I am a Mathematician

What does it mean to be a mathematician? We might start by asking: What do mathematicians do?

Like most good questions, this one does not have one right answer (other, of course, from, "Math!") One possible approach is to talk about some of the different kinds of math people do. Indeed, math is made up of a vast number of specialities, and sometimes it seems that these diverse branches have nothing to do with one another.

Here's an analogy. Both the psychiatrist and the podiatrist are medical doctors, but there is very little overlap in their day to day working experiences.

There is, however, a significant problem in presenting "math" as nothing more than a list of different specialties. Sometimes it is very difficult to draw boundaries between separate areas. The distinctions between geometry and algebra are not always as clear cut as, say, the differences between foot problems and brain disorders. Indeed, this blurring characterizes much of the most interesting mathematics.

Bear this in mind while you work through the following list of "different" areas. Try to think about how they might connect. We'll look at some examples later.

We begin on the broadest level possible, splitting modern mathematics into three areas:

• algebra
• analysis
• geometry

Now let's look at some combinations:

• differential geometry and differential topology
• algebraic geometry and algebraic topology
• fractal geometry
• knot theory

There are many other areas of mathematics, some of which have posters of their own.

• number theory
• dynamical systems and chaos

The different areas of math really are intimately related. Take, for example, the recent proof of Fermat's Last Theorem, a problem in number theory, whose solution draws from algebraic geometry and complex analysis. (You may want to find out more about Fermat.)