I agree w Eric that this looks like a motte/bailey, esp looking at the replies to Matt (a mix of reply-to-motte, reply-to-bailey). We can talk about useful maths conventions, the research environment, etc. but we can't pretend these are all the same convohttps://twitter.com/EricRWeinstein/status/1126156211970138112 …
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I'm not a mathematician and have low confidence in all of these positions, and tbh at each layer I don't think "Is this socially constructed?" is a particularly useful question — though I think it's a more useful question at the top of the stack (re: institutions).
But I wouldn't bemoan anyone asking or answering it at any layer **as long as they're clear about the layer they're working on.** When Matt relies on a "philosophy of math" motte & then follows up by tweeting about trans athletes, I feel very 
https://twitter.com/mattyglesias/status/1126228807273336833 …
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Why is that? I don't see the Motte and Bailey here. Both are socially constructed, neither of which confers a moral value on the construction. Indeed, in the case of both gender and math, it invites criticism that long held beliefs that are held to be may not be true
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By that definition of social construction, almost everything is socially constructed. Which, yeah, is true. Language and definitions drive understanding, Wittgenstein did get some things right there.
End of conversation
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