Timeline for Individual mathematical objects whose study amounts to a (sub)discipline? [closed]
Current License: CC BY-SA 2.5
35 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 12, 2010 at 16:07 | comment | added | Pietro Majer | Although I like the question, I have the feeling that this list could be made very very long. The aspect that seems interesting to me is, how objects that where initially exceptions or counter-examples became themselves archetypes of sub-disciplines or even new theories. Examples of this are the Peano's and von Koch's curves, born as counterexamples to properties linked to differentiability, now archetypes of fractal objects. | |
| Dec 12, 2010 at 16:03 | comment | added | S. Carnahan♦ | Sorry, I think the question as stated is not sufficiently focused to match the purpose of this site. | |
| Dec 12, 2010 at 16:01 | history | closed |
Kevin H. Lin Daniel Moskovich Denis Serre Harry Gindi S. Carnahan♦ |
off topic | |
| Dec 12, 2010 at 14:00 | answer | added | Marcin Kotowski | timeline score: 3 | |
| Dec 12, 2010 at 13:48 | answer | added | Guillaume Brunerie | timeline score: 1 | |
| Dec 12, 2010 at 10:17 | comment | added | darij grinberg | David: thanks a lot for the link. And you reminded me of this: a generic (i. e., the vertices are independent variables in a rational function field) inscribed hexagon ("inscribed" can mean inscribed in a circle, or, more generally, inscribed in a conic). Think of Pascal's theorem, and all that comes after it: Steiner points, Kirkman points, Cayley lines, Plücker lines... Oh, and of course the generic triangle is a whole science in itself. | |
| Dec 12, 2010 at 9:10 | history | edited | Denis Serre | CC BY-SA 2.5 |
added 2 characters in body
|
| Dec 12, 2010 at 6:09 | answer | added | sleepless in beantown | timeline score: 3 | |
| Dec 12, 2010 at 6:02 | answer | added | sleepless in beantown | timeline score: 0 | |
| Dec 12, 2010 at 5:21 | answer | added | Yemon Choi | timeline score: 2 | |
| Dec 12, 2010 at 4:17 | answer | added | Vivek Shende | timeline score: 9 | |
| Dec 12, 2010 at 2:20 | comment | added | David Feldman | cont.-- I wanted...and I'm getting...a list of objects about which I can say...here are some things (as opposed to methods or facts or constructions) that mathematicians get excited about. I don't mean to reduce the study of mathematics to these objects, but merely to emphasize an aspect of mathematics for which most undergraduates I encounter in my teaching never get a feeling. | |
| Dec 12, 2010 at 2:19 | comment | added | David Feldman | @Ryan Thank you for pointing me to that question - some of those examples are useful here too, but I see a distinction. Namely this: a counterexample may alter the direction of a discipline or subdiscipline or field or line of research ... without become a focus thereof. Here's my philosophy. Many students of mathematics come away with the view that mathematics is a tool rather than a science. Students of the physical sciences often get excited about the objects studied by those sciences: galaxies, black holes, viruses, dinosaurs, quasicrystals, DNA, etc. | |
| Dec 12, 2010 at 2:06 | history | made wiki | Post Made Community Wiki by David Feldman | ||
| Dec 12, 2010 at 2:04 | comment | added | Ryan Budney | @David, this thread appears to becoming a duplicate of: mathoverflow.net/questions/4994/fundamental-examples Do you have a specific distinction between this list and the other? | |
| Dec 12, 2010 at 1:53 | answer | added | Dick Palais | timeline score: 4 | |
| Dec 12, 2010 at 1:41 | answer | added | Amit Kumar Gupta | timeline score: 2 | |
| Dec 12, 2010 at 1:35 | answer | added | Georges Elencwajg | timeline score: 3 | |
| Dec 12, 2010 at 0:29 | comment | added | David Feldman | @Darij That deserves to be an answer! As for the 27 lines, this gives some idea of the richness of the story: en.wikipedia.org/wiki/Cubic_surface | |
| Dec 12, 2010 at 0:20 | comment | added | darij grinberg | I think $\mathrm{U}_q\left(\mathfrak{sl}_2\right)$, the quantum deformation of $\mathfrak{sl}_2$, is an example. In contrast to $\mathrm{SL}_2\left(\mathbb R\right)$, the interesting things about $\mathrm{U}_q\left(\mathfrak{sl}_2\right)$ are algebraic and still interesting over $\mathbb C$. | |
| Dec 12, 2010 at 0:14 | comment | added | darij grinberg | ... and for every prime power. ;) But probably the one for $p=q=2$ is already mysterious enough. | |
| Dec 12, 2010 at 0:10 | comment | added | David Feldman | @Darij I think you grok my intentions. I would rather have too many suggestions than too few though. I anticipated that "the one versus the many" issues would arise. I think only an expert can say when the gluing of many objects into one is artificial. It would surely spoil my question to accept all answers of the form "the category of...," but sometimes one really does study a category primarily as an object unto itself rather than merely as a collection of interesting objects. Likewise, someone suggested "the Steenrod algebra" but of course there's one for every prime. | |
| Dec 12, 2010 at 0:02 | answer | added | Andrey Rekalo | timeline score: 6 | |
| Dec 12, 2010 at 0:00 | history | edited | David Feldman |
edited tags
|
|
| Dec 11, 2010 at 23:56 | answer | added | Gerry Myerson | timeline score: 6 | |
| Dec 11, 2010 at 23:46 | answer | added | J.C. Ottem | timeline score: 8 | |
| Dec 11, 2010 at 23:44 | answer | added | J.C. Ottem | timeline score: 5 | |
| Dec 11, 2010 at 23:40 | comment | added | darij grinberg | ... artificial way to collect the properties of various Galois extensions of $\mathbb Q$. Also, what is the theory of the 27 lines on a cubic? | |
| Dec 11, 2010 at 23:40 | comment | added | darij grinberg | OK, let me try to fiure out what you want: you want objects which looked small and hand-tame when they were discovered/introduced, but turned out to be full of complexity and mystery when studied. So things like "the Mandelbrot set" is okay because it was originally defined in its entirety, but things like "the category of representations of the symmetric group" are not because first came the representations, and only later they were artificially collected into a category. Now, I think "the absolute Galois group of the rationals" is more an example of the latter kind, as it is just an ... | |
| Dec 11, 2010 at 23:33 | answer | added | Bill Johnson | timeline score: 2 | |
| Dec 11, 2010 at 23:18 | answer | added | Todd Trimble | timeline score: 8 | |
| Dec 11, 2010 at 22:47 | comment | added | David Feldman | @Ryan - >Perhaps you have a pretty light definition of a subdiscipline, but I would imagine any such object would have to strictly contain at least one member -- someone that primarily lives in that realm? I take yours as a semantic quibble. Can you find me a better word than sub-discipline? In any case, it's not important to me whether any particular mathematician "lives primarily in that realm." If the single object has a large literature and tends to feature in the titles of works that study it, that might suffice for me. | |
| Dec 11, 2010 at 22:13 | answer | added | Fedor Petrov | timeline score: 5 | |
| Dec 11, 2010 at 21:54 | comment | added | Ryan Budney | I don't agree with your premise. Take any of your examples and look at the main contributors to their discovery and development and you'll notice few if any of those researchers lived inside a field devoted to the study of these objects. Douady, Hubbard, Fatou and Julia would certainly object to being described as Mandelbrot set theorists. Perhaps you have a pretty light definition of a subdiscipline, but I would imagine any such object would have to strictly contain at least one member -- someone that primarily lives in that realm? I doubt any of your examples satisfy this condition. | |
| Dec 11, 2010 at 21:47 | history | asked | David Feldman | CC BY-SA 2.5 |