Timeline for Was lattice theory central to mid-20th century mathematics?
Current License: CC BY-SA 3.0
20 events
| when toggle format | what | by | license | comment | |
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| Mar 13 at 0:43 | history | edited | Jukka Kohonen |
tag fix (order lattices)
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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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| May 29, 2014 at 4:58 | answer | added | Tri | timeline score: 7 | |
| Feb 12, 2014 at 13:43 | answer | added | user46855 | timeline score: 25 | |
| Feb 3, 2014 at 10:30 | answer | added | Gejza Jenča | timeline score: 4 | |
| Dec 24, 2013 at 0:03 | comment | added | Marcus Johnson | Let me quote Dieudonné in the Bulletin of the AMS, 1953, vol 5, p483, reviewing Jacobson's 'Lectures in abstract algebra' vol II: "...a whole page is devoted to the "modular" law in the lattice of subspaces, which is never used any more (and is there apparently for the sake of those who still believe lattice theory is an important part of mathematics!)." | |
| Dec 18, 2013 at 19:03 | answer | added | Gerhard Paseman | timeline score: 8 | |
| Dec 18, 2013 at 17:53 | answer | added | Pasha Zusmanovich | timeline score: 7 | |
| Dec 5, 2013 at 1:11 | answer | added | Benjamin Steinberg | timeline score: 16 | |
| Dec 2, 2013 at 23:12 | comment | added | Timothy Chow | One anecdotal piece of evidence that many people believe that lattice theory is currently not central is the fact that Wehrung's solution to one of the biggest open problems in lattice theory was rejected by JAMS on the grounds that the paper lacked "interaction with other areas of mathematics." See item [68] on the page math.unicaen.fr/~wehrung/pubs.html for more information. If lattice theory were considered central to mathematics, then I think it is unlikely that Wehrung's paper would be rejected with a phrase like that. | |
| Dec 2, 2013 at 17:26 | comment | added | Benjamin Steinberg | I am hoping a real expert like Richard Stanley will pipe in. Lattice theory was more fashionable than people like to admit. Dedekind considered them, Stone was interested in them and created Stone duality, which was the precursor of Gelfand duality and Zariski spectrum, to understand boolean algebras and distributive lattices. Think about the spectrum of the lattice of radical ideals! von Neumann also studied lattices to some extent in connection with logic and other areas of math. Geometric lattices are important in matroid theory and semimodular lattices are related to the greedy algorithm. | |
| Dec 2, 2013 at 10:00 | comment | added | Misha | Incidentally, lattices understood as discrete subgroups of locally compact groups with finite covolume (which is, of course, different from OP's question), are indeed central in mathematics, and realizing this centrality can indeed be traced to mid 20th century. This centrality comes from their connection to number theory, representation theory, topology and Riemannian geometry. | |
| Dec 2, 2013 at 8:08 | comment | added | KConrad | What was the book you were reading, even if it's not easily available online? | |
| Dec 2, 2013 at 4:54 | answer | added | Joseph Van Name | timeline score: 5 | |
| Dec 2, 2013 at 3:13 | comment | added | Joseph Van Name | There are only 16 questions on this site tagged lattice theory, so it is probably safe to conclude that lattices are nowhere near taking over mathematics yet. | |
| Dec 2, 2013 at 3:11 | comment | added | Andy Putman | Rota claimed in many places that lattice theory is a central topic (e.g. here : ams.org/notices/199711/comm-rota.pdf; I believe that he said a lot more in either "Discrete Thoughts" or "Indiscrete Thoughts", but I don't have either handy). But of course you should keep in mind that he liked to be provocative... | |
| Dec 2, 2013 at 3:07 | history | edited | Brian Rushton | CC BY-SA 3.0 |
added 193 characters in body
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| Dec 2, 2013 at 3:01 | review | Close votes | |||
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| Dec 2, 2013 at 3:00 | comment | added | lmg | I don't have enough reputation to comment, but I wonder how meaningful it is to talk about the centre of mathematics. An earlier question about this concept did not go over so well: mathoverflow.net/questions/131800 | |
| Dec 2, 2013 at 2:41 | history | asked | Brian Rushton | CC BY-SA 3.0 |