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As an avid lurker, I truly enjoy the expertise offered by this site and I think it is remarkable that most questions have thoughtful, in-depth answers relatively quickly.

It really is quite amazing the turnaround time here. I am curious - do some users sit in front of a computer with a pen and paper ready to answer questions?

If this is the case, I am wondering if knowledgeable users treat the SE like a brain challenge, or a fun activity to kill time between work or their own thoughts.

Even more remarkable are the length of the responses; I have seen some questions answered with seemingly full treatises on the subject 5-10 minutes after posting.

I suppose this is a soft question with no real answers but I am interested in others' experiences on this site and how they can be so efficient. Thanks.

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    $\begingroup$ When I was more active, I'd 100% treat this as a brain challenge -- I'd troll through the feed of incoming questions with pen/paper in hand, then answer ones I thought were interesting. $\endgroup$ – apnorton Jul 14 '17 at 21:29
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    $\begingroup$ I wouldn't assume that you're referring to any answers that I've written but I think I've posted a few pretty good (and lengthy) answers in my areas of interest, such as fractal geometry and complex dynamics. That's, in part, because I receive email notifications when new questions with those tags are posted. $\endgroup$ – Mark McClure Jul 15 '17 at 0:21
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    $\begingroup$ Some questions happen to match a topic that I have some private notes for, which are maintained in LaTeX. Of course this speeds things up a bit. $\endgroup$ – ccorn Jul 15 '17 at 3:43
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    $\begingroup$ I do plenty of work on my laptop, so that stackexchange is open. I come once in a while to have a break, and in those times I pounce on questions which are easy for me to answer, and since I type quite fast there have been occasions of the kind you are describing. Yes, you can say I'm an addict, but if that's wrong, then I'm very happy being wrong! $\endgroup$ – Teresa Lisbon Jul 15 '17 at 17:18
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    $\begingroup$ This only happens for easy or trivial question. Ive never got a proper answer to any of my questions... $\endgroup$ – Brethlosze Jul 15 '17 at 21:22
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    $\begingroup$ Personally, I just type the solutions rather than using pen and paper, which would admittedly consume every scrap of paper I have in no time. $\endgroup$ – Simply Beautiful Art Jul 15 '17 at 21:32
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    $\begingroup$ Pro users just exploit a super-secret time machine, they have complete answers before the questions arrive, that is the trick. $\endgroup$ – Jack D'Aurizio Jul 15 '17 at 21:54
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    $\begingroup$ @Jack, I have an alternate hypothesis, made an answer. I would have posted earlier, but sometimes it takes me a day to put the ingredients together properly. $\endgroup$ – Will Jagy Jul 15 '17 at 22:32
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    $\begingroup$ This has something to do with the fact that MSE is addictive. See math.meta.stackexchange.com/q/26466/72031 $\endgroup$ – Paramanand Singh Jul 16 '17 at 2:46
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    $\begingroup$ There are also some seasoned answerers who seem to use the following tactic. First post a one or two line hint. Then spend the five minute grace window polishing it. Because all the edits come within the grace period, you get an exceptionally early timestamp to your answer, and no evidence of the editing will be available. Mildly questionable, perhaps, but mostly harmless :-) $\endgroup$ – Jyrki Lahtonen Jul 16 '17 at 12:16
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    $\begingroup$ Something else that might happen to you is that you answer a question very quickly and then it gets closed as a duplicate. And it might also happen that when you look at a duplicate question, it turns out that you had given an answer for that question. $\endgroup$ – Robert Soupe Jul 16 '17 at 17:28
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    $\begingroup$ @RobertSoupe Nothing questionable in fixing typos. That is what the grace period is there for! I'm mildly miffed about the grace period being used this way systematically, but I guess that's just a part of the game they want to play. Also, yes it often happens that nearly identical ideas are posted while typing. IMHO you can still post yours. We "know" who is capable of coming up with a given solution under their own steam (and also who is plagiarizing). Great minds think alike and all that! $\endgroup$ – Jyrki Lahtonen Jul 17 '17 at 5:41
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    $\begingroup$ @JyrkiLahtonen: +1 for "we know who is capable..." BTW I have seen many instances where users are humble enough to delete their post if the same content has been posted by users just a minute ago. Perhaps those who are capable are also a bit humble (but there can be exceptions which I am yet to see). $\endgroup$ – Paramanand Singh Jul 17 '17 at 13:02
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    $\begingroup$ @JackD'Aurizio, you left out a crucial fact. It's not just a time machine; answerers don't just predict questions. In fact, the truly expert answers are the causes of the questions they answer. It's an accident of SE procedures that one must wait for the question to be posted before posting the answer. $\endgroup$ – Mars Jul 25 '17 at 17:50
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    $\begingroup$ @JackD'Aurizio, yes, if you answer quickly enough, your answers seem shorter to readers. Or is it longer? Depends on perspective. Your mass may change, temporarily. as well. $\endgroup$ – Mars Jul 25 '17 at 17:54
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Yes, I do on occasion sit and wait for questions I can answer, although usually I will have on some background tv or news. I don't just intently stare at the screen hitting the refresh button every 5 seconds :) Here are some reasons why (for reference, I am starting grad school this fall):

1.) this gives me a chance to work on my teaching and exposition skills

2.) it keeps me sharp. I can't tell you how many theorems/propositions/proof techniques I would forget if I didn't use them occasionally to answer questions

3.) in some instances, I have had very similar questions and received very nice answers from others outside of SE; I enjoy being able to pass on this information to people in similar situations that I have been in

4a.) I learn A LOT from reading other answers, either because they used a completely new method or simply because they know how to present the same method in a much more illuminating manner

4b.) There are so many interesting questions on here that I have truly benefited and learned from, but would never have thought to ask. Thus I read for the questions just as much as I read for the answers.

I'm sure there are different reasons for different folks, but this is just what comes to my mind

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I think I have worked it out, based on a crucial scene in The Sum of All Fears with Ben Affleck. I do not think it a coincidence that there is no mathematics book (yet) named The Fear of All Sums. Compare.

Clearly, people are working up quality answers, little bits of mathematical prose that make them proud. Then, behind the scenes, they contact junior users to post questions for which these will make good answers.

In the movie, after the explosion, Nemerov has his staff work up a statement of sorrow and a denial of complicity. He asks that these be sent fairly soon after being contacted by Fowler; so quickly that Fowler and his aides conclude these were composed before the bomb went off, so this is evidence that Russia really did cause the explosion.

Nemerov is Ciaran Hinds, I like him. He was Julius Caesar in the series.

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    $\begingroup$ I think "The Fear of All Sums" sounds like a good working title for a second semester Calculus text. $\endgroup$ – James S. Cook Jul 21 '17 at 19:09
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From my side, and since I'm a newcommer to SE - well, as an answerer (if that exists in English) at least - I can say that the main motivation for me was to refresh my former maths knowledge and sharpen my current. As student who has recently - almost, due to bureaucracy - graduated from a mathematics department, I wanted, at a first level to keep at a "good shape", in terms of mathematics.

Moreover, as I'm not a native speaker, SE is a perfect chance for me to imporve my english with respect to mathematical terminology etc and a nice chance to have a closer touch with a part of the mathematics community and see what's hot on mathematics nowadays, as well.

Another fact is that, now, that it's summer, I have enough leisure time to look around SE and answer questions and thus, feel a little bit as aprticipating to this really nice initiative. And, it is many times that I catch myself trying to find an appropriate answer to a question that has not yet got enough attention and, actually having much fun doing so.

Lastly, it is surely a chance to explore exactly what can be my large interest with respect to my post-graduate level studies. As a person I cannot take decisions easily, and hence I cannot decide which of the fields I like could I follow the next year so, answering questions and "measuring" my sense of fulfillment each time, is a nice way to find out what I want most.

P.S. Not to forget that I really enjoy the way this community works! :)

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One reason people can answer questions very quickly is that they are experts both in the mathematics and at explaining mathematics.

People can actually get hired for doing this, they are called mathematics teachers.

Some of those people, if they really like teaching mathematics, may actually enjoy doing it for free on this site, in addition to being paid to do it by their school.

It also helps if those people learned to type early in life, including typing in TeX.

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