I'm 12, and really like mathematics and physics. I was just wondering what does a 'theoretical mathematician' do?
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There are several things that mathematicians do:
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.