I don't think mathematicians look scornfully upon people doing the mapping between applied and theoretical domains. On the contrary, I think there's a lot of respect (and perhaps some envy). It's an entirely different set of skills, and a lot of great math has been inspired by applications, which would never have been possible if pure mathematicians worked in isolation. (The respect/envy comes from the fact that most mathematicians don't have those skills but recognize their value.)
I'm thinking in particular of a lot of stuff in mathematical physics and PDEs.
> I don't think mathematicians look scornfully upon people doing the mapping between applied and theoretical domains. On the contrary, I think there's a lot of respect (and perhaps some envy).
Proper abstract mathematicians view applications not with scorn, but as a challenge to come up with even more abstract math. :)
I'm thinking in particular of a lot of stuff in mathematical physics and PDEs.