Timeline for Grothendieck - sheaves as meter sticks
Current License: CC BY-SA 3.0
15 events
| when toggle format | what | by | license | comment | |
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| May 25, 2017 at 21:27 | comment | added | Todd Trimble | There's a famous story of the koan Grothendieck put to Schneps and Lochak: "One of the members of the mathematical establishment to come into contact with him was Leila Schneps who, with her future husband, Pierre Loschak, tracked him down and found him “obsessed by the devil which he sees at work everywhere in the world” . In a subsequent letter to Leila Schneps, Grothendieck said he would be prepared to share his research into physics with her if she could answer one question: “What is a metre?” " (telegraph.co.uk/news/obituaries/11231703/…) | |
| S May 25, 2017 at 20:22 | history | edited | José Hdz. Stgo. | CC BY-SA 3.0 |
added algebraic geometry tag
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| S May 25, 2017 at 20:22 | history | suggested | descenso |
added algebraic geometry tag
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| May 25, 2017 at 20:09 | review | Suggested edits | |||
| S May 25, 2017 at 20:22 | |||||
| Dec 14, 2015 at 11:11 | comment | added | bolbteppa | It's unsurprising that the master thought in terms of 'vague metaphors' while the students have trouble with this :p If you think of open sets as formalizing collections of points that can be 'measured by a ruler' mathoverflow.net/a/19156/38721 then sheaves would be the collection of rulers measuring those points. This is very similar to the perspective Nestruev takes in amazon.com/Smooth-Manifolds-Observables-Graduate-Mathematics/dp/… | |
| Nov 24, 2015 at 21:43 | vote | accept | Arrow | ||
| Aug 10, 2015 at 10:50 | comment | added | Peter LeFanu Lumsdaine | What was the original French wording, does anyone know? Some subtlety or alternative meaning might have been lost in translation. | |
| Aug 10, 2015 at 8:17 | answer | added | Simon Henry | timeline score: 12 | |
| Aug 10, 2015 at 5:09 | comment | added | Qiaochu Yuan | Different metaphors are useful for different people, and what was useful and meaningful to Grothendieck may not be useful or meaningful to you (or perhaps the process by which it becomes useful and meaningful, if ever, is what grghxy suggests). Don't worry about it. For what it's worth, I suspect he meant nothing more than that a sheaf might measure some property of a space (e.g. its sheaf cohomology might contain topological information). | |
| Aug 10, 2015 at 2:33 | comment | added | Noam D. Elkies | Looks like an attempt at an allusion to Einstein's relativity, where the observed length of a meter stick may help you think about what happens to distances in different reference frames. No idea whether such a metaphor could be useful here, though sure the one-dimensionality of the stick isn't the point. | |
| Aug 10, 2015 at 0:48 | comment | added | grghxy | I speak from the experience of understanding EGA, SGA1, SGA2, SGA3, etc. like the back of my hand. One gets intuition not from vague metaphors (which in my experience are useless), but from examples which provide motivation and allow one to understand interesting older results in a new light. Serre often provided the "spark" leading to Grothenieck's grand ideas by deeply studying good examples. A single good example is more valuable than any number of vague metaphors. The fact that you are led to wonder about "one dimension" for a meter stick shows that the metaphor is leading you astray. | |
| Aug 9, 2015 at 22:53 | comment | added | zeb | I always think of line bundles on $\mathbb{P}^1$ as types of graph paper, i.e. $\mathcal{O}_{\mathbb{P}^1}(n)$ is the graph paper you would use if you wanted to graph a degree $n$ homogeneous polynomial in two variables. I imagine Grothendieck would think of this graph paper as a family of meter sticks indexed by $\mathbb{P}^1$, but since he does everything in families, he would drop the (implied) word "family" and just call it a meter stick. | |
| Aug 9, 2015 at 22:47 | comment | added | Arrow | @grghxy Why should one come at the expense of the other? Also, I don't think trying to understand vague metaphors by someone like Grothendieck is a waste of time. | |
| Aug 9, 2015 at 22:02 | comment | added | grghxy | I recommend to ignore such vague metaphors, which are no use whatsoever. Having a good understanding of examples of interesting sheaves (especially the diversity of interesting ones on a given space) and how their use clarifies classical problems and theorems (such the role of topology in complex analysis) is a far more instructive and illuminating thing to do. | |
| Aug 9, 2015 at 21:15 | history | asked | Arrow | CC BY-SA 3.0 |