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Why do you post answers on math.stackexchange?

As a math student, this is a very helpful resource.

This could be asked for any forum, but I would like to understand the motives why people are answering questions here. Obviously there are motives like

  • helping others
  • contributing
  • ...

But more specifically: why?

Also, can people do something useful with their "points" earned on the site?

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    $\begingroup$ There is an older discussion related to the question you posed at the end: What is the Real Use of Reputation? $\endgroup$
    – Martin Sleziak
    Commented Mar 8, 2014 at 15:57
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    $\begingroup$ helping others...contributing...an ego the size of a small whale... $\endgroup$
    – user1729
    Commented Mar 8, 2014 at 16:15
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    $\begingroup$ Why do you post answers on math.stackexchange? - Because, without me, you'd all be lost. :-) $\endgroup$
    – Lucian
    Commented Mar 8, 2014 at 16:43
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    $\begingroup$ Dear jacob, See also this question and its answers. Regards, $\endgroup$
    – Matt E
    Commented Mar 8, 2014 at 20:07
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    $\begingroup$ With respect to redeeming points, there was an interesting discussion on SO about points helping you get a job... See here $\endgroup$
    – user1729
    Commented Mar 8, 2014 at 20:48
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    $\begingroup$ 200 se.math points plus $3.50 will get you a free latte at Starbuck's. $\endgroup$
    – MJD
    Commented Mar 8, 2014 at 21:50
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    $\begingroup$ I was hoping for a t-shirt :-). $\endgroup$
    – copper.hat
    Commented Mar 9, 2014 at 8:40
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    $\begingroup$ @copper.hat: You can have mine. I have no need for white t-shirts. $\endgroup$
    – Asaf Karagila Mod
    Commented Mar 9, 2014 at 16:40
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    $\begingroup$ If I knew why I do it, then I could stop. $\endgroup$
    – Carsten S
    Commented Mar 10, 2014 at 10:40
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    $\begingroup$ Why do I smoke? $\endgroup$
    – André Nicolas
    Commented Mar 10, 2014 at 22:19
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    $\begingroup$ @AsafKaragila: Smoking (tobacco) is no longer cool. Until the meaning of cool changes, answering questions on MSE will not be cool. $\endgroup$
    – André Nicolas
    Commented Mar 10, 2014 at 22:31
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    $\begingroup$ Hannibal Smith is, and will always be, the coolest badass on television. And he smokes cigars. Columbo also smokes cigars, and you want to tell me it's just an accident that they're both very cool? (Oh, and one more thing... I love it when a plan comes together.) $\endgroup$
    – Asaf Karagila Mod
    Commented Mar 10, 2014 at 22:34
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    $\begingroup$ @AndréNicolas: spoiler alert. . . . . Columbo will never be dead because he's really an angel, as revealed by Wim Wenders in "Wings of Desire"/"Himmel über Berlin". $\endgroup$
    – David
    Commented Mar 13, 2014 at 21:38
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    $\begingroup$ @user1729 No, you are wrong. $\endgroup$
    – jacob
    Commented Mar 16, 2014 at 12:53
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    $\begingroup$ @user1729 Navel-gazing is on-topic on Meta; I suggest adding navel-gazing as a tag here, to make it easier to ignore. $\endgroup$
    – user127096
    Commented Mar 21, 2014 at 1:53

31 Answers 31

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I am needy and insecure and derive validation from the gratitude of strangers.

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    $\begingroup$ Boy do I hear that one! Me too! $\endgroup$
    – Robert Lewis
    Commented Jan 14, 2015 at 6:31
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    $\begingroup$ I think this is the best answer to any question on the site (main and meta). $\endgroup$
    – Ron Gordon
    Commented Dec 8, 2016 at 13:36
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    $\begingroup$ This is the best answer I've ever read on this site xd. $\endgroup$
    – Xam
    Commented Dec 13, 2016 at 18:51
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    $\begingroup$ I would replace 'from the gratitude of strangers' by 'from anywhere I can get it.' $\endgroup$
    – copper.hat
    Commented Apr 10, 2017 at 17:03
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Because solving mathematical problems is interesting, fun and it helps to keep mental acumen.

I also find my teaching abilities, and perhaps writing abilities, to improve much faster because of this site. Also my grasp of advanced set theoretical concepts.

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    $\begingroup$ As the years go by, I'm certainly focusing more on questions that amuse me, less on the idea of successfully tutoring anyone in the way I believe such tutoring ought to happen. Nice one today, though, a bunch of comments, some legitimate back-and-forth, and the student figured it all out, just half an hour ago. $\endgroup$
    – Will Jagy
    Commented Mar 8, 2014 at 19:39
  • $\begingroup$ @WillJagy I think it depends on who you are that determines how you think about this topic. $\endgroup$
    – Simply Beautiful Art
    Commented Mar 31, 2016 at 23:08
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    $\begingroup$ @Asaf If you insist on forcing your opinion onto my writing, could you please have the courtesy to restore the original non-LaTeX emphasis as it was in 2011 (which in fact did render intalicied in those days). If I were you I would recuse myself from such given our strong disagreements in the past regarding formatting (color, etc), But obviously we have different viewpoints on such matters of ethics - nothing surprising there given prior history. $\endgroup$
    – Bill Dubuque
    Commented Jul 12, 2019 at 13:44
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    $\begingroup$ @Bill: First of all, I can agree to policies that I have a personal problems with (e.g. overuse of color when other alternatives are available). Secondly, I don't understand why you are so insistent on being exclusive to about 1 in 10 men on the planet that have problems with color vision anyway. Finally, I don't remember the minor things like Markdown in titles back in 2011, but at least according to this question, it seems that even in 2010 they were already against Markdown in titles. And anyway, restoring a faulty title, why? $\endgroup$
    – Asaf Karagila Mod
    Commented Jul 12, 2019 at 13:50
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    $\begingroup$ @Asaf Rather than we both waste more time on this, why not simply compromise and put it back the way it was in 2011? I will agree not to change it to LaTeX. At least it gets some emphasiis that way (and no one objected for 8 years). $\endgroup$
    – Bill Dubuque
    Commented Jul 12, 2019 at 14:02
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I read a story about some guy who was deathly sick and to pass the time before he expired he began to read Euclid's Elements. Needless to say he made a miraculous recovery. I was also close to buying the farm so I joined a bunch of math forums and became a little active on a few here and guess what? I feel like a 85 year old again. Sharing what you have no matter how small, giving back for everything that was given to me, that is what life is about. Sure trying to find people who know less than I do to help is hard but even a blind squirrel can find an acorn now and then.

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    $\begingroup$ This sounds a little like the story/legend about Wolfskehl, that he was going to commit suicide but got distracted by a math problem and decided math made life worth living. See en.wikipedia.org/wiki/Paul_Wolfskehl. $\endgroup$
    – Gerry Myerson
    Commented Mar 13, 2014 at 12:17
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    $\begingroup$ +1 for "needless to say" $\endgroup$
    – Guy
    Commented Mar 21, 2014 at 12:26
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    $\begingroup$ If you don't mind me asking, how old are you, that you say "I feel like an 85 year old again" to mean "feeing youthful" $\endgroup$
    – Stella Biderman
    Commented Mar 29, 2017 at 23:46
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    $\begingroup$ @Stella Biderman The girl that works at the supermarket asked me that question. I told her, visualize your daddy's daddy's daddy's daddy. Can you see that? I could be his older brother. $\endgroup$
    – bobbym
    Commented Mar 30, 2017 at 0:14
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"Karma."

Whenever I use a new program, get an error message or install a new hardware, I use google to find my problem on some forum where usually someone already answered it free of charge. This person will never even know that I was helped by the answer. Whenever I have a question about language that is not well answered by my textbook or a question about a fact, I use wikipedia and I find that someone compiled answers for free that are way better than my books. No feedback on the usefulness for me reaches the many editors of the respective articles.

One should contribute in some capacity to this collection of knowledge, and at some times, this is a place where it is more agreeable for me to do so than somewhere else.

The gamification might play some role there, but for me this is counteracted by the restriction on human contact. It is much more important to me that the interface just works reasonably well and allows others to find my answers reasonably easily.

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    $\begingroup$ Yes! Be a construction worker on the world you want to live in :) $\endgroup$
    – Ben Millwood
    Commented Mar 15, 2014 at 15:59
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There's something entertaining about answering questions that are hard enough to hold my interest but not so hard as to be a grueling experience. Also it's good to be helping students with math. I rarely use mathoverflow because the problems there are much harder and would take a while to solve if I even could. The problems in my field there often involve technical issues in other people's research.

To be honest, this site is also a way to pass the time when I have nothing else to do :) It's more intellectually stimulating than watching TV or whatnot.

Reputation doesn't play much of a role for me, possibly because I don't use my actual name here.

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    $\begingroup$ This describes my feelings entirely, except I use my real name. It's not like my participation here or on MO will get me a job, improve my reputation among the group(s) that matter to me, get me a grant or anything else that matters. $\endgroup$
    – Sam Lisi
    Commented Mar 15, 2014 at 18:17
  • $\begingroup$ This is mostly my feelings. I often don't have anything to do and am just sitting around watching netflix so I'll open this site up on auto-refresh and just look at any question that seems to be something I'd know or be interesting. Some of the problems I've found have even temporarily stumped the math professor I work with. $\endgroup$
    – ruler501
    Commented Mar 21, 2014 at 20:36
  • $\begingroup$ This site is definitely "intellectually stimulating" for the right person. $\endgroup$
    – Simply Beautiful Art
    Commented Mar 31, 2016 at 23:11
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My answers on MathStackexchange are usually not too high level questions, simply because I'm not an expert in any math field.

Now I notice that when I write an answer it is mostly when I see the problem and think I can write a concise "cool" answer or apply a tool that surprised my when acquiring it. If you have an aha-moment, you feel like now you're the one who gets it and want to induce that point of view in others.

I also don't find answering particularly rewarding, because when a $\gg 10\,\mathrm k$-user answers in the same thread, he will automatically get more votes than me and I don't think it's always because of the answer, but because of established trust.

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    $\begingroup$ "when a ≫10k-user answers in the same thread, he will automatically get more votes than me...." And your evidence for this is ... ? $\endgroup$
    – Gerry Myerson
    Commented Mar 10, 2014 at 6:13
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    $\begingroup$ Maybe it's the other way round: The reason they have >>10k rep is because their answers are usually better. (However @GerryMyerson it would be fun if this comment you made got more upvotes than the actual answer!) $\endgroup$
    – Thanos Darkadakis
    Commented Mar 10, 2014 at 6:48
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    $\begingroup$ @GerryMyerson: Just a general observation. If I browse my answers where I'm not the only one answering, there are for example this, this, this, this etc. $\endgroup$
    – Nikolaj-K
    Commented Mar 10, 2014 at 8:47
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    $\begingroup$ @ThanosDarkadakis: You say "Maybe it's the other way round:.." but what you say isn't contrary to what I say. I'm also not even saying I use StackExchange differently - it certainly has practical value to know it's e.g. Qiaochu Yuan who answered the question. I just say the reputation system is discouraging because the gamification makes it a competition and the reputation marks in the bottom corner of each question point out "this user is more knowledgable/trustable than the others by 10k". $\endgroup$
    – Nikolaj-K
    Commented Mar 10, 2014 at 8:53
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    $\begingroup$ Well, the reputation marks can be interpreted to say, this user has been here longer than the others, or spent more hours per day here than the others, neither of which makes this user any more knowledgeable or trustworthy than the others. $\endgroup$
    – Gerry Myerson
    Commented Mar 10, 2014 at 9:15
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    $\begingroup$ @NikolajK. There are many excellent answers from some of the best teachers here that have $0$ votes, while other answers have many votes simply because they were quicker. So the remark in your final paragraph is not true generally. $\endgroup$
    – Bill Dubuque
    Commented Mar 10, 2014 at 16:36
  • $\begingroup$ @NikolajK. In the examples you linked here, I can see why people might prefer the upvoted solution over yours. $\endgroup$
    – Phira
    Commented Mar 12, 2014 at 8:27
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    $\begingroup$ @GerryMyerson From my own experience, the reality is even worse. A >10k user often gets upvoted even if he read the question so carelessly that his answer is completely wrong (and admits it in the comments). If I feel forced by the wrong answer to take the time to write a correct answer to avoid spreading misinformation, it often doesn't receive any upvote at all. $\endgroup$
    – Thomas Klimpel
    Commented Mar 12, 2014 at 8:45
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    $\begingroup$ @GerryMyerson Let me add another more typical example. Somebody with high reputation provides a correct but overly sloppy answer, with a proof that would be completely false if read literally. Somebody else later tries to correct this by providing an additional answer explaining how the sloppy argument can be made rigorous. He may even receive downvotes in this case, which in case of a new user can lead to the effect that this was the first and last answer the new user ever provided on that site. $\endgroup$
    – Thomas Klimpel
    Commented Mar 12, 2014 at 9:10
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    $\begingroup$ @GerryMyerson I interpreted your "And your evidence for this is ... ?" as a request to present one or two concrete examples. I'm not thrilled by your comment "But may I say that two examples do not constitute a proof, or even a trend; they just constitute two examples". Yes, I know of some more examples like this, but I decided for myself some time ago that bringing this up on meta won't be worth the trouble, especially since the users with the wrong answers (or upvoted comments) are often people I highly respect (like JDH or Peter Smith). Your initial comment has 4 upvotes now -> atmosphere $\endgroup$
    – Thomas Klimpel
    Commented Mar 12, 2014 at 15:03
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    $\begingroup$ @GerryMyerson Sorry to add one more comment. Do you really believe that a normal user will ever receive 29 upvotes on an answer to a slightly technical question, even if the answer would be perfect in every respect? So I think one doesn't really need technical competence in order to see that the "typical" example I gave represents a real effect. I admit that in most cases such high rep users don't give wrong answers, but the fact that they receive upvotes independent of the actual technical quality of their answers remains. $\endgroup$
    – Thomas Klimpel
    Commented Mar 12, 2014 at 15:13
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    $\begingroup$ @GerryMyerson, it is purely argumentative to first ask for evidence and then set increasingly impossible standards that the evidence must satisfy to escape a dismissal. There are obvious and large social biases for and against particular users in the voting, which does not matter much where it concerns imaginary "reputation" points, but does bias the evaluation of answers. $\endgroup$
    – zyx
    Commented Mar 19, 2014 at 20:48
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    $\begingroup$ @zyx, what's large and obvious to you is inconspicuous or absent to me. Quite possibly, I am just oblivious. It wouldn't be the first time. But I still wish someone would do a well-designed study of voting patterns, so we wouldn't have to rely on impressions and anecdotes. $\endgroup$
    – Gerry Myerson
    Commented Mar 20, 2014 at 0:07
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    $\begingroup$ @GerryMyerson, have a look at the vote patterns on (main site) answers from "popular" versus "unpopular" users of the meta. Biases go well beyond that but it is one pattern that is visible. $\endgroup$
    – zyx
    Commented Mar 20, 2014 at 0:55
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    $\begingroup$ @zyx, that would require me to know what "vote patterns" means and how to have a look at them, also to know which users of meta are "popular" and which ones are "unpopular". Am I popular? are you? $\endgroup$
    – Gerry Myerson
    Commented Mar 20, 2014 at 5:25
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Here is my totally honest, non-high-flown answer:

I'm just trying to become better at math. Learning from a book and by homework exercises is not that interesting to me, but I really do enjoy teaching others. In addition, I find that I tend to give the clearest and most rigorous answers when I'm trying to explain something to someone who doesn't understand, rather than to a grader or to myself.

Moreover, gamification i.e. the reputation system really works for me. I like collecting internet points, and they give me an incentive to do as much as I can (when I have time).

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    $\begingroup$ Haha, this answer calls to me (+1) $\endgroup$
    – Simply Beautiful Art
    Commented Mar 16, 2017 at 20:19
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In 2010 a psychology graduate student did one or two surveys on motivation for people using, and especially answering, on MO; see here. Tausczik eventually published her results in psychology journals. She had been an undergraduate math major at Berkeley when MO was still in its formative stages, so she had an early interest.

I was one of the ones telephoned. At the time, I gave a lot of high-flown reasons, helping people, what have you. I think that is how many people feel for the first year or two of contributing on a site of this type. For me, there was a middle era where i mostly felt i was just showing off what i knew (this is more MSE, really), finally a relaxed time where I just answer when I feel like it. Similar with MSE, just a delay of a year. Things being what they are, it appears that those who go full blast answering questions for years at a furious pace are fairly likely to quit completely when that becomes tiresome.

Anyway, the sites are not parallel in one way that is significant for the question. On MO it is peers helping peers. On MSE it is more one-sided, more strictly teaching, and motivation does differ. I suppose I have mixed together descriptions of my behavior on the two sites. Oh, well.

It occurs to me that I can be quite specific about reputation. On MO, before it joined stackexchange proper, it was possible for a 10K user to search deleted posts, including questions deleted by the person asking, all the way back to the beginning of the site. I did this in connection with this unpleasant episode. Under the circumstances, I felt it was desirable to quickly get up to 10K here on MSE, but was disappointed to find that I had severely limited ability to search deleted posts, and no way at all to see self-deleted questions. Also there was something about not being 100% trusted until 20K. So I did that, and found no improvement in searching. After that, I felt that I had no specific benefit in answering tons of questions that I did not necessarily enjoy, or tinkering with adequate answers so as to get more points, so I just slowed down.

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    $\begingroup$ The topics posted on MO are mostly about a certain very specific part of mathematics, like abstract algebra, topology, and category theory. MSE, on the other hand, has tons of questions and answers concerning calculus. In my opinion, that is the real difference between the two. Being a huge fan of impossible integrals, infinite series, and infinite products, MO is mostly like a huge desert for me. BUT, then again, to be perfectly fair, calculus questions which find no answer on MSE, sometimes for months and years on unend, almost always find one on MO, so... $\endgroup$
    – Lucian
    Commented Mar 9, 2014 at 8:30
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Well I hope this doesn't sound naive, but I just love teaching. At work I get paid for it, which of course is brilliant, getting paid for doing something you enjoy. But I'm still happy to do more, so there's MSE. And I guess reputation is payment of a kind. So in a way I suppose you could say it's all about me, though I do also think that helping (in however small a way) to raise the world's competence in and appreciation of mathematics is a worthwhile aim.

To be a bit more specific about what I get out of teaching: a significant number of students who ask questions (whether face-to-face or online) do not really understand what their difficulty is. It may not be the question they are actually asking, but rather some very deep-rooted misunderstanding. Identifying what their real problem is and trying to answer in such a way as to address both the question asked and the deeper issues is one of the most intellectually satisfying aspects of teaching.

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  1. My education does not feel for naught when I can answer a rare, specific question. This increases my satisfaction in learning.

  2. Every question is a challenge. Can I come up with the answer? If already answered, can I come up with a different answer?

  3. Climbing the reputation ladder is fun. Given my current reputation, I feel like I am a valuable contributor to the community.

  4. The problem in question is a very satisfying question to have answered for myself, personally. I'd rather figure it out myself than have someone else answer it for me.

  5. Occasionally I do enjoy helping people, but I tend to stay away from the typical calc stuff.

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I think for three reasons.

I am not now a mathematician or in a mathematical job, but I have enjoyed maths all my life (done pretty well too), and I want to keep myself sharp and learn what's going on. I have discovered that I get more out of participating than reading - it varies over seasons and how busy I am how much I contribute here. But I enjoy it, and I learn from the engagement.

Second, I want to share my enjoyment of maths with others, and the tricks and insights and ideas I've learned along the way.

Third, which I've discovered by participating, I relish the challenge of helping someone to understand something when they seem to be stuck, not just giving the answer to the problem, but also some understanding which will develop mathematical skill and knowledge, and open up useful new ways of thinking about what to do when you are stuck.

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The best way to learn is to teach, and answering questions helps me learn. Sometimes I recover lost knowledge, sometimes in attempting to answer a question in a different way I learn something new. I enjoy teaching, but I work in industry, so my opportunities to share insight are otherwise limited.

Because of my limited time, I try to limit myself to questions that I can answer quickly, and where I believe I can transmit a genuine insight to the OP. I enjoy lots of homework and algebra-to-calculus level questions, because I feel that math education is sorely deficient in these areas, and that if I can provide insight instead of an algorithm, then I am doing that person a favor.

Also, answering questions helps keep my LaTeX and communications skills sharp.

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Self-esteem. Sometimes, when I read or hear things like Youtube comments, poorly spelled Facebook posts, oversimplified political rants on blogs, TV, bars, et cetera, I start feeling incredibly smart. I know I'm not, I just feel that way.

So I need to meet somebody smarter to guide me, to challenge me, to prove me wrong, to point at my mistakes, or to offer me interesting new points of view. I come to Math.SE, and I immediately realize how dumb I actually am. (And I start feeling incredibly sorry for who posted the Youtube comments.)

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  • $\begingroup$ Amazing. I as well resort to Math.SE to be humbled. $\endgroup$
    – Omar Shaaban
    Commented Aug 23, 2020 at 19:31
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I've been in love with Stack Exchange long before I finally decided to participate. My three main reasons for answering questions here are

  1. There is a constant stream of questions to keep me occupied when I get bored.
  2. The site is well-organized and well-run, so the experience is very smooth.
  3. This is the big one: The site is run as a meritocracy.

You are promoted based on your ability and the quality of your contributions, and I think that is precisely how a site like this should run.

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This will probably be different than many people's answers, but aside from the basic "it feels good to help people", my primary motivators are probably:

  1. Figuring out what sort of explanations people are looking for can be an interesting puzzle, and articulating them can be good practice.
  2. Mathematics is beautiful, and it feels good to have more people appreciate it more, even a little bit, even if that appreciation comes in the form of "this particular problem I'm forced to do is no longer as big of a headache".

Then the question becomes, why Math Stackexchange as opposed to some other forums (which can have their benefits over MSE)? The answer is probably that MSE is a Skinner Box, albeit one in which I have other good reasons to stay in.

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    $\begingroup$ +1 for #2. Chapeau bas! $\endgroup$
    – Omar Shaaban
    Commented Aug 23, 2020 at 19:17
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I have not been posting answers to SE for a very long time, I have been asking questions for a while though, and generally using the site(s) to find answers that elude me.

The reasons I have for contributing range from noble to... not so much.

First would be the idea of paying it forward. Or maybe pay it back since I have improved my career and education by asking questions on various sites.

I am also making an effort to learn to be a more effective communicator, making posts is good practice for learning to write better. And the positive and negative feedback provides a good indicator of how well I am doing and if I need to edit my response.

Honestly I am also hoping that gaining reputation and more importantly engaging with people who run a business (more so on StackOverflow) will lead to an increase in job potential. Although I am not sure how well this mechanism will work.

And helping people really boosts self esteem.

As for why most of my time is spent on the Mathematics site? I can answer more questions consistently as a B.S. of Mathematics then as a self taught programmer of three years, also math is more fun where as programming is my job.

Just my experience, but I thought I would share it.

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I've been 'researching and teaching mathematics' at a German university for about 10 years -- from 1992 till end of 2001 -- and then got a job in the industry. My current job is rather far away from any mathematics. I think I do this for several reasons:

  • continue to do some math, every now and then, since I really like to do it
  • I'm curious how today math teaching is done, and how the curricula look like
  • I'm curious whether I still recall how it works and sometimes it's simply fun to try out these muscles again (which I usually cannot do in my job). It kind of helps me to not forget all the stuff I was glad to know and able to apply.
  • I do see people come from university and sometimes would really love to see that they knew better. Not only math or their area of technical expertise, but also cooperating, asking questions which are worth looking at, formulating ideas. Maybe I do hope that answering questions here (and commenting on questions...) might be a small chance to improve on this in general. This is a rather vague idea, though.
  • finally I do think that in todays complicated world it is important that people know about basic math and that many have a hard time learning it. Answering questions on this site might (hopefully) reduce the general aversion against math.

While this was not asked for, I cannot reply to this question without at least remarking that this site has also some shortcomings which make me think of wanting to have my account deleted (I've done this once some time ago already)

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A few reasons. First, I like learning about math. There are interesting questions and well written answers on here. Second, I like teaching math. There have been a few pedagogically interesting questions on here. One I saw recently (can't remember the link) was a student being confused about a "ball" in the $xy$ plane. They said no matter how small the radius was, a "ball" would come out of the plane to get some $z$ points. This was an interesting misconception and I'm glad I saw it. Third, all the bells and whistles and reputation and badges. I love positive feedback. Reputation makes me feel so accomplished.

Long term, I feel like the site has matured me. Some of my earlier answers (not THAT long ago) I wouldn't give now. Not that they're wrong, but I just would present things better. This maturity has helped in math outside of SE.

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To add to the chorus above, here are my reasons:

  • Good communication is vital, and I find that by having to explain (relatively) complicated things, I learn how to be a better communicator in my daily life at work. Alan Alda is a (rightfully) a huge advocate of this. (He held a contest where the challenge was to explain fire properly to an 11 year old child.)
  • Learning from others.This site is great resource for me not just for book advice but also for playing around with concepts and looking at them in a new way.
  • Giving back. Others have helped me understand things, so I think it's only fair that I pay it forward and help other people when I can.

So, all in all, I think it's one of the most "productive" ways to spend time on the Internet. A huge portion of the Internet is dedicated to people passively consuming media or being mindlessly entertained. I like sites that "make" users participate/engage in a meaningful way that hopefully impacts their real-life work/study in a positive way. (We're not hammering out solutions to war/poverty/famine that will never be implemented because we're not in a position to implement them. We're tackling smaller-scale problems that will likely be implemented and help people in their study/work. And I think that's pretty neat.)

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Because I hate my job and need the daily distraction.

But seriously, the short answer is to teach and to learn.

I left academia several years ago and have recently begun to miss (parts of) it. This site is a great way to stay involved at what feels like just the right level. I can share knowledge, refresh my own, keep my $\TeX$ skills sharp, and learn cool new things.

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Improve my teaching skills and to share neat tricks that I've picked up along the way. Most of the time I use the site to browse or ask questions, so when a question pops up that I actually do know how to answer, it feels good. (I am a high school senior)

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Lovely question! Here it is my personal miscellanea of reasons:

  1. My small whale is a killer whale: I wish to appear in the all-time top $10$, in a year or so;
  2. Gamification has a tremendous impact on me and I love challenges, really much;
  3. I love learning new things and teaching others cheap&dirty tricks;
    Maths for me is the perfect mix of extreme rationality and wizardry;
  4. It improves my teaching and language skills;
  5. I love being in contact with people all over the globe, it makes me feel less trapped in my small and unglorious life;
  6. I often gather interesting material for my Calculus&beyond notes;
  7. To have this fantastic resource and not to use it to share knowledge is almost a crime.
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    $\begingroup$ But 11 is a much better number, and you could be done in a month! :-) $\endgroup$
    – quid
    Commented Mar 8, 2017 at 19:23
  • $\begingroup$ Hm... you are quite close to your goals, but the competition sure is rough XD $\endgroup$
    – Simply Beautiful Art
    Commented Mar 16, 2017 at 20:24
  • $\begingroup$ If only I could upvote this answer more than once.. $\endgroup$
    – Omar Shaaban
    Commented Jun 30, 2020 at 17:05
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I think it's a mix of reasons, some self-serving and some not. Most have been covered above, but here's one I didn't see:

  • I think I'd be happier living in a less ignorant world (and that does not exclude myself)
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First reason is, I am an academician. My field is Computer Science. I love math, and I love to teach. The purpose of my life is to share information. Share knowledge.

Second, I believe there is not a single thing on earth that cannot be explained using mathematics. History, linguistics, everything can be modelled or formulated.

The answer to second question would be: When I apply for a job, I'll refer to this site and say "Look at my math.stackexchange reputation. It is so high." :) Just kidding.

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I feel obligated to give back something... So that the rest of the community has spare time to solve my problems.

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Everyone is so modest that they're giving semi-selfish reasons like:

  • It's for my ego (half joking).
  • I think teaching is fun.
  • It helps me learn.
  • I want to give back to the community that answered my questions.

Those are all true, but somebody just needs to say the real reason: it's for the greater good.

I post on math.stackexchange because helping people understand math helps to advance science.

Math and science are progressing super fast these days, which is extremely exciting. But with this progress comes a major pedagogical challenge: people need to learn a vast amount of stuff before they can start pushing math and science further.

Helping people learn math efficiently and understand math deeply is a big part of helping science advance quickly.

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To:

  • Practice my English
  • Keep my math skills up to date
  • Get a gold badge in real-analysis or sequences-and-series
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I'd say I write my answers and am an active participant on this site in my respective tags because

  • It is "intellectually stimulating" -Zarrax

  • It gives me a feeling of satisfaction.

  • It sharpens my math/proof-writing skills.

  • I'm really bored.

  • I love math.

  • I can drive my friends mad with everything I learn here. ;)

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For me, answering here is not only to help others, but also to learn new techniques as well.

Often, a mathematics question can be solved in different approaches. And when I post answer here, I can compare my answers to the others and find out the witty ones. It is also worth it since people may leave comments under my answer suggesting improvement of my approaches. It helps me to solve math problems in a more concrete and careful manner.

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    $\begingroup$ "Docendo discimus" - a 2,000 year old Latin proverb meaning, "by teaching, we learn." $\endgroup$
    – Adam Rubinson
    Commented Mar 27, 2020 at 1:10
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Let's see:

  • The fact it was talked about on another math forum I used to visit.
  • The fact I'm too lazy to clean.
  • The fact that I know parts of different levels of ideas, and think differently.
  • The fact it's a legal possibility.
  • The fact I can do it without getting out of bed.
  • The fact it distracts me from suicidal ideation.
  • The fact it combines interest and math is everywhere.
  • The fact it's better than Facebook...
  • The fact that I can treat it as a job.
  • The fact that I get to be around people with relatable experiences.
  • The fact that I'm a showboat.
  • The fact that it partly grounds me in logic and reasoning.
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