To add slightly more detail:
Most research math programs in the US are 5(ish) year 'combined' masters+phd programs. The first couple years are basically course work, seminars, finding your area and advisor, and then the rest is the actual research work. It's not uncommon to leave after the first couple years with a Master's degree.
> Normally you have a master of science as well. And for that you require a bachelors.
Many Master’s programs require Bachelor’s as a prerequisite for admission, and some of the others include a Bachelor’s at some point, but not all do. (The same is true of the Ph.D. and the stereotypically preceding degrees, and also of some professional degrees and Bachelor’s degrees.)
I have a Master’s and never got a Bachelor’s. Universities can admit people more or less as they please, subject only to the very forgiving scrutiny of accreditation agencies or whatever government department officially supervises them.
