To add to your claim that math is fundamental to computer science, I think there's a big factor that isn't being mentioned: knowing math future-proofs your career better than knowledge of any technology or language.
Mathematical depth is the irreducible core of a computer scientist's value. Fundamentally, what computers provide is the mechanization of knowledge. In the same way that robotics came along and mechanized all of the entry-level manufacturing jobs (the root of the current "skills gap" in manufacturing, more so than outsourcing in my opinion), over the coming few decades I expect that computers will mechanize most entry-level knowledge workers' jobs, if they haven't already.
And the wacky thing about comp. sci. is that our entry level positions are in fact basic knowledge-work. As the field matures, the fields that are the bread-and-butter of basic vocational computer science are increasingly swallowed by more sophisticated technical solutions that are more mechanized and productized. Comp. Sci. is an ouroboros, eating its own tail of unskilled positions.
The most obvious example currently is sysadmins: computing infrastructure is being productized and sold under the umbrella of "cloud computing," and its main value proposition is that you can cut your sysadmin budget by a huge margin. Similarly, QA and software testing departments are having their lunch eaten by better testing practices and automated solutions such as CI: the jobs aren't disappearing entirely, they are just being consolidated into a tiny department (maybe even one dev, part time) that can maintain an automated infrastructure. At a more basic level, data entry positions started drying up years ago with the advent of OCR, and now most of the big easy targets are entirely mechanical (ex. the post office/shipping).
In short, the best way to provide enduring value is to provide mathematical insight that can't be mechanized. If you can recognize optimizations and opportunities that take advantage of the unique structure of your domain, you are unlikely to be swallowed by someone with a productized version of your livelihood. If all you can manage is CRUD apps for enterprise, then when someone comes along with a general product that reduces your department from many guys writing software to one guy managing the product, you aren't gonna convince anyone of your value. At that point your only defense is the behemoth of bureaucracy, but the competitive nature of business suggests that it won't be a great defense for long.