Math minor-> top schools Math PhD. Chances? Very important. Please share with your opinion.

[simplybetter]

  Hello, everybody. I am very new to this forum. Now, I am an International sophomore in Korea. We have to choose our majors, and this decision is very hard to make. Now, I have Physics as my major and Computer Science as minor. In few days, I have to come up with the decision and I was going to change my major and minor(Computer Science as major and Mathematic as minor). I am trying to change my major to Computer Science because I believe it will be safer and gives more freedom to earn money, and it is important because I need to help my family(btw, first generation college student from very low-income family). I don't want to risk and I believe with good grades I can have the good opportunity to live well. (No major in Computer Science)

  Here's the thing. Don't laugh pls.   I am very ambitious and always have been. I want to devote my life into the many sciences. Many of you can probably recognize want to understand the mathematics, nature(physics), want to help prolong life and study biological sciences. I am thinking of taking prerequisites for Med School, and take Math as my minor and Computer Science as my major. Let's say I can have 2 years of experience in researches(1 year Math, 1 year Physics(for myself)). Let's also assume I will have very good scores in GRE Subject test, TOEFL and in General GRE. Can I then be considered as a good candidate for top schools in the US for Math or I have no chance if only my minor is Math(6 classes only 18 credits)? I will try to study math by myself(but, how can I prove it, though?)

 I know some of you could say focus on something, and I agree that it would be much easier if I had only passion. However, I want to give a shot, and try devoting my youth to studying. May be, who knows, this worth to do once in life? The reason I am choosing Math is that I think there are many examples that after being a mathematician, people tend to contribute a lot to physics too. However, not so many examples the other way around.

Also, I would like to know how it is hard (1)to get accepted for two PhDs and (2) if you're accepted to study that. I can put my energy if I am allowed to study two PHDs simultaneously. I would love to get accepted for two programs in Ph.D.(One, in this case, will certainly be Biology. I want my parents live very long ). I really think, at least for now, that intellectual prosperity is the most important thing. For Biology PHD I will have only MCAT(let's assume very good scores), GRE and TOEFL, prequisites.

Projected GPA: 3.75(converted to 4. In fact, we have 4.3 as maximum)

Projected number of credits:153

Projected length of my undergraduate study:3.5-4 years

Please, share your opinions. Detail answers would be very welcomed. I would love to read each of them Thank you a lot, and I hope you'll have a nice day!

[biona001]

I think if your top schools are like Princeton, Harvard, Berkeley...etc, and when you say math you mean pure math, then your chances are very low. As you may know, a very large proportion of math majors are pursuing a Ph.D. I did my undergrad studies in Berkeley for math and everyone of my math major friends (not very many of them) applied or will be applying for Ph.D. What about you are better than these people? Quite frankly, six classes, even if they are upper divs, is hopelessly insufficient. Grad math schools care about your research ability above all else, and I don't think six classes can enable you to make meaningful contributions. Research in math certainly helps, but keep in mind that people generally think undergrad math research means basically nothing, so don't expect too much strength from it. In addition, since you are international, it would be considerably harder for you to be accepted compared to residences with equal caliber. You'd essentially have to be "the best" among all international applications (who knows how many there are). Are you one of these people? 

I'm sure you are bright and desire challenge, and you should certainly do whatever you want with your life. However I personally know people who give up EVERYTHING ELSE to get into a good math grad school. If you still want to be on par with these people and not give up things like they did, then you'd have to make it very clear what makes you so good. Exceptional intelligence and very hard work is expected, not your strength. Perhaps one of the few ways to prove your worth is doing good on the putnam, like honorable mention. Otherwise, maybe you could try applied math in biology or physics, at least that way that field and your background match up better.