<p>I took something like a gap year after graduating high school. Would grad schools look down on me if I graduate in 3 years? I planned it all out. I'll have all my math major requirements fulfilled as well as my GEs by the end of three years.</p>
<p>Nope, but you only have three years to get the research experience that many of your peers got in four years. It’s a disadvantage to you in applying for graduate programs but they won’t penalize you for finishing in 3 years.</p>
<p>I don’t see why any graduate program would directly penalize you for graduating early. But it could possibly cause indirect harm, as belevitt pointed out.</p>
<p>You should keep in mind that many applicants to the top graduate schools will have completed far more than the courses required to graduate with a math degree (unless they went to a school which had unusually high requirements). </p>
<p>Of course we don’t know exactly what classes you’re taking and what your record is. Perhaps you’re the next Terence Tao and you’re taking graduate courses for all three of those years. 
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<p>If you’re just doing the ordinary sequence, like undergraduate analysis, abstract algebra, (point-set) topology, and maybe a few others (complex analysis, number theory, etc.), personally I’d consider not trying to rush it and taking graduate classes the final year. Try to figure out the broad area of research you’d like to pursue and take graduate courses in that area. You don’t have to figure out precisely what you want to research, of course, but you’ll probably have an idea about whether you want to focus on analysis (Banach spaces, PDEs, and so forth), algebra (commutative rings, noncommutative algebra, and so forth), or geometry/topology (algebraic topology or differential geometry; I suppose algebraic geometry would probably fall under this category as well). Graduate schools really like to see that you’ve taken a graduate course in the area that you want to focus on in graduate school itself. If anything, it helps reassure them that you’ll be able to make it through.</p>
<p>In summary, just be cautious. Make sure you’re getting as much out of your college experience as the ordinary four year graduate does. Clearly you can get the same degree they do in three years, but can you gain the same knowledge and expertise in mathematics and can you gain the same research experience?</p>
<p>What if I decided to get a Master’s degree in Mathematics, then apply to grad school? Would that be fine? My university offers a progressive degree program for certain majors, such as Mathematics, that lets students earn MAs in as little as 5 years, in my case 4.</p>
<p>Thus, that way, I would get enough research time and take some grad school courses before starting a PhD.</p>
<p>if you plan to study your graduation study in Maths, you could directly apply the Phd, where you could gain more experience in research. I don’t see any advantages of the Master degree in Maths</p>
<p>I was thinking of getting the masters, so I would have experience with grad school classes and more research experience.</p>