Timeline for Which revolutions in topology and geometry can we expect in the next 20 years? [closed]
Current License: CC BY-SA 4.0
29 events
| when toggle format | what | by | license | comment | |
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| Feb 1 at 13:53 | history | left closed in review |
Alex M. Mikhail Katz Lee Mosher |
Original close reason(s) were not resolved | |
| Jan 30 at 0:38 | comment | added | Andrea Marino | @YemonChoi: I don't think changes in perspective and language are narrative-based, but I agree that the conditions allowed the change to happen. I made that point in my question, and I was exactly trying to ask for "which soil is preparing a shift?". As a metaphor, there are people studying the same in geopolitics; it is very hard to predict the future, but the discussion is nevertheless worthwhile. People writing the past (and the narrative) work in a different field. | |
| Jan 29 at 22:25 | comment | added | David White | I very much appreciate folks putting their reasons for voting to close here and below my answer. I cannot help but point out that a casual reader of MO is seeing a pretty wild variation in terms of when the "opinion based" closure reason is invoked and when such questions are left to dominate the front page. I wrote about this a month ago on Meta. For me, the OP being a research mathematician, and the research focus of the question (only have finite time; not sure what best to study) makes all the difference, compared to a big list for its own sake. | |
| Jan 29 at 17:42 | comment | added | Andy Putman | @YemonChoi: I agree, and I concur I also voted without intending any malice towards the OP. | |
| Jan 29 at 17:40 | comment | added | Yemon Choi | @AndyPutman FWIW I voted to close (with no malice intended towards the OP) selecting the "Opinion-based" option. I think that a lot of these narratives get written in hindsight, and overemphasise "breakthroughs" and "revolutions" while ignoring lots of the incremental work that provides the soil in which dramatic ideas can take root | |
| Jan 29 at 16:46 | comment | added | Andy Putman | I voted to close the question for exactly the reason Sam Hopkins stated, which I also expressed in my comments (the non-geometric nature of the examples was more of an aside in those comments). Whenever I vote to close, I always choose "not about research level mathematics" as the reason, which I interpret as "inappropriate for MO". Obsessing about the minutia of exactly which closing justification on the list most closely matches the actual issue with the question seems to me like a poor use of one's time. | |
| Jan 29 at 14:46 | comment | added | Sam Hopkins | The reason I don't think this question is appropriate for here is because I don't think it is really answerable. It asks us to guess about the future. A question like "which of the six remaining Millennium Prize problems will be resolved next?" would similarly be inappropriate (even if it is clearly about research math in a certain sense). | |
| Jan 29 at 14:09 | comment | added | Andrea Marino | I agree that the question is research level, so I guess it should be closed for other reasons (e.g. subjectivity). Nevertheless, I take the closing act as an indirect answer to the question "Can we predict ..?" with a bold "We can't". I theoretically disagree, but there are many experienced researchers that expressed this opinion, so I guess in practice it is very hard (probably, it is only possible in hindsight). Also, I am glad not to open MO to handle controversy, so I agree with its closure. | |
| Jan 29 at 13:18 | comment | added | David White | The question has been closed for reason "not about research level mathematics" but I think that's an error, so I voted to reopen. The OP is a research mathematician who makes clear that he wants to know which areas to focus his time on, to stay up to date with developments, because these areas are likely to be related to future research. The question is +17/-9. The comments make it seem like the votes to close have to do with a lack of geometric examples or the idea that the question is hard to answer. But, I do think it's about research level mathematics. | |
| Jan 29 at 13:14 | review | Reopen votes | |||
| Feb 1 at 13:53 | |||||
| Jan 29 at 9:36 | history | closed |
Andy Putman Fernando Muro Sam Hopkins Yemon Choi Bruno Martelli |
Not suitable for this site | |
| Jan 28 at 18:36 | history | edited | David White | CC BY-SA 4.0 |
A lot of the pushback against this question has to do with difference of opinions about what constitutes "geometry." To try to mitigate this, I edited slightly. If the OP disagrees, please feel free to roll back. I also retagged since a comment pointed out that none of the tags have "geometry"
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| Jan 28 at 0:32 | comment | added | Andy Putman | @AndreaMarino: I don't think those are any more predictable. | |
| Jan 28 at 0:31 | comment | added | Andrea Marino | @Andy Putman: I am not sure I emphasized this enough, but my stress is on language and formal changes more than on results and discoveries. As I mentioned, my motivation is: will I still be able to read geometric articles being published in a neighborhood of algebraic topology without studying too much background? For example, if I got my PhD fifteen years ago, I guess I would have struggled a bit to learn infinity categories in the spare time (I am considering to leave academia). I found it nice to include big perspective shifts in the question, which have an interest oon their own. | |
| Jan 28 at 0:29 | comment | added | Andrea Marino | @Deane Yang: to my surprise, tunless I am screwing something up, there is no tag "geometry". Free to edit if I am wrong! | |
| Jan 27 at 20:16 | review | Close votes | |||
| Jan 29 at 9:41 | |||||
| Jan 27 at 19:57 | comment | added | Andy Putman | The title doesn’t seem to have much to do with the non-geometric examples the OP has in mind. Also, “revolutions” are almost by definition not things you can predict. All you are going to get as answers are breathless invocations of whatever is being hyped at this moment. I entered grad school 22 years ago, and there is almost no relationship between what was being hyped then and what actually lead to advances in the intervening years. I have therefore voted to close. | |
| Jan 27 at 17:21 | comment | added | Deane Yang | From my limited perspective, revolutions come out of nowhere and blindside everyone. So they're rather hard to predict. I'm also older and I don't know that much about algebraic geometry. But it seems to me that the revolution in algebraic geometry and topology really originated in the introduction of category theory itself. It originated as an abstract seemingly empty framework for organizing proofs in algebraic topology. But it turned into much more than I think anyone imagined it would. There certainly have been revolutions within this, but I think you have to start there. | |
| Jan 27 at 17:12 | comment | added | Deane Yang | Isn't it a little odd to have a question about geometry that doesn't have a single tag with the word "geometry"? | |
| Jan 27 at 17:11 | history | edited | David White | CC BY-SA 4.0 |
Added a missing word to the title, to make it a sentence.
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| Jan 27 at 17:11 | comment | added | Deane Yang | Differential geometry is a huge omission. In my view, there was a revolution sparked by the work of Taubes and Uhlenbeck which led directly to Donaldson’s spectacular work. Parallel to that were more geometric approaches developed by many but perhaps most spectacularly by Gromov. Yau and Schoen, among others used all of this and more to build a new area, now called geometric analysis, and connected it to topology. Hamilton also came along and launched a revolution within a revolution using geometric heat flows, which culminated in Perelman's proof of the Thurston conjecture. | |
| Jan 27 at 15:21 | comment | added | YCor | @DavidWhite to complement Asaf's comment: one could make one's own question CW before, but it changed (maybe 5 years ago?). So the solution, both for OP and for you as a reader, is to flag asking the post to be made CW. | |
| Jan 27 at 15:15 | comment | added | TheSimpliFire | Circles, and not just in the next 20 years. | |
| Jan 27 at 15:00 | answer | added | David White | timeline score: 0 | |
| Jan 26 at 20:19 | comment | added | Asaf Karagila♦ | @DavidWhite No, that's not true. You can't mark a question CW. Only moderators can. You can mark an answer that you are posting as CW. But that's different. | |
| Jan 26 at 20:19 | history | made wiki | Post Made Community Wiki by Asaf Karagila♦ | ||
| Jan 26 at 17:21 | comment | added | David White | Big list, subjective questions should generally be CW. You can edit and check the box to make it so. See, for example: meta.mathoverflow.net/questions/4112/… | |
| Jan 26 at 16:58 | comment | added | Andreas Blass | I'd add, to your list of past revolutions in Geometry: Euclid's Elements, coordinates (analytic geometry), projective geometry, unprovability of the parallel postulate, geometry over fields other than the reals. | |
| Jan 26 at 9:02 | history | asked | Andrea Marino | CC BY-SA 4.0 |