Timeline for Should every modern day mathematician care about category theory? [closed]
Current License: CC BY-SA 4.0
42 events
| when toggle format | what | by | license | comment | |
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| Sep 16, 2021 at 10:27 | history | left closed in review |
Alex M. Alexey Ustinov Johannes Hahn |
Original close reason(s) were not resolved | |
| Sep 14, 2021 at 19:17 | comment | added | Emil Jeřábek | @AlexM. The question currently has three votes to reopen. I’m not much into reviewing, but I think that the way it works is that any vote to reopen the question pushes the question into the reopen review queue unless it is already pending there, and apparently, this may happen repeatedly if a new vote to reopen arrives after the previous review was finished. Note that anyway, a “leave closed” review has hardly any effect; what matters are the votes. | |
| Sep 14, 2021 at 18:26 | comment | added | Will Sawin | @AlexM. Is O.P. responsible for this? I wouldn't think question askers can trigger reopen votes without editing. | |
| Sep 14, 2021 at 18:21 | comment | added | Alex M. | @WillSawin: What is happening right now is a total abuse: this question has been closed with 5 out of 5 votes. Next, the reopen process got completed once with 3/3 "leave closed" votes. A second reopen process had the same fate with the same score. Now a THIRD reopen process has been triggered! And all this IN THE TIMESPAN OF A SINGLE DAY! Don't you think it is a bit too much, and too aggressive? And for what? For a question that invites more to chatting, rather than to giving objective answers - which is exactly what MO is not (a discussion forum, or a mailing list). O.P., PLEASE STOP THIS! | |
| Sep 14, 2021 at 17:31 | review | Reopen votes | |||
| Sep 16, 2021 at 10:27 | |||||
| Sep 14, 2021 at 16:25 | comment | added | Will Sawin | I don't know whether you are satisfied with the answers you have received or want more. If you want more, you certainly shouldn't be discouraged by having the questions closed - if you edit the question to be less opinion-based, it will most likely be reopened. This would likely consist of (1) deleting the comments about disliking category theory or replacing them with something else, (2) explaining what kind of mathematics you do or want to do. People will be able to give much more precise answers on how category theory is or isn't needed for your area than in general. | |
| Sep 14, 2021 at 14:07 | history | left closed in review |
Alex M. Johannes Hahn Anton Fetisov |
Original close reason(s) were not resolved | |
| Sep 14, 2021 at 9:24 | review | Reopen votes | |||
| Sep 14, 2021 at 14:07 | |||||
| Sep 14, 2021 at 9:01 | history | left closed in review |
Alexey Ustinov Alex M. Johannes Hahn |
Original close reason(s) were not resolved | |
| Sep 13, 2021 at 22:34 | review | Reopen votes | |||
| Sep 14, 2021 at 9:01 | |||||
| Sep 13, 2021 at 20:31 | comment | added | Andy Putman | @NoahSnyder: I mostly roll my eyes when young people do this, and I certainly had many embarrassing opinions at that age. But there are an alarming number of purported adults who cheer them on. Like so many ways in which our culture is degenerating, I blame the internet. | |
| Sep 13, 2021 at 18:49 | comment | added | Noah Snyder | @AndyPutman: There are certain topics that tend to attract people at a younger age. It's quite rare to find an 18-year old who is really into Symplectic Geometry, but it's much more common with Number Theory, Logic, and Category Theory (and I say this with great sympathy as someone who thought Number Theory was the one true topic when I was 18). I think this kind of fervor about the "one true way" is common among the young. Of course some people stick with that opinion after they're no longer 18. | |
| Sep 13, 2021 at 18:13 | comment | added | dhy | (I know this is tautological.) I've never found it useful to learn subjects of math that I don't care for just because they were supposed to be "important." If they really are important, usually I eventually see those tools used in some very cool way, and then I feel motivated to learn them. | |
| Sep 13, 2021 at 18:11 | comment | added | dhy | ...There have been a lot of comments on the interconnectedness of mathematics, and how categorical notions appear in other subjects, etc. A more indirect (but IMO more important) argument: every field has some standard collection of proof strategies and philosophies. Learning other fields exposers you to a wider variety. E.g. I have a purely algebraic AG paper where the main argument is inspired by the use of Sobolev spaces to construct Donaldson invariants. On the other hand, my experience is that this sort of inspiration only happens when you find the field in question inspiring... (cont.) | |
| Sep 13, 2021 at 17:57 | comment | added | dhy | Two conflicting comments: 1. I think that the "minimal required amount of knowledge" about any subject for a mathematician, even one working in that subject, is quite a bit lower than often claimed. E.g. Most algebraic geometers I know would only be able to read 10% or so of what gets published in the math.AG tag on arxiv. A significant portion of them know very little category theory, despite AG being more categorical than most subjects. If you really don't like any one subject, it's not that hard to avoid it. 2. You can draw inspiration from almost any part of math... (cont.) | |
| Sep 13, 2021 at 17:30 | comment | added | Yemon Choi | As concrete advice to the OP: you might find the answers to this older question mathoverflow.net/questions/19356/… valuable in the broader context of People's Views On What Everyone Should Do Or Know. FWIW I think Noah's answer to your question is a wise one. | |
| Sep 13, 2021 at 17:28 | comment | added | Dave L Renfro | @Andy Putman: It's hard for me to conceive that category theory might one day be another small corner of math, but of the things I listed, someone in the late 1940s might have said the same thing about lattices, which at the time were "seen everywhere" in general topology, set theory, functional analysis, logic, algebra, etc. | |
| Sep 13, 2021 at 17:19 | comment | added | Andy Putman | @DaveLRenfro: You'll notice that now that the hype has died down, all the subjects you list are just ordinary little corners of math, like everything else. None of them lived up to their initial rhetoric. | |
| Sep 13, 2021 at 17:13 | comment | added | Dave L Renfro | @Andy Putman: I don't know much category theory, and I have rarely felt the need to learn more (although this may change, as it seems a very useful for some things I've recently been looking at), but it clearly provides unifying language and principles to a lot of contemporary pure mathematics. That said, I can't help but feel that history is repeating itself when one looks back at what was said about quaternions in the late 1800s, about lattices in the 1940s and 1950s, about catastrophe theory in the 1970s and 1980s, about chaos and complexity, $\ldots$ | |
| Sep 13, 2021 at 17:01 | comment | added | Andy Putman | I'm mostly trying to stay out of fights on the internet, but I'm just kind of weirded out that category theory seems to constantly attract a sort of quasi-religious devotion from its fans. It seems way out of proportion to its actual importance, and I don't understand the sociology here. My own thinking is moderately categorical, though I try to be eclectic. But when I start seeing these nutcases on the internet I want to pretend that I know nothing about the subject. It's just embarrassing. | |
| Sep 13, 2021 at 16:46 | comment | added | Yemon Choi | It feels to me like some respondents here are relitigating derogatory/ignorant comments they may have heard from other people who sneered at category theory, rather than responding to an inexperienced student who has just been told "every mathematician who ignores category theory will be left in the gutter". I find that line deplorable, and I would still find it deplorable if the words "category theory" were replaced by "Banach spaces" or "operator algebras" or "PDE", etc | |
| Sep 13, 2021 at 16:18 | comment | added | Philippe Gaucher | I have voted to close this question because I am more than tired by this kind of question. Nobody would never ask such a question by replacing 'category' by anything else you prefer. It is based on prejudices and I would like to share my annoyance here. | |
| Sep 13, 2021 at 16:14 | history | closed |
Paul Taylor Steven Landsburg godelian Gro-Tsen Philippe Gaucher |
Opinion-based | |
| Sep 13, 2021 at 15:26 | comment | added | Vivek Shende | @DavidBen-Zvi I think between the original question and your comment one sees exactly the source of this attitude: category theory is presented as high-brow mathematics. Compare: many people dislike combinatorics, but one would never call them "anti-intellectual" -- instead, one would say they "don't like to get their hands dirty". | |
| Sep 13, 2021 at 15:05 | history | made wiki | Post Made Community Wiki by Stefan Kohl♦ | ||
| Sep 13, 2021 at 14:37 | answer | added | Igor Belegradek | timeline score: 28 | |
| Sep 13, 2021 at 14:28 | comment | added | David Ben-Zvi | This question reminds me of the kind of response many of us get when describing our profession, "Oh, I've always hated math.." and the underlying sentiment that they don't actually need it in life. Certainly many mathematicians don't need category theory in any way, but the phrasing of this question (and other comments on the subject around the site) strike me as embodying an anti-intellectual attitude towards the subject which for some reason is more acceptable in the math community than a similar distaste for [name your favorite mainstream area]. | |
| Sep 13, 2021 at 13:54 | comment | added | Simon Henry | I mostly agree with Tim Campion's answer, but I would add that it also higly depends on the kind of math you're doing. Some areas use a lot of category theory ( not just topology) and you can't survive without it, other don't really but are somehow prone to such uses and even though you might get away without it, it might be good for you to learn about it, and others areas are just very far from it... So, as a starting PhD student, I would recomend you to ask their opinion on this to your advisor(s) and peoples working in fields that are of interest to you. | |
| Sep 13, 2021 at 13:45 | review | Close votes | |||
| Sep 13, 2021 at 16:17 | |||||
| Sep 13, 2021 at 13:35 | comment | added | Hans | @PaulTaylor yes I'm ignorant, that's why I'm asking this question. | |
| Sep 13, 2021 at 13:32 | comment | added | მამუკა ჯიბლაძე | I would say singing praises and having dislike are equally unreasonable stances | |
| Sep 13, 2021 at 13:30 | comment | added | Paul Taylor | This is the first time I have ever voted to close a question, because usually that is done to shut down any genuine discussion of professional issues. However, this "question" is wholly based on ignorance and malice. | |
| Sep 13, 2021 at 13:29 | answer | added | Noah Snyder | timeline score: 39 | |
| Sep 13, 2021 at 13:21 | comment | added | mme | The point isn't that it's impossible to avoid category theory. The point is that as a mathematician it is useful to know many things. On a separate note, don't pay attention to polemics, you can do mathematics you enjoy. | |
| Sep 13, 2021 at 13:21 | answer | added | Tim Campion | timeline score: 26 | |
| Sep 13, 2021 at 13:19 | comment | added | Carl-Fredrik Nyberg Brodda | @Hans DenisNardin is not saying that it is not possible to avoid category theory -- they are saying that trying to avoid any specific area is not a very good idea (and I agree). | |
| Sep 13, 2021 at 13:16 | comment | added | Carl-Fredrik Nyberg Brodda | "Category theory is used mainly in topology" [Citation needed] | |
| Sep 13, 2021 at 13:08 | comment | added | Denis Nardin | If I can give a more general comment, trying to avoid as much as possible any area of math is a failing strategy. Math thrives in unexpected connections. | |
| Sep 13, 2021 at 13:08 | comment | added | Sam Hopkins | Yes, it is possible to survive in current mathematics without caring about category theory. Mathematics is large (it contains multitudes); some areas don't interact with category theory at all. | |
| Sep 13, 2021 at 13:07 | history | edited | Sam Hopkins | CC BY-SA 4.0 |
deleted 5 characters in body; edited title
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| S Sep 13, 2021 at 13:06 | review | First questions | |||
| Sep 13, 2021 at 13:37 | |||||
| S Sep 13, 2021 at 13:06 | history | asked | Hans | CC BY-SA 4.0 |