Not signed in (Sign In)

Vanilla 1.1.9 is a product of Lussumo. More Information: Documentation, Community Support.


    I think that having a list of counterexamples in algebra is a Good Idea. I don't think that MO is the appropriate place to host it. Here's my reasons:

    1. One doesn't want to sort such counterexamples by popularity! One wants a decent index, cross-referenced, and all that jazz. At the very least, a wiki if not a proper database (though I'm not sure how to set such up usefully).
    2. It won't get added to after an initial surge, and later additions won't get checked against earlier additions. So it will remain incomplete, but anyone wanting to do it properly will get told 'This is on MO'.
    3. As a question, it's not focussed: it's not easy to think of what would make an answer that could be accepted!
    4. As a question, it's too broad.

    Original question:

    • CommentAuthorCSiegel
    • CommentTimeJun 22nd 2010
    I'm in agreement here, Andrew. This seems like a good project to go on a wiki somewhere (I don't have the ability to host one at the moment, sadly!) and eventually be published as a book to sit beside the others. (And in fact, I've got in my "to write" list, aside from notes on all the things I'm learning, a counterexamples in AG document) Anyone who's willing to host such a project, I'll gladly give my time and effort to help it grow, but MO isn't the right place.

    Having just finished grading a load of papers, I felt inspired to act on my own recommendations:


    (PS If you don't have anywhere better to put your "counterexamples in AG", why not try the nLab?)

    • CommentAuthorCSiegel
    • CommentTimeJun 22nd 2010
    I intend to add them, once I can find them! Sadly, I may have lost quite a bit of it when my old laptop died, and now I can only find an old skeleton of my collection. Well, I can scour the MO archives for a few of them.
    • CommentAuthorgilkalai
    • CommentTimeJun 22nd 2010
    Andrew: "One wants a decent index, cross-referenced, and all that"

    If somebody is willing to take the effort this is certainly possible. One can devote a designated answer to index+cross reference.

    Certainly the collective outcome of answers to such a question can be used as a s resource for doing it on another platform.
    Why not leave it up for a few days, then close it to keep it from repeated bumpings (same as "math jokes")?

    I think, in addition, that it'd be rather inconsistent to close this one, when many others such as "What are some correct results discovered with incorrect (or no) proofs?" (, "Papers that debunk common myths in the history of mathematics" (, "Famous mathematical quotes," (, and so on. The question of concern will probably prove very useful to students with its answers, while the questions just listed are of primarily historical or non-mathematical interest (and so, I think, should be considered less important to this website), and yet they were left open (at least for a significant length of time).
    1. Arguing "But question X wasn't closed" is a Bad Idea with me. My reaction is usually to go back and vote for the others to be closed as well! After all, I've clearly decided right now that I don't like the current question (as an MO question, let's be clear on that) so saying that certain others are like it is more likely to make me think that those others aren't good MO questions than to make me revise my current opinion.

    2. Exactly how will the answers to this question be useful to students? Compared to, say, a wiki page such as this one. Let's be clear on this: I am definitely not saying that this question has no point to its existence whatsoever. I am saying that it doesn't make sense for it to be on MO when there's a better place for it to be. Often when I vote to close some discussion question (like the "should π be 2π?" one) then I get the plaintive wail, "Where else should I ask this?". Most times, I just shrug and say, "Don't know, I just know it shouldn't be here.". Here, at last, I can actually say where it should be!

    3. (Addressing Gil's point). Having copied over most of the answers, I can attest to the fact that it would be much, much better if people added their counterexamples directly to the nLab page. It would be a pain to click on each question, view the source, cut-and-paste, modify for different syntax, and repeat. In fact, I just rewrote each question but whilst that was okay for about 20 answers, it would rapidly get annoying for more. Far, far easier if everyone adds their answer to the right place first off - no more work for them, no additional work for anyone else.


    @Akhil Mathew: I voted to close all of those too. Just because some of us are inconsistent doesn't mean that we now have to leave open every big-list question. Imagine getting arrested for something and telling the judge "but one of my friends did it one time and the cops let him go, so come on..."

    • CommentAuthorgilkalai
    • CommentTimeJun 22nd 2010
    MO is more suitable place to ask this question compared to nLab simply because in nLab the question will attract fewer answers and fewer readers. It is legitimate to not like big list problems and, in fact, the big list tag was created precisely to allow people who do not like them to ignore them. But a hostile attitude to big list questions is not justified and is inappropriate. It is also not reasonable to vote to close a question simply because one feels that there is a better platform on earth for this question. One has indeed to argue why is this question worse than others, or why we need a change in policy.

    I'm going to ignore most of what Gil's just said (my blood pressure won't take it) and focus in on one very specific aspect:

    MO is more suitable place to ask this question compared to nLab simply because in nLab the question will attract fewer answers and fewer readers.

    I would like to say that MO is a more suitable place to ask this question than the nLab, but the nLab is a more suitable place to answer this question.

    If I didn't think that this question had any merit whatsoever then I would have just voted to close and ignored it for the rest of time. I've actually spent a fair amount of energy on this question, maybe more than anyone else today!, because I think that the answers to this question are worth putting somewhere better than MO. So actually, I'm not hostile to this question at all and such an accusation shows that I haven't made my case properly.

    I don't remember exactly where I saw this, but somewhere on SO is a Venn diagram with wikis, forums, and blogs as the main sets and SO as the intersection. I think that's a good diagram, but I think that I take from it something that the person who drew it didn't intend. Rather than saying that SO combines the best of wikis, forums, and blogs, I see it rather as SO simply combines them. But in so doing, it has to sacrifice some of the strengths of each. This particular question is a clear case where the strengths of a wiki would be an enormous benefit. Has anyone looked at that page that I created? I just copied over the answers; since then, Urs Schreiber has organised it by area and added loads of hyperlinks. So now someone who sees a particular counterexample can click on the relevant links and remind themselves of what the definitions are! (Admittedly, some links are awaiting filling, but then there aren't so many algebraists on the nLab.)

    • CommentAuthorHarry Gindi
    • CommentTimeJun 22nd 2010 edited

    There aren't so many algebraists on the nLab

    All of you algebraists hear that? We'd love you to contribute. There is a noticeable dearth of algebraic geometers...

    • CommentAuthorCSiegel
    • CommentTimeJun 22nd 2010
    For some blatant self-aggrandizement, I organized it into sections, and Urs cleaned it up from there...I'm still trying to find my damn AG list to add to it, might just have to go in by hand and try to recall them...and maybe Ravi can be persuaded to add some of the nice counterexamples he's constructed on his website?
    Thanks much for your help on this question! It probably was better suited for a wiki- good call. On a more general note, however:
    While I haven't been on the site long, I have noticed a rather unfortunate tendency for questions to be closed very quickly. It seems to me that closing a question is something that should only be done if we have given the community enough time to vote it up or down. After all, MO is supposed to be quite democratic, and it seems silly to rush to a decision like closing until a large number of people have gotten a chance to weigh in. Now, I realize that there are some questions that are very clearly inappropriate, and these can surely be moderated... but for borderline cases, I think we should let MO do its thing for a bit until we close.

    On yet another note: How exactly are "big questions" and "soft questions" supposed to be used? They are, by there very nature, much less focused than normal questions. I agree that in my case the question was better for a wiki, but, honestly, is there an example of a big list that ISN'T better for a wiki? By their very nature big lists SHOULD be categorized and organized by type of answer, etc. But I don't think MO should just get rid of the "big list" tag, because MO has a huge audience (bigger than any wiki I've seen) that can offer a wide variety of answers. Andrew, I'd rather you not ignored this part, but nLab, by definition, is targeted towards category theorists (I'm NOT saying those are the only people who visit the site, far from it). So, supposing someone had asked for a list of Counterexamples in Analysis (and the book had never been written), would you have moved that discussion to nLab? It wouldn't seem appropriate.

    Am I making any sense? I suppose my main points are: if a few people can get together and close a question very easily, what's the point of voting up or down? and: if big lists are better formatted in wiki's, why do we have them at all in MO? My answers are: closing questions should be done more diplomatically, and big lists should be accepted and encouraged, even though they are not the optimal layout, there are usually some very interesting responses!
    • CommentAuthorCampaigner
    • CommentTimeJun 22nd 2010
    @Andrew Stacey: Why isn't the nLab using some wiki software as backend? It would look so much prettier.
    One point I'd like to make is this. I'm usually pretty left wing about leaving questions open. I think that if a mathematician has a genuine question that MO can help answer, then it is best to leave it up even if it isn't strictly what MO is about. However, questions like this are just fishing expeditions; I don't see how they help anyone. Moreover, they tend to acquire lots of answers over a long period of time and stay at the top of of the list of questions. I thus think it is best to close them.

    Of course, there are exceptions. For instance, is a great question. Maybe a good policy is that people should be discouraged from asking these sorts of big-list questions until they are active on this site in other ways first. If they really, REALLY want to ask them before they have been active for a while, then they should first ask on meta whether it is a good question.

    Questions like this are just fishing expeditions.



    @Dylan, and others who wonder why we close questions.

    The overall mechanism of the site results in "broad" and "easy" questions getting lots of upvotes, with "narrow" or "technical" questions getting fewer, solely as a result of the relative readerships! As such, there is a natural tendency for pretty much all of the questions that "we don't like" to receive lots of upvotes --- because these questions tend to be relatively comprehensible to a wide audience. If we want to promote (as we do!) the use of MathOverflow for answering narrow and technical questions, there will always be some tension between voting totals and community moderation.

    Moreover, we're strongly committed to maintaining MathOverflow at the "research-oriented" end of mathematics discussion on the internet. Our target audience is at one extreme of potential audience for "mathematics on the internet". If we have an entirely democratic policy, it seems there's just no way to control the slide towards mediocrity. That said, we've always wanted meta to provide the sort of democracy we don't really believe in via the "voting" system, so make your case! :-)


    @Charles: many apologies! I should have checked the page history. Urs told me (via the nForum) that he'd edited the page and I assumed that that was the next edit after mine. Mea culpa, and welcome to the nLab!

    @Dylan: the closure system is the community in action. I am not a moderator, nor affiliated with any in any way. I've just been around a long time (comparatively speaking) and so have learnt what does and does not work on MO. In order to encourage what does work, then I often vote to close on stuff that I know (from experience) won't work. I'm sometimes more forceful on questions like this one where it's close to the borderline because I know that the obviously bad questions will just get ignored. Ultimately it's selfish - I want people spending their time looking at questions that are directly useful to the questioner, not on other questions. In the spirit of "blatant self-aggrandizement", I'd say that my latest question is a good example of MO working as it should: there was something that I didn't know and that would have been very difficult for me to track down by myself; but to someone who did know then it took only seconds to point me in the right direction. Lots of time saved for me, almost no time lost for KP Hart.

    As for how "big questions" and "soft questions" are meant to be used, that's simple: they aren't. They're tolerated to some degree, but if it's felt that there are too many then they get stamped on. Sometimes people post here saying "I think there are too many" and then others will probably go through and vote to close a few; sometimes, everyone just gets fed up with them.

    In your case, I'd remind you that I did/do see value in the question! If it could work, I'd be happy with a system whereby someone posted a question "I've started a list of counterexamples in semiquasihemidemi-ring theory; if you have a favourite counterexample, please add it to the list at <link>" which by design would not have any answers itself but which would direct everyone to the more useful place. However, I'm sure that there are flaws aplenty with that which haven't occurred to me right now.

    And so to the nLab itself (by the way, I didn't ignore what Gil said; I just didn't respond to it). You're right. It is just for the category theorists. Clearly pages on Banach spaces, DF spaces, Frechet spaces, Hilbert spaces, barrelled spaces, bornological spaces, the closed graph theorem, complete topological vector spaces have no place there whatsoever. And most certainly there is no place for a nice diagram of properties of locally convex topological vector spaces.

    Silliness aside, yes I would have moved "counterexamples in analysis" to the nLab. Even faster than counterexamples in algebra! I certainly don't describe myself as a category theorist - I'm a differential topologist if I'm anything. I invite you to take a closer look and learn what the nLab is really all about since from what you wrote above, you don't know yet. (That isn't your fault, I admit we don't do a lot of PR, but then we're too busy actually working there!)

    @Campaigner: normally I just silently ignore any post by someone who won't even deign to tell me their name, but that was just so funny! Thanks for lightening the tone.

    • CommentAuthorCSiegel
    • CommentTimeJun 22nd 2010
    @Andrew, thank you for the welcome. I've used the nLab when I had categorical stuff I needed to get definitions for before (I tend to get there from n-category searches) and do intend, when I have time, to work out a bit of an algebraic geometry section...likely it will involve porting over, with modifications, a bunch of my old blog posts...hopefully that's acceptable, I don't know nLab culture yet.

    Please do! If you're not sure about the nlab culture, just come to the forum and ask!


    Questions like this are just fishing expeditions.


    Quantum field theory??

    • CommentAuthorHarry Gindi
    • CommentTimeJun 22nd 2010 edited

    Quoted for truth.

    I knew when I posted that, someone was going to ask about quantum field theory (perhaps in jest)?

    >As for how "big questions" and "soft questions" are meant to be used, that's simple: they aren't.

    I'd like to point out that Ben Green and Andreas Blass made their first contributions to MO in answer to a soft question of mine.
    Who says that soft questions drive good mathematicians away from MO?
    I disagree too with the thesis that all soft questions are bad. I've learned a lot from some of them! I just think it takes a special talent and feel for the community to create a good one, and thus people should be discouraged from asking them before they've gained that experience by actively participating in non-soft questions.

    I think what Andrew was trying to get at is that soft questions are missing the point of MO, which is (to borrow a buzzword from Michael Nielsen) to redirect expert attention. The fact that people learn a lot from soft questions doesn't invalidate the fact that they are somewhat contrary to the basic purpose of the site; if anything, the fact that soft questions are so popular means they take up space on the front page and make it harder for experts to read the questions they can answer. Of course, there are experts like Terence Tao who excel at and enjoy answering soft questions, but they are rare exceptions!

    (Not that I've never asked or enjoyed a soft question. But as the site grows I find myself becoming more and more of a "strict constructionist" with respect to the FAQ.)

    • CommentAuthorVP
    • CommentTimeJun 22nd 2010

    I am in agreement with Gil Kalai both in that "such a question can be used as a resource for doing it on another platform" and that "It is also not reasonable to vote to close a question simply because one feels that there is a better platform on earth for this question". Let me state up front that when I saw this particular question, my first reaction was: "Oh, no, not again!". While I recognize its potential merit, I am not particularly biased in its favor. Andrew's desire to find the best forum for the question is praiseworthy and his effort in setting up a hosting page is acknowledged. However, there is an important issue of unintended consequences to consider.

    Transferring a question to your favorite site and closing it here may be aggravating to other people, as well as ineffective.

    For example, I am not a member of nLab, I am not familiar with its overall purpose, editing software, or editing culture, and I don't want at this very moment to commit to participation there (I followed the nLab link before reaching this decision). Thus while it will take mere moments for me to contribute to answers at MO, I will most certainly not do it over at the other site. The argument of the type "I spent a huge effort just copying the answers and adjusting, why can't people just do it themselves?" just invites a response: "Why should they do something that you like, and they may disagree with?" Additionally closing the question on MO is unmistakenly dictatorial and this seems like a truly Bad Idea.

    MO exists because of good will of its participants and we have to ask ourselves whether alienating people for an illusory and subjective purpose of "maintaining purity" is a worthwhile trade-off (as John Stillwell's remarks indicate, the issue of what's best is far from simple). Andy Putman's suggestion that big-list questions from inexperienced users should not be encouraged is worth listening to: can this be codified somehow? I know that FAQ explicitly mentions it, but as regular flare-ups on meta demonstrate, this, evidently, is not robust enough.

    Where I agree with Andrew Stacey is in that maintaining two synchronized copies of the answers is a tedious task. But highlighting the fact that the migration process is tedious, even for an experienced user of both systems like he, only reinforces my impression that things should best be left alone for a while. Any kind of editorial work is tedious, and I can see an advantage in eventually creating an authoritative version of the answers, which is rubricated, supported by citations, cross-referenced, and edited for style and uniformity (just like a real book!). It is short-circuiting the process that I find both short-sighted and ineffectual.

    @Andrew- I just don't think that "big lists" and "soft questions" aren't meant to be asked at all... these make for very interesting reads on the site! Anyway, isn't there an option on the site that allows you to ignore big questions so they never pop up? It sort of follows from the very fact that there are two sides in this argument that there are some people who enjoy the big lists and others who don't, so why close them down when you can just ignore them? That way everyone wins: you don't see them if you don't want to! (On another note: I realize that nLab may have articles on various non-category-theoretic items, I'm just saying it is geared towards category theoretic thinking. Case in point: "This is a wiki-lab for collaborative work on Mathematics, Physics, and Philosophy- especially from the n-point of view: insofar as these subjects are usefully treated with tools and notions of category theory or higher category theory." If I'm not mistaken that's the description of the site.)

    @VP and John Stillwell- Thanks! Solid points.

    I would have voted to close because as Andy said, this question seemed like a fishing expedition. It was very much like a "I'm not particularly interested in anything in particular, so everybody write down a bunch of crap I can read!"

    It's almost identical to a thread "What are your favorite theorems in algebra?", which is more clearly off-topic.

    I do agree that a wiki is perhaps the optimal format for this particular question, but as others have pointed out, the question will likely get much more attention on MathOverflow. I do not recall the precise statistics of usage, but I doubt someone would have a better way of getting the attention of a really wide array of mathematicians than by asking on MathOverflow (unless the person operates a really high-profile math blog like Terence Tao's or SBS). This is why I had advocated a level of "judicial activism" with respect to certain borderline questions. Since MathOverflow has become so popular and has a wide readership, I think its scope can be expanded slightly. The present question may have been a vague fishing expedition, but while deciding to close the usefulness of such questions to the community at large should also be considered.

    For the record, I agree that questions of purely historical interest, "favorite theorems," and homework or calculus level questions, should be closed mercilessly. Also, if the question is to remain closed, including a link to the nLab page in the question itself was definitely a good idea.
    • CommentAuthorYemon Choi
    • CommentTimeJun 23rd 2010

    Ive been a bit busy to formulate a coherent contribution to tis thread, but for the record my first impulse/inclination is closest to Andrew Stacey's than to others. I am not instinctively sympathetic to the reasoning that "now MO is more popular and has reached a broader audience, it should cater to them" - going back to Andrew's own oft-repeated point that MO can do one thing very well (bringing a specific question to the attention of people for whom it is easily answerable) which is not done well elsewhere, and it is something of use to research-active mathematicians. I don't really want it to be some kind of "portal/gateway for the mathematical community", although that may not be what people are suggesting it should be - forgive me for any misreadings caused by haste.

      CommentAuthorJon Awbrey
    • CommentTimeJun 23rd 2010 edited

    In the light of what has been said above, it seems that the motto ensconced in the “welcome” box may be logically ambiguous. “A place for mathematicians to ask and answer questions” leaves open the interpretations (1) that people other than research mathematicians are welcome to ask questions of mathematicians and (2) that people other than research mathematicians are welcome to answer questions asked by mathematicians. Perhaps a stricter grammatical construction would serve to close out these misinterpretations.

    • CommentAuthorChuck Hague
    • CommentTimeJun 23rd 2010 edited
    I too would prefer to see fewer soft questions on MO. It seems as though there's been a massive influx of such questions recently. As to worrying about overly enforcing the purity of math overflow, certainly we can all agree that a line has to be drawn somewhere; it's just a question of where to draw that line. My understanding is that MO is a place for asking questions that are connected to mathematical research, and I can't think of a way in which soft questions aid research. Rather, they are just a fun topic of discussion, and saying that they are not appropriate for math overflow is not to say that they aren't worth talking about in general -- it's just that I don't think they're appropriate for a site aimed for researchers. Such a distinction is clear; it isn't illusory.

    The explosion of soft/discussion-y questions, as well as the fact that the community seems to be more and more supporting of them, has made me less interested in MO recently. I expect the same is true for many other research mathematicians as well, and having lots of questions like this will alienate more distinguished people than will be retained (I hasten to add that I don't include myself among the group of distinguished mathematicians). Furthermore, such questions clearly run counter to the spirit of MO. From the FAQ: MO is for "research level math questions" with "a specific answer," and soft questions definitely fail the second criterion; in my opinion they also fail the first. Also from the FAQ: MO "is not a discussion forum." To me, this pretty clearly outlines the purpose of MO.
    Ok now I'm even more confused. As I understand it, my question was closed for being too broad. But, Andrew, here is one of YOUR questions (or at least, a question which you supported): "Theorems for nothing (and the proofs for free)." Now, this asks for a `big list' of theorems with weak hypotheses and strong results... Certainly in any sense of the word broad, this question is equally, if not more, broad than "Counterexamples in Algebra."

    Can we at least admit to a slight bias here? People with a higher reputation (real reputation, not reputation points) are more likely to get a break when it comes to closing questions... Shouldn't a question be closed or open solely based on how good of a question it is, not who asks it? It all seems a bit silly, yeah?

    @Dylan: Tu quoque

    Anyway, Andrew has said a number of times that his opinions have changed since he first came here.

    @Harry- Whoops! Alright, I concede that point (because I dislike fallacies as much as the next mathematician). Though I still maintain that questions asked by more reputable people are given more leniency... I mean, that's almost unavoidable- we are all human. But is there a way to moderate this? Should it be moderated?

    For the record, it's really Anton's oft repeated point that MO should do one thing and do it well. It took me a while to come round to it, as witnessed by questions like "Theorems for nothing" (which I've just voted to close, by the way, since I would not ask it now), but I'm now fully convinced that he's right. As I changed my mind on this issue, I am perhaps more vocal than others who were in agreement with Anton all along. It's worth all of us remembering that these issues have been discussed before, so those to whom they are fresh should be aware that the others of us have done so, and those of us who have discussed it before should be aware that the newcomers haven't!

    I can think of a way that this question could have been put which I would have been happy with:

    I'm learning some algebra, beyond the normal undergraduate syllabus, and am getting a bit bewildered by all the different types of structures that there are. In other subjects where I've encountered this, such as topology, I've found it useful to have a list of examples showing the subtle differences - often these are called counterexamples. In topology and analysis, there are the classic "Counterexamples in X" books but there doesn't seem to be one in Algebra. So I'm compiling my own. I've made a start at link but, as I'm sure will be appreciated, it's hard for a beginner to find counterexamples for everything. So I'd like to ask if anyone has a favourite counterexample in algebra.

    Community wiki rules, of course. And I'll add the answers to my list (though anyone is welcome to add them themselves since it is a wiki) and I hope that it will be a useful resource for others.

    Reasons why I'd be happier with that:

    1. The person asking explains why they want the list to be made and how it will help them in their current work.
    2. The person asking has already done some work towards answering the question themselves.
    3. The person asking has thought about how best to use the answers once they've been given.
    4. The project is bigger than the question.
      CommentAuthorJon Awbrey
    • CommentTimeJun 23rd 2010

    Et tu, tu quoque?

    So you're saying that diagonalization is a logical fallacy?

    At any rate, observing discrepancies between espoused values and enacted values affords invaluable information toward the design and maintenance of social-technical architectures. When people persistently behave in ways that depart from their touted principles, it may be an indication that (1) there is a problem with their actions, (2) there is a problem with their principles, (3) all of the above.


    -1 Jon Awbrey. I never know what the heck you're talking about.

    @Harry: Thanks for the link "Tu quoque". I knew the phrase but the cartoon with the Sutherland Highlander really made me roar with laughter. Reader, go and look at it even if your Latin is on a par with Virgil's.
      CommentAuthorJon Awbrey
    • CommentTimeJun 23rd 2010

    @ QFT (Quantum Fishing Trip?) — Not to worry, someday there will be an app for that.

    "I too would prefer to see fewer soft questions on MO. It seems as though there's been a massive influx of such questions recently. As to worrying about overly enforcing the purity of math overflow, certainly we can all agree that a line has to be drawn somewhere; it's just a question of where to draw that line. My understanding is that MO is a place for asking questions that are connected to mathematical research, and I can't think of a way in which soft questions aid research. Rather, they are just a fun topic of discussion, and saying that they are not appropriate for math overflow is not to say that they aren't worth talking about in general -- it's just that I don't think they're appropriate for a site aimed for researchers. Such a distinction is clear; it isn't illusory."

    Hm, I hadn't thought of the point that allowing questions like "counterexamples in algebra" would drive away research mathematicians (which isn't surprising, since I'm definitely not one). But, come to think of it, I think other mathematicians have expressed a similar distaste for them on meta in the past.

    Since I'd consider attracting good research mathematicians to the website a much more important goal than indulging big lists, I drop all my past objections to closing them (and have "come around," to use Andrew Stacey's phrase).

    I do hope the other math site proposed on area51 gets off, though, so these soft questions will get asked somewhere where they have a good chance of being answered.
    • CommentAuthorEmerton
    • CommentTimeJun 23rd 2010

    I am a research mathematician who read the answers to the question under discussion and learnt something from some of them, so I am happy that it was asked. As John Stillwell already remarked, one shouldn't presume that these kinds of questions are disliked by all participants. As with many things, some like them, some don't.

    If the question is good enough for Emerton, then it is good enough for me! I retract my criticism and just voted to reopen.
      CommentAuthorJon Awbrey
    • CommentTimeJun 23rd 2010 edited

    It seems to me that much of the continuing dissonance at MO Math U is really a problem of software design, in particular, the fact that we are using a 1-page attention buffer, in effect, a 1-room schoolhouse model. Try to imagine your average math department scheduling all of its diverse and sundry graduate seminars in the same room at the same time. How could anything but gnashing of teeth and grinding of gears be expected to result?


    @Andy: you're worse than a politician! Agreeing with the last person who spoke!

    For once, I think that Jon's said something sensible! If we think of MathOverflow as the be-all and end-all of maths on the internet and the only place that we (as mathematicians) can interact, then it will break under the pressure. If we treat it as a part of a larger game then it has a chance to work and to be something really useful.

    I don't think that the answer is by partitioning MO (using tags or whatever) as the boundaries are too fluid. Rather, we need other sites that can be used in conjunction with MO. Then everyone can pick and choose the bits that they like according to taste. Big one-stop shops are ugly and frustrating. It may be necessary for me to buy my groceries in a massive supermarket, but it doesn't mean that I enjoy the experience at all. Browsing the shops in a mall, or a quaint English village (with a pub, of course) is a much more pleasant experience.

    The argument that that doesn't exist yet doesn't wash. I'm busy building my area of this vast conglomeration, Anton and Scott (and ...) are busy building theirs. If you like what you see, great! But if you think something is lacking then build it yourself! It's a lot of fun and there's plenty of space around.

    I've learnt things from reading the answers to these "soft questions", just like the others have. I've even answered a few. However, it's not an efficient way for me to learn things, or an efficient way to communicate my "wisdom" (such as it is). So if that becomes the predominant type of question at MO then sheer economics of time will mean that I'll not come here. There are so many little bits of lore in all sorts of places that missing out on the few buried deep in the junk at MO will not discombobulate me overmuch. Losing the ability to short-circuit the journey from "topological spaces in which singleton sets are G_delta subsets" to "countable pseudocharacter" would be a far greater loss.

    In summary, I see MO as a place where research-level mathematicians come when they are in research mode. So that's completely different to when we visit blogs and the like. I suspect that many are coming here when they are in "goofing off" mode and I don't like that because it's distracting. Anyone with kids will have seen this: when all are playing nicely and quietly then it's great, but once one starts acting up then it doesn't take long before they're all at it.

    • CommentAuthorHarry Gindi
    • CommentTimeJun 24th 2010 edited

    For once, I think that Jon's said something sensible!

    If you say enough things with no regard for the topic at hand, you will probably eventually say something relevant.

    Then again, Andrew, remember that you only "think" that he's said something sensible. You may be reading too much in to it.

    • CommentAuthorgilkalai
    • CommentTimeJun 24th 2010 edited
    Dylan, all

    I think that the question in question is an OK question. It is not a particularly good or surprising question but it is acceptable, and it led to many rather good answers in a very short time. So it created some excitement which I did not see good reasons to stop. (I know that some people think that you cannot judge a question by the answers it attracts but I disagree with them.) I am a little bit worried about some of the arguments which are rather weak and some which are "theological" (in the sense that they refer to a imaginary reality and imaginary notions.) There is this idea that experts who come to MO with good intentions are driven away by the "big list" questions. This seems false. (Note that there is a distinction between soft questions like those about beamers and blackboards and jokes and about big list questions which are entirely research oriented, but what I say refers to both categories.) There is the related specific claim that "allowing questions like "counterexamples in algebra" would drive away research mathematicians". Again, this seems nonsense. It is true that some like such questions and some don't. However, I do not see why such a question will drive away even a research mathematician who do not like this question, and I dont see any evidence for that.

    However, I do not see why such a question will drive away even a research mathematician who do not like this question, and I dont see any evidence for that.

    I don't think that I've ever argued that such questions will drive away research mathematicians. I've tried to argue that it will drive away me since that is the only data point that I can be sure of. I've also tried to explain why it would do so so that others can decide whether I'm just being unreasonable or I might be indicative of a wider group.

    • CommentAuthorgilkalai
    • CommentTimeJun 24th 2010 edited
    Andrew, it is unreasonable to think that an ordinary MO participant who is a research mathematician or an expert will be diven away by a small percentage of (legitimate) problems that he does not like. If one finds reading and contributing to certain questions "inefficient" then he or she will simply not do it. There is a small fraction of highly devoted participants who have strong views (but not the same views) about how MO should be, and indeed it may be the case that a few of those will be driven away if things will not run the way they want. This is understandable, but is still somewhat unreasonable.