Computing has revolutionized mathematics research. For example, the Birch and Swinnerton-Dyer Conjecture, a Millennium Problem, originally arose from computations about elliptic curves.
Although it is possible to write a PhD in mathematics without ever writing a line of code (beyond LaTex), we strongly advise you to hone some serious computing skills while in graduate school, whether you come in with no coding skill at all or you studied CS as a major in college.
Even if you intend to do all your own research with paper and pencil, gaining computer skills will make you a stronger and more employable mathematician: you will better poised to collaborate with others, better able to supervise student research, more informed as a mentor, a more versatile teacher of undergraduate math classes, and more aware of the trends and important issues facing our profession.
Words of Wisdom from Professors
Teaching Opportunities in Computer Science