Timeline for Reasons for the importance of planarity and colorability?
Current License: CC BY-SA 2.5
22 events
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Jan 21, 2011 at 18:05 | answer | added | Kristal Cantwell | timeline score: 0 | |
| Jan 21, 2011 at 14:45 | answer | added | Gil Kalai | timeline score: 4 | |
| Jan 13, 2011 at 2:20 | answer | added | Anonymous | timeline score: 0 | |
| Jan 12, 2011 at 19:45 | history | edited | Gil Kalai | CC BY-SA 2.5 |
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| Jan 11, 2011 at 20:01 | comment | added | Qiaochu Yuan | I agree with Alex. I have no idea what an objective reason internal to mathematics looks like; any explanation of the form "X is important because it is related to Y" just suggests the question "why is Y important?" and this seems deeply circular to me. | |
| Jan 11, 2011 at 12:48 | comment | added | S. Carnahan♦ | This question is now Community Wiki. | |
| Jan 11, 2011 at 12:47 | history | made wiki | Post Made Community Wiki by S. Carnahan♦ | ||
| Jan 11, 2011 at 10:01 | answer | added | Gjergji Zaimi | timeline score: 8 | |
| Jan 11, 2011 at 9:30 | comment | added | Alex B. | That seems like a prototypical "time had to come and show it and it's just a historical and evolutionary incident" type of explanation, since it is ultimately a consequence of the order in which things were discovered, so I am afraid I am still confused by what the question is really asking. | |
| Jan 11, 2011 at 9:19 | comment | added | Hans-Peter Stricker | @Alex: I think of an argument like "concept XYZ is 'important' because it connects previously unconnected areas in a fruitful way" - like a cut vertex in a graph (without the fruitfulness). But that's only one kind of argument. | |
| Jan 11, 2011 at 8:59 | comment | added | Alex B. | I guess what I am getting at is: can you give me an example of what a good answer to "are there objective reasons internal to mathematics for why concept XYZ is important" would look like? I am having a hard time imagining such an answer that wouldn't ultimately confuse mathematics and physics. | |
| Jan 11, 2011 at 8:57 | comment | added | Alex B. | As for your question why "importance" questions enthuse people less than actual mathematics: maybe importance is just not the right kind of measure in pure maths. What does importance mean, anyway? If I talked to the man on the street, I would have a hard time convincing him that anything I do is important. I don't even believe it myself, when I view it in the context of global challenges that humanity is facing. If you are simply asking for a [big-list] of examples of applications of these concepts, then maybe you should say so. | |
| Jan 11, 2011 at 8:32 | answer | added | gowers | timeline score: 12 | |
| Jan 10, 2011 at 21:28 | comment | added | Tony Huynh | I think half of your question is asked (and answered) here: mathoverflow.net/questions/7114/… | |
| Jan 10, 2011 at 21:11 | answer | added | David Eppstein | timeline score: 13 | |
| Jan 10, 2011 at 20:58 | comment | added | Yaroslav Bulatov | Maybe they are computationally special? Tree decomposition works because we can solve problem on trees, holographic reduction works because we can count perfect matchings on planar graphs | |
| Jan 10, 2011 at 20:54 | comment | added | Hans-Peter Stricker | Post-delivered motivation: I wonder why questions for "importance" - of concepts and theorems - are in general not taken as seriously as questions for hard facts. Wouldn't this - taking them equally important - be a real step further in the venture of mathematics? (I admit that questions for importance may be trivial - because importance may be obvious in special cases - or mistaken, because there is no importance at all of trivial concepts.) | |
| Jan 10, 2011 at 20:48 | comment | added | Hans-Peter Stricker | Maybe your answer wasn't meant entirely seriously (but maybe it was), anyway it may be taken seriously. (It has to do with my side note on our living on a two-dimensional plane.) | |
| Jan 10, 2011 at 20:36 | comment | added | Cristi Stoica | Maybe because paper is 2D. | |
| Jan 10, 2011 at 19:13 | history | edited | Hans-Peter Stricker | CC BY-SA 2.5 |
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| Jan 10, 2011 at 19:05 | history | asked | Hans-Peter Stricker | CC BY-SA 2.5 |