I'm 12, and really like mathematics and physics. I was just wondering what does a 'theoretical mathematician' do?
closed as offtopic by Fernando Muro, Daniel Moskovich, Ramiro de la Vega, David White, Willie Wong Oct 22 '13 at 14:44
This question appears to be offtopic. The users who voted to close gave this specific reason:
 "This question does not appear to be about research level mathematics within the scope defined in the help center." – Fernando Muro, Daniel Moskovich, Ramiro de la Vega, David White, Willie Wong

12$\begingroup$ We prove new theorems! I'm glad you are excited about math, but I'm afraid that this is not the right place to ask your question. This forum is intended to be a place where research mathematicians (mostly professors and graduate students) can ask technical questions about their research. $\endgroup$ – Andy Putman Oct 21 '13 at 17:11

6$\begingroup$ A book suggestion for you: R. Courant and Robbins, What's Mathematics? $\endgroup$ – Alexandre Eremenko Oct 21 '13 at 17:15

16$\begingroup$ I feel like paraphrasing the old Star Trek monologue: we explore strange new mathematical worlds, we seek out new mathematical life ... ! Best wishes for your studies, and hope to meet you again here in future years. $\endgroup$ – Todd Trimble♦ Oct 21 '13 at 17:17

3$\begingroup$ As your question was put on hold here, I recommend you the site math.stackexchange.com. Also, the great mathematician Alfréd Rényi said that "a mathematician is a machine for turning coffee into theorems", but there are counterexamples (e.g. I never had a cup of coffee in my whole life). $\endgroup$ – GH from MO Oct 21 '13 at 20:33

3$\begingroup$ You probably should not advertise the fact that you are 12. The Term of Service for StackExchange websites requires you to certify that you are 13 or older. $\endgroup$ – Willie Wong Oct 22 '13 at 14:48
There are several things that mathematicians do:
 teachers of mathematics teach math, and you surely know some of those,
 applied mathematicians use their knowledge of mathematics to help engineers, physicists, chemists, and other scientists solve math problems. For example, they help engineers calculate how water is going to flow around a ship that the engineer designed. Or they might help doctors calculate how a flu is going to spread and how many people will get sick.
 theoretical mathematicians figure out new math that nobody has done before. For example, they solve open math problems that nobody has been able to solve. Or they think of new interesting math that nobody has ever done before. Sometimes they invent new math that allows physicists and other scientists solve physics problems that they could not solve with old math.
Most mathematicians do a bit of everything. For instance, I teach at a university, I do theoretical math, but I also do applied math because my research is about math and computers. So I often figure out how to program computers so that they can do math by themselves, which means that I need to write programs as well as invent new math that allows me to write even smarter programs. If you would like to know examples of this, just ask.

$\begingroup$ An exciting example of applied math is the computer graphics research being done by Joseph Teran at UCLA. $\endgroup$ – littleO Oct 22 '13 at 8:39

4$\begingroup$ I large agree, but I wouldn't distinguish between applied and theoretical mathematicians this way (applied = using math to assist others, theoretical = figuring out new math). To me, theoretical mathematics generally means pure mathematics, although it's a more ambiguous term for it. Theoretical and applied research both involve figuring out new mathematics, just with different motivations. Of course applied mathematics also covers a lot of nonresearchers applying known mathematics, as indicated in the answer. $\endgroup$ – Henry Cohn Oct 22 '13 at 13:16

3$\begingroup$ You should write your own answer, while taking into account the fact that the person who asked this is 12 years old. $\endgroup$ – Andrej Bauer Oct 22 '13 at 18:47

5$\begingroup$ Oops, it's been "put on hold" (which is the disohnest way of saying "closed"). $\endgroup$ – Andrej Bauer Oct 22 '13 at 18:47