We have the terms computer scientists and computer engineers; why not add the terms computer logicians and computer mathematicians to the mix?
I do think that computer mathematicians and computer logicians are somewhat different from a computer scientist. For instance, @shriramk is a true computer scientist; he experimentally derives new empirical facts about computing. The type theory community has historically mostly consisted of computer logicians and computer scientists, but for instance HoTT, SOGATs, synthetic Tait computability, brings type theory into computer mathematics. Domain theory is of course an early instance of computer mathematics as well.
(I somewhat prejudicedly associate “computer logician” with tedious syntactical proofs and “computer mathematician” with semantic proofs.)