Timeline for What definitions were crucial to further understanding?
Current License: CC BY-SA 4.0
29 events
| when toggle format | what | by | license | comment | |
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| Dec 23, 2018 at 0:00 | comment | added | Philip Oakley | Is there not a Counter Question of "In what areas is there a lack of suitable definitions to facilitate further understandings?". As someone from the engineering community, the lack of terminology for the equivalent phenomena in the particle space of the wave-particle duality is a significant problem. E.g. There is no (well defined) equivalent of the Doppler effect in the time domain, to the point that the dual is denied. | |
| Dec 15, 2018 at 3:05 | review | Close votes | |||
| Dec 15, 2018 at 19:17 | |||||
| Dec 7, 2018 at 18:55 | comment | added | Lee Mosher | I will mildly dispute the premise of the question with a story. Whether you are new to a field or not, when writing up a paper you may find yourself writing the same words over and over: "Let $X$ be a BLAH that satisfies the properties FNORK and SNERD". At some point, you tire of writing those words yet again, and decide on the spot to write a definition: "Define a GRACKLE to be a BLAH that satisfies the properties FNORK and SNERD". Then you go through and edit your paper, rewriting to use your new terminolgy GRACKLE, and you smile smugly when the paper loses 2 pages in length. | |
| Dec 6, 2018 at 12:48 | answer | added | Agnishom Chattopadhyay | timeline score: 5 | |
| Dec 5, 2018 at 7:33 | history | edited | Rodrigo de Azevedo |
Added tag.
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| Dec 4, 2018 at 23:21 | answer | added | Michael Hardy | timeline score: -2 | |
| Dec 4, 2018 at 19:52 | answer | added | Aryeh Kontorovich | timeline score: 32 | |
| Dec 4, 2018 at 15:39 | answer | added | Abdelmalek Abdesselam | timeline score: 20 | |
| Dec 4, 2018 at 3:39 | answer | added | Nate Eldredge | timeline score: 20 | |
| Dec 3, 2018 at 21:33 | answer | added | Francois Ziegler | timeline score: 8 | |
| Dec 3, 2018 at 18:39 | history | edited | Marcel | CC BY-SA 4.0 |
edited to clarify issue about duplication and original intent
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| Dec 3, 2018 at 18:30 | review | Close votes | |||
| Dec 4, 2018 at 10:07 | |||||
| Dec 3, 2018 at 18:14 | comment | added | Timothy Chow | Possible duplicate of Examples of advance via good definitions | |
| Dec 3, 2018 at 18:07 | comment | added | Qfwfq | The functor of points | |
| Dec 3, 2018 at 17:45 | answer | added | Gabe K | timeline score: 26 | |
| Dec 3, 2018 at 17:44 | comment | added | Marcel | @NikWeaver Fair point. My goal was to collect the stories associated with those moments of definition and change of perspective, not just a dry list of 'important' definitions. I thought I was making this clear, but some of the answers so far indicate that I have not. | |
| Dec 3, 2018 at 17:15 | comment | added | Nik Weaver | @Marcel: sure, that's why I qualified it with "well-known". Was the definition of an abstract group crucial to further understanding? The definition of a manifold? Banach space, topological space, probability measure? Well, of course. | |
| Dec 3, 2018 at 16:37 | history | edited | Denis Serre | CC BY-SA 4.0 |
added 4 characters in body
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| Dec 3, 2018 at 16:30 | comment | added | Marcel | @NikWeaver Any paper is filled with definitions that are rather natural and therefore not crucial in the psychological sense described in the question, i.e. they did not arise out of struggle and they did not change the whole perception about the subject. | |
| Dec 3, 2018 at 16:27 | answer | added | Sam Hopkins | timeline score: 16 | |
| Dec 3, 2018 at 16:25 | comment | added | Nik Weaver | Seems like it would be harder to find examples of well-known definitions that weren't crucial to further understanding. | |
| Dec 3, 2018 at 16:03 | comment | added | benblumsmith | I don't really know the history, but it seems to me the (re)definition of "continuous function" as "pullback of open is open" must have been what allowed for the definition of a topology. | |
| Dec 3, 2018 at 15:41 | answer | added | Andrés E. Caicedo | timeline score: 24 | |
| Dec 3, 2018 at 15:23 | comment | added | user19475 | The definition of a site (Grothendieck realising that one only needs the notion of a covering to define cohomology) and sheaves on them leading to étale cohomology (and other cohomology theories). | |
| Dec 3, 2018 at 15:07 | answer | added | Dirk | timeline score: 6 | |
| Dec 3, 2018 at 14:30 | comment | added | Sam Hopkins | There is the famous example of Grothendieck’s definition of a scheme. | |
| Dec 3, 2018 at 14:22 | answer | added | Alexandre Eremenko | timeline score: 42 | |
| Dec 3, 2018 at 12:33 | history | made wiki | Post Made Community Wiki by Todd Trimble | ||
| Dec 3, 2018 at 11:51 | history | asked | Marcel | CC BY-SA 4.0 |