than what natural language can. | |
| May 25, 2018 at 4:52 | answer | added | Victor Protsak | timeline score: 11 | |
| May 25, 2018 at 4:25 | answer | added | Alexandre Eremenko | timeline score: 28 | |
| May 25, 2018 at 3:08 | answer | added | Gerhard Paseman | timeline score: 8 | |
| May 25, 2018 at 1:35 | comment | added | Praphulla Koushik | There is some joke, half of which says, when mathematicians prove something they feel it is trivial... may bebecause they will check the proof so many times, for them it is more or less straight forward so they do not add anything other than the proof for example some outline first... most of them do not even mention the set up correctly :D | |
| May 25, 2018 at 0:59 | comment | added | Anthony Quas | I think the answer to your question is yes: it is really good to some kind of high level description of the proof before you get into it. But, as you hint at, it is critical that a high level description should be expressed in terms that make sense to a general reader who is knowledgeable in the field of the paper. I have seen terrible high level descriptions that sort of conjure up an image of how the author sees the proof (something like "the proof is like making toffee, and then adding nuts at the end"), which convey nothing to the reader who is not in the author's head. | |
| May 25, 2018 at 0:31 | comment | added | Gerry Myerson | Just to clarify: are you only asking about writing papers for research journals, or are you also asking about giving talks to specialist audiences, giving talks to general mathematical audiences, giving lectures to advanced classes, giving lectures to precalculus classes, and so on, and so forth. | |
| May 25, 2018 at 0:00 | comment | added | Thomas Kojar | it is more about the curse of knowledge problem, which is common in academia in general. The authors think that their proof is already clear and so they don't bother easing us into it. | |
| May 24, 2018 at 23:57 | history | made wiki | Post Made Community Wiki by Todd Trimble | ||
| May 24, 2018 at 23:55 | history | asked | SBK | CC BY-SA 4.0 |