Personally, I’d be perfectly happy to say that our hypothetical hermit is doing mathematics despite the complete absence of social connections; but I wasn’t endorsing the claim that mathematics is a social activity, merely explicating it. (And of course it’s possible that my explication fails to match what Anthony would have said.) I am not confident enough of my understanding of Anthony’s position to guess at his answer to your hypothetical question.
(But, for what it’s worth, if for some reason I were required to defend the mathematics-is-social claim against this argument, I think I would say that it suffices that mathematics as actually practiced is social; making political speeches is fairly uncontroversially a social activity even though one can imagine a supergenius hermit contemplating the possibility of a society that features political speeches and making some for fun.)
Personally, I’d be perfectly happy to say that our hypothetical hermit is doing mathematics despite the complete absence of social connections; but I wasn’t endorsing the claim that mathematics is a social activity, merely explicating it. (And of course it’s possible that my explication fails to match what Anthony would have said.) I am not confident enough of my understanding of Anthony’s position to guess at his answer to your hypothetical question.
(But, for what it’s worth, if for some reason I were required to defend the mathematics-is-social claim against this argument, I think I would say that it suffices that mathematics as actually practiced is social; making political speeches is fairly uncontroversially a social activity even though one can imagine a supergenius hermit contemplating the possibility of a society that features political speeches and making some for fun.)