Timeline for Awfully sophisticated proof for simple facts
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Jul 31 at 9:31 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
http -> https (the question was bumped anyway)
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| Oct 18, 2010 at 23:55 | comment | added | Thierry Zell | @Hugh: You are absolutely right. I tried to temper my statement by writing "almost obvious", but in hindsight, even that wording was too strong. | |
| Oct 18, 2010 at 22:25 | comment | added | Hugh J | I am not sure it is so intuitive, even in the nice $C^1$ case. For example, could you explain to a child why the results holds in the plane and not in the torus ? | |
| Oct 17, 2010 at 22:52 | comment | added | Thierry Zell | The Jordan curve theorem is not intuitive: it deals with continuous curves, and at that level of generality it is quite legitimate to expect the worst. The result is almost obvious for $C^1$ curves, of course, but there is a chasm between $C^0$ and $C^1$, and I can think of a couple of "intuitive" results like this which are not yet even proved in the $C^0$ case. See e.g. the square pegs & round holes problem quomodocumque.wordpress.com/2007/08/31/… which may be close to being solved, but has been open since 1911! | |
| Oct 17, 2010 at 19:01 | comment | added | HJRW | unknown - for suitable definitions of 'heuristic' and 'simple', yes, I do. But the key word in the question is 'disproportionate'. | |
| Oct 17, 2010 at 18:12 | comment | added | Qfwfq | @Henry: but you admit it is a very "simple" fact from the heuristic view point? :) | |
| Oct 17, 2010 at 17:40 | comment | added | HJRW | I think the idea of this question is to judge the simplicity of the fact by the length of the shortest possible elementary proof, not by the length of the statement. | |
| Oct 17, 2010 at 17:03 | comment | added | Qfwfq | I don't know...It looks a very "intuitively simple fact", despite it's actual mathematical nontriviality. Maybe it's a bit offtopic w.r.t. the OP's question? | |
| Oct 17, 2010 at 16:58 | comment | added | Robin Chapman | Is that a "simple fact"? | |
| Oct 17, 2010 at 16:56 | history | answered | Qfwfq | CC BY-SA 2.5 |