This is a tricky question, because it's easy and difficult at the same time. Easy, because there is a lot of resources that potentially can help you make a decision on the topic. Difficult, because the situation is very different for a particular person (not to mention that their interest might change at any time), which makes extremely difficult for other people to give you a good advice and for you to make the right decision.
As for data science career options, you can certainly consider a degree path (MS or MS + PhD), but you need to be aware of other options. For a comprehensive resource, dedicated to data science and related degree programs (both traditional and online), please visit this page: http://www.kdnuggets.com/education/index.html. A comprehensive review of all these offerings is IMHO an enormous task and is far beyond an answer here on Stack Exchange or, even, a lengthy blog post.
However, nowadays one is not limited to traditional educational options and I think it's important to be aware of other educational options. One of the other options include certifications (linked at the above-mentioned page, but, in my opinion, the only certification worth considering is the Certified Analytics Professional as a solid and vendor-neutral certification from a reputable INFORMS). Another option is recently booming data science intensive educational offerings, from short-term (and often too commercial, to put it lightly) bootcamps to more solid offerings, including free, but competitive, ones, such as Insight Data Science Fellows Program, where one needs to be a PhD to apply, or its sister program Insight Data Engineering Fellows Program, which doesn't have such requirement. Finally, there is yet another option: self-study. It partially intersects with the certificate option, if one uses massive open online courses (MOOC) (a review of which deserves a separate comprehensive post), but there are open curricula that might suit one better, such as the Open Source Data Science Masters curriculum, linked in my earlier relevant answer.
P.S. While your question focuses on data science, I think that it may be wise to at least consider another career path, given your math background. I'm talking about operations research field, which is not that far away from data science (and even somewhat intersects with it). While similar, data science is IMHO more statistics-focused, whereas operations research is more math-focused, at least that's how I see it. Despite all the popularity and "gold rush" of data science, operations research career is a solid one, just not as hot. Of course, if you're excited about things like artificial intelligence, machine learning and, especially, deep learning, data science career is the way to go. Whatever you will choose, the good thing is that with your math background it will be easy to change focus, should you decide to. Hope this helps. Good luck!
