Timeline for Trichotomies in mathematics
Current License: CC BY-SA 4.0
96 events
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| Oct 4 at 23:30 | history | edited | LSpice | CC BY-SA 4.0 |
Tidying and links, while this is on the front page
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| Oct 4 at 19:55 | history | edited | ThiKu | CC BY-SA 4.0 |
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| Oct 4 at 19:20 | answer | added | Joshua Grochow | timeline score: 0 | |
| Aug 7, 2023 at 6:37 | comment | added | Pietro Majer | (On a side note, I've always found a bit funny the word "trichotomy", that should also mean "hair cutting") | |
| Aug 7, 2023 at 6:00 | answer | added | José Hdz. Stgo. | timeline score: 1 | |
| Apr 6, 2019 at 15:59 | comment | added | user137767 | $\mathrm{Spec}\, \mathbb{Z}$ is not the analogue of $S^3$. You have to compactify at archimedean place, otherwise it is a punctured sphere (whose homotopy type is very different) | |
| Dec 30, 2017 at 15:20 | review | Close votes | |||
| Dec 30, 2017 at 23:05 | |||||
| Jun 26, 2017 at 17:54 | answer | added | user56097 | timeline score: 3 | |
| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Apr 21, 2016 at 13:33 | answer | added | Sean Lawton | timeline score: 4 | |
| Mar 17, 2015 at 13:08 | answer | added | Steve Huntsman | timeline score: 4 | |
| Nov 7, 2014 at 5:09 | answer | added | Gerry Myerson | timeline score: 14 | |
| Feb 13, 2013 at 9:42 | answer | added | shane.orourke | timeline score: 3 | |
| Feb 13, 2013 at 6:47 | answer | added | LeBlanc | timeline score: 6 | |
| Feb 11, 2013 at 17:07 | answer | added | Alexander Chervov | timeline score: 14 | |
| Feb 9, 2013 at 7:57 | history | edited | Vesselin Dimitrov | CC BY-SA 3.0 |
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| Feb 9, 2013 at 5:43 | comment | added | user30304 | mathoverflow.net/questions/22927/… | |
| Feb 9, 2013 at 5:41 | comment | added | user30304 | mathoverflow.net/questions/13029/… | |
| Feb 9, 2013 at 5:40 | comment | added | user30304 | mathoverflow.net/questions/40178/freshmans-definition-of-sinx/… | |
| Feb 8, 2013 at 21:53 | history | reopened |
Gil Kalai Alexander Chervov Todd Trimble Gjergji Zaimi Benjamin Steinberg |
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| Feb 8, 2013 at 21:46 | history | edited | Vesselin Dimitrov | CC BY-SA 3.0 |
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| Feb 8, 2013 at 17:48 | comment | added | user30304 | For a Riemannian signature Einstein AH structure on a compact n-manifold there holds one of the following mutually exclusive possiblities: 1) It is proper and exact with parallel scalar curvature. 2) Its scalar curvature is identically zero and it is closed. 3) It is not closed, and its scalar curvature is not parallel. arxiv.org/pdf/1203.2575 | |
| Feb 8, 2013 at 17:43 | comment | added | user30304 | Structure of Kac–Moody algebras: finite type, affine type, and wild type. | |
| Feb 8, 2013 at 17:06 | comment | added | user30304 | Tautology/contingency/absurdity for propositional forms and the analogous valid/satisfiable/unsatisfiable. books.google.com/books?id=t5r79vZ9ogoC&pg=PA75 | |
| Feb 8, 2013 at 17:04 | comment | added | user30304 | An infinite locally finte homogenneous geometry is isomorphic to 1) trivial geometry, 2) projective geometry over a finite field, or 3) affine geometry over a finite field. books.google.com/books?id=8NTWRFD5lZ8C&pg=PA367 | |
| Feb 8, 2013 at 16:16 | history | edited | Vesselin Dimitrov | CC BY-SA 3.0 |
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| Feb 7, 2013 at 17:14 | comment | added | Emil Jeřábek | The natural classification of theories based on their stability spectrum is not a trichotomy, but a tetrachotomy (unstable, strictly stable, strictly superstable, totally transcendental), reinforcing the argument that this question is rather arbitrary. | |
| Feb 7, 2013 at 17:10 | comment | added | Jonathan Beardsley | Perhaps more interesting would be investigating a function whose value at $n$ is "the number of interesting examples of $n$-chotomies in mathematics" as I suspect it would decrease rather quickly. However, philosophically, there is a probably a good reason that there are many examples of dichotomies and trichotomies, as opposed to, say 11-chotomies. Perhaps this is connected to the relative smallness of the human mind, in some sense. Additionally though, such a philosophical argument would show that such a question is pretty silly. | |
| Feb 7, 2013 at 16:47 | comment | added | Gil Kalai | There was a somewhat related discussion on "trialities" (The 3-analog of "dualities") over the n-category cafe here golem.ph.utexas.edu/category/2007/01/… | |
| Feb 7, 2013 at 16:41 | history | edited | Gil Kalai | CC BY-SA 3.0 |
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| Feb 7, 2013 at 16:22 | comment | added | Gil Kalai | There is an important trichotomy in model theory between super-stable theories, strict-stable (stable but not superstable) theories, and non stable theories. (There are other important trichotomies in model theory and set theory.) | |
| Feb 7, 2013 at 6:09 | history | closed |
Gerald Edgar Franz Lemmermeyer Dan Petersen Misha Chandan Singh Dalawat |
no longer relevant | |
| Feb 6, 2013 at 21:05 | answer | added | Axel Boldt | timeline score: 21 | |
| Feb 6, 2013 at 18:46 | answer | added | Lee Mosher | timeline score: 11 | |
| Feb 6, 2013 at 18:40 | comment | added | Todd Trimble | Ah, excellent Terry. I have just posted an answer based on this. | |
| Feb 6, 2013 at 18:39 | answer | added | Todd Trimble | timeline score: 4 | |
| Feb 6, 2013 at 17:50 | comment | added | Terry Tao | Analogously: a natural number is either a unit, a prime, or a composite. | |
| Feb 6, 2013 at 16:13 | comment | added | Todd Trimble | Oh hey, here's one from another recent thread (see Terry Tao's comment here: mathoverflow.net/questions/120536/is-the-empty-graph-a-tree/…): a space is either unconnected, connected, or disconnected. :-) | |
| Feb 6, 2013 at 8:16 | history | edited | Vesselin Dimitrov | CC BY-SA 3.0 |
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| Feb 5, 2013 at 16:57 | comment | added | user9072 | @Franz Lemmermeyer: A simple reason can be that a user cannot yet upvote ;D Actaully subtracting these two, and accounting for the fact that two other users have two answers (visible) we arive at 21=21. Not taking potentially downvotes into account. But likely it is true not everybody answering upvoted, in general I see no problem with this. (I upvote things I find good and answer as long I find it acceptable [and am able to]. Seems reasonable to me.) | |
| Feb 5, 2013 at 16:01 | comment | added | Franz Lemmermeyer | MO is becoming more and more ridiculous. I don't even understand why people bother answering questions they do not even think worthy of upvoting. | |
| Feb 5, 2013 at 10:11 | history | edited | Qfwfq | CC BY-SA 3.0 |
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| Feb 5, 2013 at 9:16 | history | edited | Ryan Budney |
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| Feb 5, 2013 at 0:08 | answer | added | André Henriques | timeline score: 16 | |
| Feb 4, 2013 at 23:17 | history | reopened |
Jonah Sinick GH from MO user9072 Asaf Karagila♦ Vesselin Dimitrov |
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| Feb 4, 2013 at 22:02 | comment | added | GH from MO | I think this question is a good one, because it generates interesting answers. | |
| Feb 4, 2013 at 20:46 | history | closed |
Tom Goodwillie Eric Wofsey HJRW David White Felipe Voloch |
not a real question | |
| Feb 4, 2013 at 19:16 | comment | added | Todd Trimble | Do I understand correctly, unknown (yahoo), that your comments are meant to undermine the question so that it gets closed? If so, then I get it. And if so, please cut it out already. | |
| Feb 4, 2013 at 17:54 | comment | added | user30304 | Underdetermined, determined, overdetermined. | |
| Feb 4, 2013 at 16:36 | comment | added | David White | Meta thread here: tea.mathoverflow.net/discussion/1525/…. Please upvote this comment so it appears "above the fold" | |
| Feb 4, 2013 at 14:26 | comment | added | user30304 | SubX, X, superX. | |
| Feb 4, 2013 at 14:24 | comment | added | user30304 | Clockwise, anti-clockwise, stationary. | |
| Feb 4, 2013 at 14:23 | comment | added | user30304 | One, both, neither. | |
| Feb 4, 2013 at 14:23 | comment | added | user30304 | Win , loss, draw. | |
| Feb 4, 2013 at 12:29 | answer | added | user30304 | timeline score: 13 | |
| Feb 4, 2013 at 10:33 | answer | added | Guy R. | timeline score: 3 | |
| Feb 4, 2013 at 10:16 | answer | added | A. Bellmunt | timeline score: 11 | |
| Feb 4, 2013 at 10:13 | answer | added | David Corwin | timeline score: 8 | |
| Feb 4, 2013 at 10:11 | comment | added | David Corwin | In American History class, we had this theory that every single war came in three stages, and it seemed to hold up pretty well... | |
| Feb 4, 2013 at 8:03 | answer | added | GH from MO | timeline score: 37 | |
| Feb 4, 2013 at 2:29 | comment | added | Todd Trimble | Let's please not be quick to close this question. There are some intriguing clusters of answers, some along a (negative, 0, positive) axis, and others along a (closed, open, closed) axis [if I may put it crudely], and others along other axes still. There is a certain amount of erudition in both the question and answers, and there is some potential to glimpse "analogies between analogies" in the words of Ulam. It could be a useful exercise to pursue this. | |
| Feb 4, 2013 at 1:13 | comment | added | user30304 | There are three eras of mathematics: 1) mathematics, 2) relatively new mathematics, 3) emerging mathematics. Anything between Poincaré and recently is designated as "relatively new". Anything in last couple of decades is termed "emerging". | |
| Feb 4, 2013 at 0:31 | comment | added | user30304 | There are three types of people. Those that can count. And those that can't. | |
| Feb 3, 2013 at 15:12 | answer | added | Lee Mosher | timeline score: 11 | |
| Feb 3, 2013 at 14:32 | answer | added | Asaf Karagila♦ | timeline score: 30 | |
| Feb 3, 2013 at 14:17 | history | edited | Vesselin Dimitrov | CC BY-SA 3.0 |
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| Feb 3, 2013 at 13:49 | answer | added | Andrea Mori | timeline score: 3 | |
| Feb 3, 2013 at 13:45 | comment | added | Andrea Mori | Holy Trinity! That's a striking observation. | |
| Feb 3, 2013 at 13:28 | comment | added | Eric Wofsey | This feels like an awfully arbitrary and contentless question to me. This seems like asking, what are some interesting sets with 3 elements? Voting to close. A more reasonable question would be to ask for examples where there is an interesting hyperbolic-parabolic-elliptic trichotomy and connections between these examples. | |
| Feb 3, 2013 at 13:28 | history | edited | Vesselin Dimitrov | CC BY-SA 3.0 |
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| Feb 3, 2013 at 13:21 | answer | added | Joe Silverman | timeline score: 10 | |
| Feb 3, 2013 at 11:11 | history | edited | Vesselin Dimitrov | CC BY-SA 3.0 |
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| Feb 3, 2013 at 10:05 | comment | added | Benjamin Dickman | From the movie $\pi$: "Hold on. You have to slow down. You're losing it. You have to take a breath. Listen to yourself. You're connecting a computer bug I had with a computer bug you might have had and some religious hogwash. You want to find the number 216 in the world, you will be able to find it everywhere. 216 steps from a mere street corner to your front door. 216 seconds you spend riding on the elevator. When your mind becomes obsessed with anything, you will filter everything else out and find that thing everywhere." | |
| Feb 3, 2013 at 9:49 | history | edited | Vesselin Dimitrov | CC BY-SA 3.0 |
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| Feb 3, 2013 at 9:10 | history | edited | Vesselin Dimitrov | CC BY-SA 3.0 |
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| Feb 3, 2013 at 9:04 | history | edited | Vesselin Dimitrov | CC BY-SA 3.0 |
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| Feb 3, 2013 at 8:01 | history | edited | Vesselin Dimitrov | CC BY-SA 3.0 |
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| Feb 3, 2013 at 7:49 | history | edited | Vesselin Dimitrov | CC BY-SA 3.0 |
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| Feb 3, 2013 at 5:31 | answer | added | Sam Lewallen | timeline score: 26 | |
| Feb 3, 2013 at 3:44 | answer | added | Koushik | timeline score: 1 | |
| Feb 3, 2013 at 3:03 | answer | added | Terry Tao | timeline score: 19 | |
| Feb 3, 2013 at 2:13 | answer | added | Harry Altman | timeline score: 5 | |
| Feb 3, 2013 at 0:52 | answer | added | Michael Joyce | timeline score: 2 | |
| Feb 2, 2013 at 22:14 | answer | added | Alexandre Eremenko | timeline score: 47 | |
| Feb 2, 2013 at 21:41 | answer | added | Vaughn Climenhaga | timeline score: 7 | |
| Feb 2, 2013 at 21:38 | answer | added | Simon Lyons | timeline score: 5 | |
| Feb 2, 2013 at 21:24 | answer | added | Paul Reynolds | timeline score: 17 | |
| Feb 2, 2013 at 21:18 | answer | added | shane.orourke | timeline score: 11 | |
| Feb 2, 2013 at 21:14 | comment | added | user5117 | A finitely-generated infinite group has 1, 2, or infinitely many ends. (But if you leave out the word "infinite", it becomes a tetrachotomy; this seems to be a weakness of the question.) | |
| Feb 2, 2013 at 21:09 | history | edited | Vesselin Dimitrov | CC BY-SA 3.0 |
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| Feb 2, 2013 at 21:02 | history | edited | Vesselin Dimitrov | CC BY-SA 3.0 |
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| Feb 2, 2013 at 20:59 | answer | added | Mariano Suárez-Álvarez | timeline score: 8 | |
| Feb 2, 2013 at 20:51 | answer | added | Mariano Suárez-Álvarez | timeline score: 19 | |
| Feb 2, 2013 at 20:46 | history | edited | Vesselin Dimitrov | CC BY-SA 3.0 |
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| Feb 2, 2013 at 20:32 | history | edited | Vesselin Dimitrov | CC BY-SA 3.0 |
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| Feb 2, 2013 at 20:25 | history | asked | Vesselin Dimitrov | CC BY-SA 3.0 |