Pursuing a PhD in Mathematics: What Does It Require?

[MathManiac]

I really want to get a PhD in Mathematics... but what does it all require? I know it will be a lot of schooling. I am currently in high school, love math, and want to take it all the way. I'm just a little worried that I won't have the time or money for it all... so could I get some help on what it takes?

 

[chiro]

I really want to get a PhD in Mathematics... but what does it all require? I know it will be a lot of schooling. I am currently in high school, love math, and want to take it all the way. I'm just a little worried that I won't have the time or money for it all... so could I get some help on what it takes?

Hey MathManiac, welcome to the forums.

The three main areas of math are pure, applied, and statistics.

From these three areas there are many many subspecialties. A PhD is basically a research project where you do original research and make a contribution which you defend before a board of people.

You need to get exposed to a lot of math since you are in high school. If you work hard enough in uni and get the best resources you can (whether its other students, professors, books, forums whatever) then you will have good odds in getting a PhD in some field.

Its really hard for me to recommend anything else because there is a lot to cover in 3/4 years at university and you will get ideas for research as you become exposed to more math.

 

[Levis2]

I feel the same way the thread-owner does - I'm in high school aswell, and i really want to get a PhD in math. If i may give you an advice - NEVER TAKE AN IQ TEST!

I have taken an IQ test, and being farely certain i could achieve something in math before the test, i now doubt in my abilities, due to a rather low score. I got 130, which isn't low but not much from a top mathematicians perspective. Many have tried to convince me that IQ means nothing, but it's hard to believe, since these advices often come from very intelligent people themselves, so it's easy for them to say :)

My advice for you is go for it! If you really want it, you can do it. Never take an IQ test, since it won't make a difference in whether you can complete a PhD if you know your IQ. On the other hand, the result may actually - just as me - discourage you and decrease your chances of getting your PhD. So don't go into the IQ trap lol .. :) Just keep doing math because of the enjoyment you get from doing it, and it will eventually come.

Best of luck from denmark

 

[chiro]

I feel the same way the thread-owner does - I'm in high school aswell, and i really want to get a PhD in math. If i may give you an advice - NEVER TAKE AN IQ TEST!

I have taken an IQ test, and being farely certain i could achieve something in math before the test, i now doubt in my abilities, due to a rather low score. I got 130, which isn't low but not much from a top mathematicians perspective. Many have tried to convince me that IQ means nothing, but it's hard to believe, since these advices often come from very intelligent people themselves, so it's easy for them to say :)

My advice for you is go for it! If you really want it, you can do it. Never take an IQ test, since it won't make a difference in whether you can complete a PhD if you know your IQ. On the other hand, the result may actually - just as me - discourage you and decrease your chances of getting your PhD. So don't go into the IQ trap lol .. :) Just keep doing math because of the enjoyment you get from doing it, and it will eventually come.

Best of luck from denmark

I don't know if you know this but Richard Feynman's IQ was *ONLY* 120.

If you end up living and breathing math, chances are you'll make some decent progress.

 

[DarrenM]

MathManiac, I'd suggest you read the following books:

"A Mathematician's Survival Guide: Graduate School and Early Career Development" by Steven Krantz, and "Letters to a Young Mathematician" by Ian Stewart.

I make these suggestions because the study of mathematics undergoes a rather significant change partway through one's undergraduate career; math classes shift the focus from computation/calculation to proof-based problems. Reading the aforementioned books might give you an idea as to what is actually involved in, and required for, the study of mathematics. Even if you are familiar with some of these ideas the books are worth reading. Once you have a rough idea of what the study of math is like at more advanced levels, you can use that information to help guide your own studies. There are some very good books to help introduce one to proof-based math, or to delve deeper into areas that you may only have covered in a superficial way in your classes.

As for IQ... avoid the tests or not, it doesn't really matter. Don't get hung up on "how smart" you are. IQ was never meant to be used as a static measure of one's intelligence; it was supposed to be used as a measure of change. Yes, math is difficult. There will be times, if you pursue it, where you have doubts about your ability to succeed. Intelligence is required, of course, but hard work is at least as important.

 

[HallsofIvy]

I don't know why there was mention of "IQ tests" at all. That's not relevant to the topic. You will of course need to complete four years of college and get a bachelor's degree. If you are concerned about money, go to a state college- most of them are excellent. After graduating you will want to think carefully about a graduate school. Often you will find that you can get fellowships or teaching "assistantships" they will help cover the costs. Most college catalogs talk about three years for a Doctorate but there's no way to determine how long it will take you to complete your dissertation- figure 3 to 6 years. If you are certain you want to get a Ph.D. I would NOT recommend following the "Bachelor's- Master's- Doctorate" path. Most colleges will allow you to enter a doctorate program directly- but if you find you can get a master's by writing a thesis and not taking courses you don't need for your doctorate, sure, why not?

I would NOT recommend planning on working for a year or two, then going to graduate school. You will find it very difficult to quit a paying job to go back to school!