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    This is coming from this recent thread and a few other things that are going on in the background of MO these days.

    We often hear good things about how MO is useful in a mathematician's daily work. "MathOverflow is like the colleague down the hall" is something I hear very often. Our founder Anton once said: "I want(ed) MathOverflow to be useful for me!" Other moderators, including myself, have been caught saying similar things here and there.

    I would like to know how MO is useful for YOU!

    (Input from "lurkers" is especially welcome! Note that is completely separate from You don't need a MathOverflow account to post on meta. Even if you do have a MathOverflow account, your meta account is not tied to it in any way. Anonymous posts are also welcome.)

    • CommentAuthorMarc Palm
    • CommentTimeDec 7th 2012
    My thesis would not have been possible without MO, at least not in its present form.
    It helps to kill time! :-)

    Also it allows me to test the water about certain questions and answers if I am not fully confident in them. I also like how it made a lot of people accessible for questions and answers. That's always nice.

    I live on an island with few other people, let alone mathematicians. So this gives me a relatively easy place to talk about mathematics that I find interesting.

    1. The way mathematicians write is usually different from how they speak. In a way, the answers on MathOverflow have a more immediate spontaneous quality closer to spoken math. I find these very instructive, especially when they are about fields different from mine.

    2. In writing my own answers, I've found that it helps to focus my own thoughts about my subject.

    (I'm trying to focus on the positive, but I do have some mild reservations as well.)

    Besides giving me an opportunity to read and think about mathematics that I probably wouldn't encounter otherwise, MO provides a window onto how others think about mathematics, which is very interesting and useful to me. On occasion, one can see some beautiful and elegant mathematics at play in a relatively informal setting, which is very pleasant indeed. I also like the occasional challenge of answering questions that are not my own.


    MO gives a glimpse into problems that are interesting to people outside my own field (and outside my department). I don't mean the big-picture questions from other fields, for which I can read expository accounts elsewhere and for which MO is ill-suited. I mean the subsidiary technical problems which come up in the "real world" (defined in the extremely weak sense of "anything other than the subsubfields of mathematics in which I work, including other subsubfields of mathematics") that may be approachable with methods I know about. Reading, and occasionally trying to answer, such questions is a useful counter to the tendency toward mathematical navel-gazing.

    I'd like to add some input that may be a little controversial. I once read that one way to learn about something is to try to change it. That is, one learns a lot by looking at a system in trouble (rather than when it is working correctly).

    Questions that are closed interest me. By finding out what makes a question (or an answer) bad (say, lack of definitions), I learn a lot about what makes a question (or an answer) good.

    I also learn a lot about the mathematics community whenever I see controversial questions and answers in MO. What is considered acceptable? How is a consensus reached? Mathematics is a very social activity and MO allows me to be a part of it.
    1) I learn a lot by answering questions. Sometimes it forces me to work out an explicit example of something I already more or less understand, and sometimes I end up learning about something I didn't understand until I started thinking about my answer.

    2) I learn a lot by asking questions. Asking questions in general is my go-to strategy for learning new things, and I've gotten some great answers to my questions. In some cases I have received answers that I probably never would have found any other way. Bill Thurston's answer to my question about the Schwarzian derivative is a stand-out example of this phenomenon.

    3) I'd like to second Joel Reyes Noche's comment: I learn a lot from some of the questions that get closed. Sometimes questions whose answers I don't know will get closed for being too basic, and that alone tells me something about how powerful the techniques in other areas are. Also, people often sneak in an answer or comment shortly before such questions get closed, and it's like having a little example worked out for me.

    I suppose it's hard to point to something specific in my research that wouldn't have been possible without MO. I suppose this is mostly because there aren't all that many questions about what I'm working on. MO's impact on me has more been about expanding my horizons and helping me gauge my own understanding (or lack there of).
    I have found MO invaluable. Particular success stories in my research include (I'd found a periodic tiling of R^d and *knew* it had to be *somewhere* in the literature. was a similar thing.
    MO has made it possible for me to ask questions I used to only be able to ask at conferences once or twice per year. Like many other mathematicians teaching in small colleges around the country, I do not have regular access to cutting-edge ideas and feedback from "the colleague down the hall"...especially since my training is not in an undergraduate-friendly research area. MO has helped to ameliorate a feeling of futility and isolation in my research interest by giving access to an active perpetual discussion of mathematics of a broad cross-section of the mathematical community. If there is a question I simply never will have time to look into, rather than chalking it up for lost, I now can share it with the community and thereby ensure that no matter how busy things are it is always possible to make a small contribution to mathematics by at least sharing my questions. I feel like the wonderful social aspect of mathematics that sometimes dies when a mathematician is isolated from an engaged research subcommunity is preserved by MO. I am so very deeply grateful for this I cannot adequately express it.

    MO hasn't directly helped me solve any problems, but it's definitely helped convince me that certain ideas or approaches won't work (usually something which I would've figured out on my own, but would've taken much longer).

    Also, and this is related to Donu's first comment, the big picture expositions that users like Emerton have written have been especially nice. Longer expositions of these topics exist in various places, but a one-page conversational summary is much easier to digest when you're just starting out.

    • CommentAuthorvoloch
    • CommentTimeDec 7th 2012
    I've got some very nice answers to the questions I've had. But, mostly I come to MO to answer questions myself. It's an addiction, but I can quit any time. *twitch*
    I am an amateur and as seen from my low rep. I often have hard time contributing because I don't have any solid mathematical background. Having said that I try to contribute to the soft, cw-type of questions. Of course I am a fanatic and I really love MO. But such hasn't always the case and I deleted my old account. I quickly learned that one must grow thick skin and MO is a focused site.

    So from personal experience, I would love to see more of philosophy/logic related questions where I can contribute which often gets closed from the soft nature. I really love MO and the constraint and the strict moderation actually makes this a fun place.

    Not to mention once in a while you come across a question like the one below which restores faith in humanity and makes it totally worthwhile to stick around. :)

    p.s. Oh and of course where else in interweb will you find stellar and stalwarts all in one place.
    • CommentAuthordimpase
    • CommentTimeDec 7th 2012
    As USENET mathematics newsgroups are all basically dead, and forums which tried to replace them aren't too alive either, it's great to have a resource that works so well, and managed to attract a lot of high-profile research mathematicians.

    An ability to enter and edit posts in LaTeX is great, too, and I often use it just to share thoughts with my collaborators. And getting great answers to questions is invaluable too. Answering questions by others is a lot of fun and makes you learn/refresh things quite a bit, too.
    I consider myself a mathematical mutt --- no papers. Occasionally, I venture off the back porch to play in the yard with the big dogs. Usually I end up back on the porch with tail between my legs.

    I have found the Math Overflow users to be helpful and courteous, even when closing some of my posts (under real name: Fred Daniel Kline.)

    A couple of years ago, one user gave me a great deal of help structuring my first proof. By doing this, I was able to discover a flaw that was unrecoverable.

    I am just starting to formalize a new proof, using an entirely different (and simpler) approach. And I am loving every minute of it.
    • CommentAuthorAmin
    • CommentTimeDec 8th 2012
    Being in a place which is almost like third world in many important mathematical parts, especially in things I like, MO is essentially a life saver to me ! I can ask occasionally things I feel really stuck at, and equally importantly, I can have a look at what other people in better places are up to. Most of my research life I've been alone, isolated, and it's the only little contact I have with the community, so it's really, really helpful to me.
    It is fun and I learn things I never expected to by browsing it. But the real use for me is to expand my research ability. I get good answers to questions about things not squarely in my field but useful to it.
    For me, MathOverflow has been "procrastination" of the best kind. In a period when I felt a little bit listless about my continuing research, I learned a lot by trying to answer questions in MO. Not only did I learn new material and get good problem-solving practice, I also got a fresh sense of what mathematics is interesting, both to other mathematicians and to myself. Later I also asked some questions. This has also been useful for similar reasons, although in the end answering questions has been even more enlightening.
    • CommentAuthorshahrooz
    • CommentTimeDec 9th 2012
    For me, a PhD student and young lecturer, Mathoverflow is a place that I learned many new things from peoples and mathematicians around the world. With this site, I found this opportunity to talk with some famous mathematician. I asked questions and or answered, and people in this site helped me (with Positive or Negative Vote) to correct myself. I appreciate this place and all whom helped me directly or indirectly in this place. (Thanks)^n, n goes to infinity and (Thanks>1).
    • CommentAuthorJDH
    • CommentTimeDec 9th 2012 edited

    The principal draw of mathoverflow for me is the unending supply of extremely interesting mathematics, an eternal fountain of fascinating questions and answers. The mathematics here is simply compelling.

    I feel that mathoverflow has enlarged me as a mathematician. I have learned a huge amount here in the past few years, particularly concerning how my particular area relates to other parts of mathematics. I've read some really great answers that opened up new perspectives for me. But just as importantly, I've learned a lot when coming up with my own answers. It often happens that someone asks a question in another part of mathematics that I can see at bottom has to do with how something I know about relates to their area, and so in order to answer, I must learn enough about this other subject in order to see the connection through. How fulfilling it is when a question that is originally opaque to me, because I hadn't known enough about this other topic, becomes clear enough for me to have an answer. Meanwhile, mathoverflow has also helped me to solidify my knowledge of my own research area, often through the exercise of writing up a clear summary account of a familiar mathematical issue or by thinking about issues arising in a question concerning confusing or difficult aspects of a familiar tool or method.

    Mathoverflow has also taught me a lot about good mathematical exposition, both by the example of other's high quality writing and by the immediate feedback we all get on our posts. This feedback reveals what kind of mathematical explanation is valued by the general mathematical community, in a direct way that one does not usually get so well when writing a paper or giving a conference talk. This kind of knowledge has helped me to improve my mathematical writing in general.

    So, thanks very much mathoverflow! I am grateful.


    MO is useful for me because it provides a better way to waste time on the computer than any other site I visit.

    • CommentAuthorRyan Budney
    • CommentTimeDec 9th 2012 edited

    It's like a screensaver with actual human beings trapped inside the screen! :)

    • CommentAuthorgilkalai
    • CommentTimeDec 9th 2012 edited
    I find MO a good research tool, a good tool for research-oriented exposition.
    The way I see it, for me MO activity and other Internet-research are not side-matters of less importance to my other academic activities but they have become important part of my academic life.
    MO is also good for examining advantages, limitations, and drawbacks of Internet research activity.

    It is also a sort of documented microcosmos which can be quite telling. E.g., if you want to understand why it was (and still is) so hard for women to get into mathematical academic activity maybe MO can give you some hints. (Other examples are: attitude towards applied math, reputation, running collectively an academic endeavor etc.)
    • CommentAuthorrita
    • CommentTimeDec 9th 2012
    @gilkalai: could you please elaborate on your last comment?
    I'm very interested. I've often wondered how many women are active on MO. I would say not so many, but it's hard to tell because of people not using their real names.

    Apart from this, I enjoy both answering questions and reading other people answers on MO. I'm sort of shy at asking questions. I usually prefer to ask first people I know. If that fails and if the question does not turn out to be silly or, after all, not so relevant for my research, then I consider posting it to MO.
    • CommentAuthorfedja
    • CommentTimeDec 9th 2012
    "E.g., if you want to understand why it was (and still is) so hard for women to get into mathematical academic activity maybe MO can give you some hints." I'd like to see a more elaborate version of this comment too, but we'd better do it in a separate thread because it may result in a long and possibly quite heated discussion this particular thread has never been intended for. So, Gil and Rita, if you want it, we can open a separate meta thread on this (I believe there was one created shortly after Izabella Laba posted an elaborate article titled "Why am I not on MO" (or something like that) on her blog, but I cannot find it now.
    I would also be interested in an elaboration, in a new thread.

    Anyway, I. Laba's post:
    I'd like to second the answers of Donu, Greg, and Bill.

    (Those interested in continuing the discussion regarding Gil's last comment can do so in this thread.)

    I used mathoverflow to find references or explanations especially for stuff that is kind of folklore, i.e. it is known to everybody in a particular field, but not really written down anywhere. Moreover, mathoverflow helped me in my research by pointing me towards some ideas, I would not have pursued otherwise. Apart from that it is part of my daily routine to quickly browse through the first questions just to get in contact with interesting mathematics from different areas.

    MO may have helped me get into graduate school? I think my letter writers mentioned my MO participation.

    As someone who is just math-curious, I found MO often very helpful. Aside that the sort of comments and links which one normally finds (at least as amateur) not so quickly elsewhere in libraries or online (e.g. ), I can ask questions in MO, which would probably be too imprecise, global or silly to ask elsewhere. That helps bridging a difference in attitudes towards mathematics between someone who is just curious and a real mathematician - such attitude-gap is a bit like that between an "intellectual" and an "academic" given in an essay recently: "An intellectual is not an expert... An intellectual is a generalist, an autodidact, a thinker who wanders and speculates. As Jack Miles puts it, 'It takes years of disciplined preparation to become an academic. It takes years of undisciplined preparation to become an intellectual.'" ( )

    Concerning the voting, badges etc. system: I think it would have worked much better if it were designed in a manner which could by design not connect with participant's narcissism. E.g. "points" etc. attached to posts and comments, but completely disconnected to individuals. If I remember correctly, one had experimented in hospitals with anonymised evaluations, where individuals received statistical feedback on their work only, at longer intervals and unnoticeable for others, which worked very well there.
    • CommentAuthorTom LaGatta
    • CommentTimeDec 26th 2012 edited

    MathOverflow threads can be used as a focal point for aggregating useful resources on a particular topic, as well as to bring diverse communities together. For example, I just created a thread on applications of the Giry monad in probability and statistics. In that post, I write:

    "For the benefit of future researchers, I've created this community wiki thread to aggregate possible applications of the Giry monad in probability and statistics. My hope is that this thread might be a place for the structuralist and probability communities to come together and learn from each other."

    • CommentAuthorolga
    • CommentTimeDec 27th 2012
    Hello, I really appreciate MO, first of all because I learned a lot of math from here! I'm regularly spending time in looking for interesting questions/answers, then reading them in detail: both related to my field, or not. MO is just great for learning things, old or new, thank you so much.

    I also appreciate a lot the big-list, soft-discussion, history-overview and career-advice discussions, these are often so much better than what can be found on other websites. I'm however quite often sad when such discussions close prematurely, and I was wondering, is there any way of improving that?

    It would be so much nicer if MO, which has grown a lot, could go back to a more innocent way of working. It looks to me that most of the potentially interesting discussions that close prematurely are always closed by the same group of 10-20 people.. all reputed, well-known mathematicians, which have of course amassed a lot of reputation here (10-30K) and which seem to be here only for doing very very serious mathematics!

    Sorry of course for complaining - this might be not what Francois was asking for... - but I really find MO impossible to replace, extremely useful and important, and I would be so happy to see it - perhaps with some changes in the voting/closing system? - getting a bit more friendly in the future.