History of Science and Mathematics has been in beta for a good while and it is still not doing well. History is also in Beta and not doing wonderfully, but it is doing better. I feel that the two communities are very similar and we could do better as a whole. Could we consider merging them?
I'm not sure on what basis you're claiming this site is doing poorly. If you're talking about the Area 51 statistics, those are related to site graduation. This site targetting a small enough niche I doubt we'll ever graduate, but that isn't really a problem. If you mean that there are quality problems with the content here, and think that History SE could answer the questions here better, I'd want to see some evidence or reasoning behind that assertion.
Actually, History SE has been around a lot longer than this site has. If you look at their stats over time it's been fairly consistent since before this site began, with about 3-6 Q/D over the past 2 years, and most variation being seasonal. There's no evidence that this site is stealing questions that would naturally fit there; if we were we'd expect to see a persistent drop in questions around when this site was formed (November 2014). We have taken some questions from other sites, but those are the math/science sites where they were asked before and dealt with quite inconsistently, not so much History SE.
So I just don't think that merging our site into History SE would be a natural combination. They were on SE for years before us. If they were going to consolidate all the science/math questions there, it would have happened before we formed. The reason that they didn't manage this is that many of the questions are quite technical in nature while also being basically inconsequential outside their respective fields, and would not be answerable by historians without specialization in math/science, but might be answerable by mathematicians/scientists with an interest in the history of their fields (see, for example, When and how was the geometric understanding of gauge theories developed?).
In addition, it would be hard to keep some experts on math/science with knowledge about history engaged on a much larger site, and even if they were present it would not seem like a natural place to go to ask such questions. If we did close this site, I suspect most new questions would end up back on their respective math/science sites rather than on History SE. This parallels the fact that a large fraction of research in History of Science and Mathematics is done by academics in their own discipline rather than historians; the actual number of historians specializing on science and/or mathematics is small.
With all that said, of course we have no intent to impede on the progress of History SE. We aren't trying to take questions from them which happen to be on science/math, and as far as I know such questions are still considered on-topic there. What we're trying to do is address a smaller set of questions that History SE can't reasonably handle themselves, in a more coherent and consistent way than splitting them up among a dozen sites with inconsistent policies and little expertise (the old status-quo before this site).
I disagree with the premise in the current answer. It's similar in spirit to the answer that got the most upvotes in this Area 51 question. But I honestly think both of these answers are wrong.
History SE users as a group would likely be able to answer most questions that get posted here, and vice versa. The vast majority of high rep History SE users are hobbyists that work in STEM fields if their profiles are anything to go by. Only a handful are historians in an academic sense.
Personally, I'm also struggling to understand why the two SEs were initially made separate. It seems to have been based on uninformed assumptions. There's overlap in spirit and in users. Insofar as I can tell the two sites even share the same types of trolls. If SO had done the same in its early days, we'd probably have separate SEs for each programming language, with no one benefiting.
It's too late -- and probably not easy -- to merge the two stacks now. But it was a missed opportunity.