Every now and then I encounter something in the course of my work that I find I want to think about. If it's proper mathematics then I might try to write a paper or a page on the nLab about it. However, not all of my job is "proper mathematics"; or, to be a little more charitable, "research-level mathematics". So I've devised a little corner of my website for putting thoughts on things relating to my work but which aren't research-level mathematics.

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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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... then everything looks like a nail."

That's the saying, anyway. I don't actually think it's true. In my experience then the converse is more correct: "If all you want to do is bang a nail into the wall then everything looks like a hammer.". A shoe, a book, basically anything with a flat surface that can be lifted and has a bit of heft to it. That said, I'm still more interested in this post to consider how best to complete the saying, "If all you have is a hammer ...". It's not quite so snappy, but I find that if all I have is a hammer, then I just get very inventive about how I bake a cake. (Indeed, failure of our mixer at home recently led me to try to use a power drill to blend the ingredients for one dish; but that's another story.)

The "hammer" that I'm interested in is the "Wiki hammer": the ability on the StackExchange network (and on MathOverflow) to convert a post to "Community Wiki". It's a bit of a strange hammer, and its use is not always in line with the makers' instructions. The question seems to have been bugging a few people, and it's something I've thought a bit about, so I'm writing this to figure out exactly what I do think.

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I am a mathematician. I am a regular user of MathOverflow and regularly contribute to some of the StackExchange sites, in particular I was a pro tem moderator on TeX-SE. However, although I occasionally visit Maths-SE, and even ventured an answer once or twice, I don't consider myself to be a user on that site. This is an attempt to explain why, and why if it were the case that MathOverflow merged with Maths-SE, or if MathOverflow vanished and Maths-SE were the only one left, I would still not participate in Maths-SE. In summary, my reasons are:

1. I could not justify the time spent there.
2. I could not participate at a level low enough that the time used was insignificant.
3. I would not directly benefit from my particpation on that site.

I'm writing this for two reasons. Firstly, to get my thoughts straight in my own head: it's one thing to vaguely think why something might be so but writing it down forces you to be precise. Secondly, there are various proposals for sites on Area51 that are trying to follow the "two sites" model of MO/Maths-SE and which seem to be struggling in the face of a "one topic, one site" model. Perhaps my explanation here may clarify why there are some topics for which this model cannot work.

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I've argued that for research level mathematicians, then having a question-and-answer site devoted to research level questions is a good thing. So it would seem that I am in support of the two-level model as shown by MathOverflow and Maths-SE. Actually, whether or not I am in support of the two-level model is inconsequential. I think that the two-level model is unsustainable, but that it is the lower-level model that will not survive. However, merging it with the higher site will not save it, it will merely ensure the demise of both. The reason why I think this is to do with validation.

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There was a question on MO about when to teach category theory. Although I try to avoid such discussion questions on MO, after some consideration I decided to add my answer. This is probably something that I'll polish a little as I think more about it, so I'm copying it here as a starting point.

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Pushy parent: How many ways are there to choose one thing from five?
Bored child: Dunno
Pushy parent: Okay, let's count them. We can use fingers. I can put up my thumb, that's one. Or my first finger, that's two. Or my third finger, that's ...
Bored child: You can't do that! That's rude!

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