On the tex.SE site, I made the comment:

Whatever the differences [between MathOverflow and StackOverflow] are, I would tend to favour the [StackOverflow] one over the [MathOverflow] one for here because I think that the relationship between the subject and the users is closer to that on [StackOverflow] than [MathOverflow].

I've been asked to explain that remark. This is my attempt to do so.

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First, a bit of background.

The StackOverflow website is quite successful and so, understandably, the team behind it have looked for ways to find other arenas in which their software can be used. Their first round of attempts at doing this were not all that successful, with the notable exception of MathOverflow. The second round of attempts is now underway and several new Q&A websites using the software underlying StackOverflow software have been launched. They are in various stages of launching, as the process from idea to fully fledged website is a long one. As these websites grow, there are various choices that they will have to make as to how to make the best use of the software that they have. StackOverflow and MathOverflow provide two quite distinct models for these choices.

One key feature of the new round is that to get an idea off the ground, it has to have a number of committed participants. What is important in that is that not all of these committed participants count the same: people with experience from the original StackOverflow website count for more than others. That means that each of the new websites is almost guaranteed to have a good number at the start who know about the software and its capabilities. It also means that each of the new websites has a good number of people who know about how StackOverflow uses its software.

Seems reasonable. But some of the ideas that have been proposed - some of the popular ideas, I should say - are not about programming. Some are quite attractive to users of MathOverflow; in particular math.SE and tex.SE (and others). So on these sites, there is a fair number of people who know about the software from their experience on MathOverflow.

As MathOverflow came out of the first round of new websites, it didn't have quite such a close association with StackOverflow. So it had the opportunity to evolve its own set of rules without reference to StackOverflow. That is, although the software is (essentially) the same on MathOverflow as StackOverflow, various features are used in different ways.

So the scene is set for a culture clash.

In these matters, the most important thing is that each culture realise that the other culture exists and that it has valid reasons for coming to the conclusions that it did. That's where my comment comes in.

StackOverflow is about programming and its main users are programmers. MathOverflow is about mathematics and its main users are mathematicians. Seems fairly close correspondence so far. Except that on close examination, it isn't. The relationship between a mathematician and mathematics is nothing like that between a programmer and programming. In the programmers' world, a mathematician is more like a library writer: someone who makes new ways of doing things with programs. In the mathematicians' world, a programmer is more like ... well, like everyone else in the world who isn't a mathematician!

That's not to say that library writers aren't prevalent on StackOverflow; of course they are (one rather famous for it). But they are not the core audience of the website. Similarly, MathOverflow sometimes gets (and keeps) questions from non-mathematicians. But again, they are not the core audience of the website.

I don't have much experience of StackOverflow itself, so let me draw rather on my experience from tex.SE. As I said, I think that this is closer to StackOverflow than MathOverflow so I hope that it is close enough for this to be relevant.

When I look at questions with a view to answering them, I'm look for places where I can help someone. I'm concious of the fact that I shouldn't spend too much time on these websites so I want to maximise the help that I can give relative to the time I've allocated for giving it. On MathOverflow, I will concentrate on questions where I'm pretty sure that I know the answer, or where I'm sure that if I spend a couple of minutes thinking about it then I will get the right answer. And by that, I mean that I will know the answer, I will know why it is the answer, and I will be confident that no-one else will be able to find a flaw with it. (Note that I do answer questions that don't meet those criteria, mainly because there's not many that actually do, but when I answer a question that doesn't meet those criteria then I'll couch the answer in a different way.) One reason for doing this is that for most questions I can be reasonably confident that there is someone on MathOverflow who can give an answer as an expert. So if I'm not that expert, I'm wasting my time trying to provide an answer.

On the tex.SE site, although there are experts, the majority of the people are simply people that use TeX/LaTeX (and friends) and who have worked out ways of doing things and working around "features" in the system. Again on tex.SE, I look for ways to help. But since no-one's career depends on knowing the Absolute Correct Way, I feel freer in what answers I'm able to give. The person asking the question most likely just wants something that will do the trick. Of course, there are often better ways and worse ways, but until someone posts The Correct Way(TM) it's next to impossible to know that a particular question is going to get a Correct Answer. So I may as well post my attempt because even though I'm not a real TeXpert, I'll do in case one doesn't show up.

As explicit examples of questions, on MathOverflow there was a question "What kind of operations does a Tall-Wraith monoid encode?". Now, I'm a coauthor on the paper where the term Tall-Wraith monoid was coined so who else should answer this question? That's the kind of question I look for on MathOverflow. It's not usually quite that close a link, but there are other examples where I know that there's no-one better than me to answer a particular question. (Note the phrasing: I use "no-one better" rather than "I'm the best"; also, I'll admit to a little exaggeration to make a point.)

On tex.SE, a good example of a question that I'll try to answer is "How to draw a torus". It so happens that I've drawn a couple of toruses (or should it be tori?) for talks so I know a few ways of doing that. There may well be proper ways of drawing a torus, but I don't know that and the questioner doesn't know that, so my solution might just be the best that'll come along. In fact, my first solution wasn't quite what the person wanted, but I was able to come up with one that did match. But the process by which I found it didn't involve using arcane knowledge that is only known to a few monks wot live up on a mountain, but just by being curious and having a few minutes to spare. Indeed, most of my answers on tex.SE are of this form: I get curious in a question and have a few minutes to spare on trying to find an answer.

Of course, StackOverflow and MathOverflow are simply two examples and there will be many different cultures that arise as these new websites develop. But new cultures tend to develop by adapting and mixing existing cultures so it's good to look at the existing ones and decide which is the best fit for the starting culture. To decide that, one needs to look at the relationship between the subject and the users of the site. The basic question is:

Is the archetypal questioner an expert (possibly in training) in some part of the subject?

If "Yes", it's closer to MathOverflow. If "No", StackOverflow.