> When giving people advice around data I would like to train myself around many of the biases we are all so prone to.
A math degree is not the best way to go about this. (I just got one myself.) It will teach you to think clearly about groups, graphs, metric spaces and all that, but it won't teach you to think clearly in real life. That's something you'll need to learn elsewhere; although it might be true that a math degree will help you to learn.
I (dis)agree with you. One thing that a math degree will learn you very, very well is the spotting of gaps in logic. That is very applicable in e.g. software engineering/programming. For example, it will make you spot missing cases in long if/else if/else chains, both in code and in requirements. In the latter case, the risk is that you will get distracted by minor holes that do not really matter at the scope, and that other people may see as "not worth discussing now, as it distracts from the main course.".
Also, reading http://www.snhu.edu/mathematics-BA-online.asp, my main thought was "do they call THAT a math degree?" At the very least, I would put a sticker "applied" on that. That is a judgment, but not one that judges one item as better than the other. For your ambition in machine learning, it will probably be tons more useful than what I (and from his reply, I guess philh) think about when hearing the term.
For an impression of the difference: With a MS in (abstract) mathematics, you will be able to prove properties of some algorithm or formula from some preconditions, and you may be able to generalize them to some highly abstract terminology (for an example, see http://en.wikipedia.org/wiki/Measure_(mathematics), which grew about mathematicians thinking deeply about what the concept 'area' means) but you need not get any experience in recognizing those preconditions. As an applied mathematician, it is more important to have a good intuition on when an approach works then to have a good understanding on whether/why it works in esoteric cases (infinite dimensions, with less than two inputs, etc)
A math degree is not the best way to go about this. (I just got one myself.) It will teach you to think clearly about groups, graphs, metric spaces and all that, but it won't teach you to think clearly in real life. That's something you'll need to learn elsewhere; although it might be true that a math degree will help you to learn.