This could not be further from the truth. I doubt my CS professors would be able to solve a PDE (or algebraic geometry etc etc). Likewise, few math professors would be able to write a parser generator (or code worth a damn).
In contrast, I know engineers who live and breathe PDEs and tweak compilers to solve them faster.
PDE's are not discrete math. CompSci majors are more interested in topics like Combinatorics, Graph Theory etc. PDE's are more interesting to applied mathematicians and physicists.
I doubt my CS professors would be able to solve a PDE..
Beyond the basics, not even many math professors can do that. Math is too vast and people specialize. Strong algebraic geometers are not necessarily strong analysts or algebraists or logicians.
1) No such thing as universal mathematician in this day and age.
2) Engineer's PDEs(algorithms) are not the same as mathematician's PDEs(theory). Same as comparing a student in China who learned English to communicate with English speakers to English majors from English speaking countries.
It wasn't that long ago that most schools did not have a separate CS degree, but rather it was a math degree w/ a concentration in computer science (or some other verbiage to describe the same thing)
In contrast, I know engineers who live and breathe PDEs and tweak compilers to solve them faster.