Why study mathematics?

I loved math. This is what many fresh math students say. They have chosen to study what they loved. And as it is in many early relationships they discovered that they don’t know the beloved ones. Looking for an x was exchanged for searching the f(x). Multiplying and adding was pushed out of the stage to make place for integrals and matrices. N-dimensional space became a daily routine.

First day, first week, first month and you are learning more and more complicated theorems. A few resigned before the end of first term. Half of those who survived the semester will be eliminated during exams. As a result, only 50% of freshmen make the second semester. Many of them, stripped out of self-confidence are getting lost in the reality. They study hard for tests and exams which have driven a few to depression and anaemia. Finally, after approximately 4 years of hard work you left the university with a bachelor degree.

What ability do you have as a math graduated? Knowledge of a few theorems and equations useless in everyday life? Sure, you may say that you know more complex stuff than an average person. But what does it mean? You will never use a big chunk of what you have learned. You will never use the Banach–Steinhaus theorem directly in your job. Yet, you will use it everyday.

Clue of studying math is not knowledge for knowledge sake. The clue is the ability to solve and understand every problem. No matter how complex it is. You will easily understand assumptions, dig out relations and finally work out solutions. Your outcome will be more accurate and formalized than the one provided by many others.

The clue is the ability to solve and to understand every problem.

This point of view was presented to me by a math teacher from my secondary school and an interesting thing is that I’ve never heard it at university. I remembered his words once I got a job. Possibility to compare myself with “non-mathematical” colleagues allowed me to understand what the teacher meant. If you know how to carry out proof for Bolzano–Weierstrass theorem in 45 minutes during an exam, then you will execute “complex tasks” in quarter of time usually needed.

But as I mentioned, only a few got the clue during studies. It seems common to me that many third year students — those who are about to achieve their first degree — are confused about what they’ve gained during studies. It’s sad and amazing at the same time, to see people who did their best to graduate only because “they should” or “what will the others say if I resign?”.

So if you are still studying — not specifically math — and you have the feeling that you are not sure why you are doing this then stop for a moment. Think a while about what I said and discover what is hidden beneath the university knowledge.