Yes I am aware. I wanted there to be another community on lemmy.world as it is my preferred "general" instance to lemmy.ml. If in the future /c/[email protected] grows as the de-facto "main" math community in the federation then I will consider redirecting posters from here to there. As of now though there's not much activity in either.
No, communities on a given instance are completely independent from communities on other instances. There just happen to be two communities on two different instances with the same name (of course c/math is not the only case of this).
The federation makes it so that anybody on any server which is federated with both lemmy.ml and lemmy.world can see all the communities on both servers. This means you can subscribe to both the c/math on lemmy.ml and the c/math on lemmy.world. The fact that lemmy.ml and lemmy.world are federated with each other is inconsequential.
Thanks, aha, I get it now. So it looks like there are a bunch of communities fragmented between servers, presumably resulting in crossposting and stuff. I suppose that is an inherent feature of the federation scheme and something the designers wanted, but it seems like a mistake to me. Usenet's and Reddit's successes I think came from having unified groups. It shouldn't be necessary to browse 3 separate but similar XYZ communities to keep up with the topic. So I hope that the two math communities do eventually merge. The other one has been around longer but has little recent activity, so we'll see what happens.