I've just noticed that there are two areas of mathematics, Number theory and number theory. There are even the subareas Number theory > analytic number theory and number theory > analytic number theory. Before we all rush in and try to get our names attached to the counterpart of the prime number theorem in the other area (no doubt using techniques from the first), perhaps we should do something about this. Probably the best thing is to decide on a general policy about capitalization, and get the Tricki to adhere to it automatically.

My vote is for capitals on the first word. So "Number theory", "Group theory", even "Geometry and topology" (though "Topology" when it appears on its own). No particular reason, just aesthetic preference.

I vote the same way as Henry.

Olof and I have now sorted out the "Number theory" and "number theory" problem.

It seems that the problem was that someone had tried to enter "Number theory -> analytic number theory" — with "->" instead of ">", which created an area of mathematics called "number theory -".

On a related note, there are also "geometry > geometric topology > knots and links" and "topology > low-dimensional topology > knots and links". Should these be merged into one somehow? What should our policy about having subareas of the same name in different areas be?

It seems clear that some subareas can be thought of as subareas of two different areas. Dictating that the subject-graph of mathematics is a tree seems entirely contrary to the spirit of the Tricki!

I agree: I see it as a Tricki principle that the organization is as a directed graph with no directed cycles. If you want to think of it as a tree then you are free to do so by the standard trick of duplicating vertices, but I would think of that as the universal cover of the Tricki rather than the Tricki itself ...

Are the previous two posts voting in favour of merging the two different "knots and links" areas, then? At the moment, they seem to be 'duplicated vertices'. If we merge them into one area, then we have the directed graph with no directed cycles. Or is it being claimed that the two areas should be kept separate, thereby keeping the graph as a tree?

I think that the two "knots and links" should be merged; then we will have an example of a non-trivial cycle.