I decided fairly late in life (21) that I feel like studying mathematics. I've always been interested in higher maths, I've just been daunted by some of the esoteric notations and theorems. But, no longer a philistine, I'm infatuated with pure mathematics. Right now I'm pursuing a Bachelor's degree in English. Is there a way I can get a Phd via an MSc?
I guess what I'm really asking is this: Is it possible to get into a Masters program without having a Bachelors in the field?
Yes, it's possible to get a graduate degree in mathematics even if your undergraduate degree is in a completely unrelated field. (Everything I say will be assuming you are in the U.S.; otherwise, I don't know.) In practice, you'll need to acquire much of the knowledge from an undergraduate degree in mathematics before starting, although you can fill in a few gaps during a master's program.
If you have unlimited time and money, then it's straightforward. You take undergraduate courses until you have completed most of a math major, either by delaying your graduation or by taking courses as a special student (i.e., not in a degree program) after your bachelor's degree. At that point, even thought you won't have a degree in mathematics, you'll be able to make a compelling case that you have equivalent background. You may not have a strong enough application to get into a top Ph.D. program directly, but you should be able to get into a master's program in a decent department, and if you do well enough there you can apply to even stronger departments for your Ph.D.
The drawback with this plan is that it's slow (you might spend two years or more taking courses before even applying to master's programs) and expensive (you'll be being charged tuition for these courses). Instead, the real question isn't whether it's possible in principle, but rather how to get to a Ph.D. program as quickly as possible, since at that point you'll no longer need to pay anything.
How efficiently you can do this depends heavily on your background and experience. If you are just starting to take college math courses, then it may take several years to prepare yourself for a master's program. If you already have a lot of experience, then you might be ready to apply this fall. I'd recommend consulting with faculty in your math department to see what they think of your background and what they would advise.
There exist certificate or post-baccalaureate programs designed to prepare people from other fields for math grad school. (See, for example, http://departments.columbian.gwu.edu/math/certificates/gradmath.) Such a program could be useful, depending on how well it fits with your background and preparation.
From my experience, it is possible to get into a masters program without a bachelor in the field. What you do need to do though display an aptitude for the subject. Also, if you were to be admitted into a masters program, you would likely be required to take undergraduate courses to get "up to speed."
Since you are still in undergrad studies, why not make the switch now by taking mathematics courses. The additional advantage to this is if it turns out that you don't like the area, you had not invested a significant amount of effort and time.
I got into MSc program in Economics having my base degree in Engineering, and then moved to get a Ph.D. in Statistics with these two degrees. But all of them are highly math-intensive. You are at about 5-8 years disadvantage compared to Chinese and Korean applicants, and at about 3-5 years disadvantage compared to US applicants (again, assuming that you are in the U.S.). While Anonymous Mathematician, obviously, has a more in depth knowledge of what kind of applicants are being admitted to his or her department, I would say that it seems very difficult to me given your non-technical background. You can take courses in math, but if you have not been trained to think as a mathematician, you won't be able to fit into math world. (A girlfriend who was majoring in math dumped me when I was an undergrad saying "You don't think like a mathematician". So be prepared that this is a different bunch than the people you are used to in your English classes.) This had to happen throughout your secondary school; if you start math in college, you could still do engineering and economics, but pure math is nearly impossible. Furthermore, you would have to seek proof-based courses, and you may not see them until the senior year even if you major in math. (I was stunned to hear from one of my students that he only saw epsilon-delta formalism in calculus as a senior in college; I had it as a junior in high school.) If you apply to a graduate math program with just three semesters of calculus, you won't be taken very seriously. I personally think that one cannot seriously call themselves mathematicians unless they know abstract algebra and complex analysis, as these keep reappearing in pretty much every field of mathematics. (Folks at math.stackexchange might be able to give you better pointers as far as specific courses go, though. Your question being moved to Academia made some sense, but it is still very much discipline-specific.)
To get a glimpse of whether you are prepared to work in a math grad program, take GRE Math subject test. If you don't get some 80+%, you are not ready yet (folks here with scores below 60% don't go anywhere; even folks with 80+% percentile don't get accepted left and right).
