Discover new mathematical principles.
What does a Theoretical Mathematician do?
Though it sometimes seems like it was made up out of the blue to torture students, in reality, math is based on a number of theories that have been proven time and time again. When you work as a Theoretical Mathematician, you get the chance to test old theories, and discover new truths about numbers and the way they relate to one another.
Though the areas often overlap, Mathematicians tend to fall into one of two categories: theoretical or applied. As a Theoretical Mathematician, you’re a little more interested in the theory involved with mathematics. This means you often work in schools or research labs, testing new theories, researching new facts, or teaching students. You’re different from an Applied Mathematician in that they work in business or government, answering questions like “How many routes will a new airline need?”
Though it would be awesome to be able to sit around and ponder math problems all day, you’d be hard pressed to find a job that would let you do that and get paid. Instead, most Theoretical Mathematicians are found in classrooms, working with university-level students. You do all the things any other type of Professor does, like giving homework, grading tests, writing lectures, and helping confused students figure out difficult math concepts.
In your free time (that is, when you’re not working with students), you do independent research. The research you do is often a solo endeavor, so get ready for a lot of time with only your thoughts and your math books.
Though you spend quite a bit of time by yourself, you still need excellent communication abilities. This is because the research you do needs to be shared with the world at some point, so you might present it at a conference, write a paper, or publish it in an academic journal.