Master's degree in a different field while in a PhD program? I am finishing up my BS degree in Computer Science, and I have been accepted to a PhD program in Computing and Information Sciences. I was wondering if it would be possible (and how feasible it would be) to get a Master's degree in Mathematics during my PhD by doing math research with a professor and publishing something?

Would I have to apply and be accepted to the Master's program at my university? How likely do you think this is? I have quite quite a bit of math completed from my BS in CS; I would estimate about 18-30 credits left not including the [required] electives if I was pursuing a BS in Applied Math.
The question you should really ask yourself is: What is the purpose of having an extra degree? Is it to enlighten yourself and learn something new or related? Is it to improve your CV and future job prospects? 

IMO, looking at your situation, it seem a bit of a waste of time and a lot of extra effort to also pursue your math master. You can study math  on your own accord at any time with the best universities and lectures using the edX free and open university. 


Q: Would I have to apply and be accepted to the Master's program at my university? 


A: Probably not.


Q: How likely do you think this is?


A: Most universities allow for completing multiple degrees concurrently as long as your academic records are in good standing and you pay the additional costs.