Timeline for What is an important mathematical question?
Current License: CC BY-SA 4.0
47 events
| when toggle format | what | by | license | comment | |
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| May 28, 2023 at 14:32 | review | Close votes | |||
| Jun 1, 2023 at 10:05 | |||||
| Feb 27, 2023 at 12:42 | comment | added | Amir Asghari | The one that will end up with an important mathematical answer. | |
| Feb 27, 2023 at 11:42 | answer | added | Andrea Alciato | timeline score: 3 | |
| Feb 27, 2023 at 11:03 | answer | added | Carl-Fredrik Nyberg Brodda | timeline score: 7 | |
| Feb 26, 2023 at 20:02 | comment | added | Robbie Goodwin | Sorry and how is it hard to see that this Question depends far more - perhaps solely - on the Questioner's mental state than on any logic? | |
| Feb 25, 2023 at 19:53 | answer | added | usul | timeline score: 0 | |
| Feb 25, 2023 at 16:33 | comment | added | P. Grabowski | Personally, I think that the level of generality of the question asked is too narrow, i.e. a righter, sic!, question would something like: what is an important question about anything? One could try to answer this that the one that provides more meaning than other questions by its existence or by its solution or ... . But then, how do we get to a meaning? Welcome to the question of existentialism, or a Gromov's ergo-mathematics. :) | |
| Feb 25, 2023 at 16:01 | comment | added | tparker | @JochenGlueck I agree with you that the question "Which kinds of mathematical problems does the current mathematical community find important?" is important, has real-world consequences, and has reasonably objective answers. But that isn't the question that the OP asked, and (in my opinion) the OP's question is indeed opinion-based and off-topic for Math Overflow. I think that the OP's question would be on-topic for Philosophy SE, and your proposed alternative question would be on-topic for Academia SE, but neither question is on-topic for this network. | |
| Feb 25, 2023 at 14:05 | history | reopened |
Jochen Glueck Sam Nead user37214 Dustin G. Mixon M.G. |
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| Feb 25, 2023 at 14:02 | comment | added | Jochen Glueck | @LSpice: Sure, many important things are opinion-based. If, though, the important thing under consideration involves judging other people's performance at an institutional level, one will typically expect the opinions to be guided by somekind of intersubjective understanding of what constitutes a good performance. A figure skater might get different scores for the same performance, based on each juror's individual opinion. But this does not render the question "What makes the performance of a figure skater good?" completely opinion-based. | |
| Feb 25, 2023 at 10:36 | review | Reopen votes | |||
| Feb 25, 2023 at 14:07 | |||||
| Feb 25, 2023 at 9:24 | history | closed |
Najib Idrissi Alexey Ustinov LSpice Alex M. Fernando Muro |
Opinion-based | |
| Feb 25, 2023 at 5:03 | answer | added | Timothy Chow | timeline score: 13 | |
| Feb 25, 2023 at 0:03 | comment | added | bof | The most important mathematical question is the one you have just asked. | |
| Feb 24, 2023 at 22:12 | comment | added | T. King | I quite like mathematical problems motivated by physics. | |
| Feb 24, 2023 at 21:44 | answer | added | Paul Siegel | timeline score: 9 | |
| Feb 24, 2023 at 19:32 | comment | added | LSpice | @JochenGlueck, re, I'm not quite sure what to conclude from your comment. As you point out, how it is decided whether a problem is important is itself important, and needs to be known. But there are a lot of important things that are largely, if not wholly, opinion based—and I'd argue that reputation and importance are two—so that's not a contradiction, is it? | |
| Feb 24, 2023 at 19:22 | comment | added | paul garrett | @marshalcraft, of course, "as it happened", the resolution of Fermat's Last Theorem by Wiles (with help from Taylor) involved partial proof of the Shimura-Taniyama conjecture, which (to me) was something I thought I'd never see! :) | |
| Feb 24, 2023 at 18:53 | answer | added | shark | timeline score: 22 | |
| Feb 24, 2023 at 18:49 | answer | added | Libli | timeline score: 16 | |
| Feb 24, 2023 at 17:56 | comment | added | marshal craft | There are some questions that are significant or maybe not too, like p!=np if it’s true it doesn’t help much but it remains unproven. Obv if it were false it would be important cause it would improve computation times which would be useful. | |
| Feb 24, 2023 at 17:53 | comment | added | marshal craft | And as you ask all of this can be made concrete, you can explicitly state these things. | |
| Feb 24, 2023 at 17:51 | comment | added | marshal craft | I think In my opinion an important question is one that reveals a lot. So if you compared Fermat last theorem to say Galoui theory, I’d say Fermats theorem is not as important because it does not reveal as much. It may be more complex but is not more significant. I’d say too there is a tendency today for mathematics to be more complex while less significant. There has been a lot of discoveries and because of that there is a lot to explore and problems which arise while doing that. | |
| Feb 24, 2023 at 17:39 | comment | added | marshal craft | I think this is a very important question. Clearly some questions are more important in math then others. Sometimes it is a mode of operation in which motive is not important. | |
| Feb 24, 2023 at 17:34 | comment | added | Jochen Glueck | @TomCopeland: Idealistic? Well, that's certainly none of the word's that I had in mind when I wrote my comments above. I'm also not quite sure where you see a "narrative". Perceived importance of one's research is of course not the only major influence on one's careers - but it certainly is one point that has a very strong influence. | |
| Feb 24, 2023 at 17:26 | comment | added | Tom Copeland | Ex. 3) The Scottish Cafe and the Scottish Book (en.wikipedia.org/wiki/Scottish_Caf%C3%A9). | |
| Feb 24, 2023 at 17:22 | comment | added | Tom Copeland | @JochenGlueck, your narrative is a little idealistic, eh? It's the interplay between what you know and who you know that establishes viable careers. I'm sure many have examples of this. One of my favorites is Gian-Carlo Rota starting the journal Advances in Mathematics to publish his own papers, which allowed him to build a medium via which to establish a mutual-support group of individuals who could then form a consensus on what questions were 'important' to them, or central to 'progress' in their shared interests, in the fields of combinatorics and probability. Ex. 2) Abel and A. Crelle. | |
| Feb 24, 2023 at 17:11 | answer | added | coudy | timeline score: 1 | |
| Feb 24, 2023 at 16:52 | comment | added | Benjamin Steinberg | Important mathematical questions are questions raised by Important mathematicians. Important mathematicians are mathematicians who answer important questions :) | |
| Feb 24, 2023 at 16:35 | history | became hot network question | |||
| Feb 24, 2023 at 16:17 | answer | added | fedja | timeline score: 11 | |
| Feb 24, 2023 at 15:45 | comment | added | JP McCarthy | This is a question I have wanted to ask but assumed off topic. I hope it stays open. | |
| Feb 24, 2023 at 15:37 | history | edited | LSpice | CC BY-SA 4.0 |
Oops, missed one
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| Feb 24, 2023 at 15:27 | history | edited | LSpice | CC BY-SA 4.0 |
its -> it's
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| Feb 24, 2023 at 14:43 | comment | added | Jon Bannon | Here is a perhaps silly definition: a question X is important at time t if the resolution of X allows the solution to many acknowledged open questions in the literature at time t. (This is surely insufficient...but is it right to zeroth order, even?) | |
| Feb 24, 2023 at 14:22 | answer | added | Alexandre Eremenko | timeline score: 9 | |
| Feb 24, 2023 at 14:04 | history | edited | YCor | CC BY-SA 4.0 |
formatting
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| Feb 24, 2023 at 13:08 | comment | added | R. van Dobben de Bruyn | I wrote some of my thoughts on the mechanisms of what makes interesting or fashionable research in this answer. But this question is slightly different, and I would be interested to read people's ideas. | |
| Feb 24, 2023 at 12:18 | history | made wiki | Post Made Community Wiki by David Roberts♦ | ||
| Feb 24, 2023 at 10:26 | answer | added | Gil Kalai | timeline score: 33 | |
| Feb 24, 2023 at 10:02 | comment | added | Gil Kalai | There is a view that natural problems are bad problems gilkalai.wordpress.com/2019/04/25/… | |
| Feb 24, 2023 at 8:57 | comment | added | Jochen Glueck | I mean, seriously, the entire academic ecosystem is built on reputation, which relies in turn to a significant degree on perceived relevance of research questions and results. Whether your research is seen as important decides whether you publish in the Annals or in Rejecta Mathematica, whether you become a professor or Dr tried-hard-but-couldn't-find-a-postdoc. Careers and large amounts of money depend on what is considered to be important - but when somebody asks "Ok, so how do you determine what is important?", then it's suddenly entirely opinion-based? | |
| Feb 24, 2023 at 8:57 | comment | added | Jochen Glueck | I disagree quite strongly with the reason for the close vote. Of course a significant degree of opinion necessarily occurs here, but there are also quite a lot of things to say from a more objective perspective (at least at a meta-level, i.e. "what makes people consider a question to be important?"). | |
| Feb 24, 2023 at 8:56 | review | Close votes | |||
| Feb 25, 2023 at 9:26 | |||||
| Feb 24, 2023 at 8:47 | comment | added | Matthieu Romagny | This is not an easy question. You may wish to have a look at Tao, Terence, What is good mathematics? Bull. Am. Math. Soc., New Ser. 44, No. 4, 623-634 (2007). | |
| Feb 24, 2023 at 8:36 | history | edited | David Roberts♦ |
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| Feb 24, 2023 at 8:34 | history | asked | ArB | CC BY-SA 4.0 |