What's a normal day on the job for a mathematician?
It depends on your definition of "mathematician"; for example, I once thought of them only in terms of college professors (teaching, research, publishing, grant-writing, departmental administrivia), but that's an extremely narrow definition.
Mathematicians may find employment in corporate research environments (e.g., IBM, HP Labs, Bell Labs), government laboratories (e.g., Lawrence Livermore, Lawrence Berkeley, Argonne, Fermilab, Sandia, JPL/NASA), investment banks, insurance companies, Internet companies (data analysis and mining), and so forth. Frequently they do a lot of computer programming in support of that, whether in a general-purpose language like Python or Java, or a special-purpose one like R (for statistical analysis and graphing, among other things, I think). Numerical simulation of physical processes is a pretty well-established field, for example. There are even those who use mathematics to create 3D-printed art, though that's a pretty limited niche as far as I know.
Math makes a good foundation for a number of careers; I'm pretty sure there are dozens more I haven't even touched on.