Background: I’m completing a BSc Mathematics, currently in year 4.
A lot of people who have almost no mathematical background ask me what I study in university. I understand that this is a very common way (at least in my country) to start a conversation to an undergraduate, but I think that this is inappropriate.
I am not going to blame them because I believe that they truly don’t understand what mathematicians are doing (perhaps I don’t either). Also, explaining what to study in other majors appears to be much easier (at least for me). For example, a CS student may explain with an applied course (such as mobile app development). This is even easier for job-oriented subjects (law, social work etc).
I usually start by saying that MATH students study rigorous maths like theorems and proofs. There are several domains like PDE and applied maths (I’m not going to talk about analysis and algebra because the discussion will soon go into chaos, and I believe they know nothing about elementary calculus and linear algebra). My most “real-life” example is image processing (and perhaps, no other examples). However, I think emphasising such an example does not give a very clear picture of what a math student studies. They may even have difficulty understanding cooperative strategy in game theory.
Worse still, they
start feeling that studying maths is useless (and I believe that a lot of people think so).
start by teasing at people who study math. That’s fine because it is OK for me to simply ignore them after a detailed explanation (e.g. studying math trains one’s reasoning skills), but this is in no way a good situation.
start by saying something irrelevant, especially for those who entirely don’t know advanced maths. For example, they think that a 10-year-old child who won in a competition by correctly doing a large number of mental arithmetic calculation in a short time is very good at maths.
I usually try to explain in detail, slowly and patiently, but in vain. Any hint?