The importance for students to know “why”

I really enjoyed my fist year in college, however, there was something that made me feel bad about myself, that I was not good enough. All of my classes had something in common; every professor assumed that the students are familiar with the concepts of the corresponding class. Even if sometimes I was already familiar with them I always was wondering “Why are we supposed to know that?”.

Spring of 2017, I took a class about Differential Equations. The first four weeks we had an introduction to Linear Algebra since we would need it later.

Eventually, two or three weeks before finals, we were doing Laplace Transform. I was sure I’ve had heard that name before and I was excited to get started.

My professor started with the definition:

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I was like “huh, so that’s Laplace transform”.

I remember him evaluating some Laplace transforms, starting with L{1}.
I asked one of my classmates “Did I miss any lecture or is it the first day we’re doing Laplace?”. It was indeed the first time we’re doing Laplace transforms.

I was waiting to understand what was going on there, and why we were doing Laplace transform anyway, my professor kept continuing on examples.

I couldn’t keep it inside me anymore. I raised my hand, he asked me if he missed anything again “No, actually I have a question this time… Why are we doing Laplace transform?” – I asked.

He laughed and told me that it is a good question, “Laplace transform is going to be later a useful tool to solve Differential Equations with real coefficients ” he eventually answered.

I was thinking at the moment ” Why he didn’t tell us anything at the beginning of the class, how are we supposed to know why we are doing what we are doing?”.

Unfortunately, I cannot interrupt every single lecture to ask “why” or “where are we going to need it”. I guess it is every professors’ responsibility to let students know at the beginning of the lecture if needed. Sometimes even if I am a math major and understand usually everything that we are doing in my math classes, but the answer to the question why it’s not always obvious.



In Math, every single word is significant

Even if I’m studying Applied Mathematics, I always had a great interest in Number Theory, it was so “simple” and “fun” for me (at least in high school -but in general it’s not that simple at all).

Since I’m talking about Number Theory, I’m going to talk about the Prime Numbers, they are my favorites, they’re so “unique”.


When I was in the first grade of high school, I first learned about the above-mentioned theorem. I also used it a couple of times to solve/prove some problems, it was a useful one.

However, we all know that for the prime numbers, there’s no formula or function that will give you any p prime number by plugging in an i number (inN) and p will be the i-th prime number.

One day, I was thinking about that theorem, but in a quite different way ( in a wrong way). I didn’t remember exactly the theorem at the time and I had it in my head as that “any number of the form 6k+1 or 6k+5 is a prime number.”

So in my head “problem is solved”, “I can find any prime number by plugging in a number for k.”

It felt so perfect and easy to be true, I had that feeling that I usually have when I do something wrong or I have an incorrect assumption in Math.

It is easy to see that by plugging in some number for k will give you a non-prime number (for example k=15, it gives 91 and 95), I realized it the very following hour.

Then I was looking for that theorem, on a textbook, I had in my head and when I found out that I was totally off, I was like “yeah, you’re really smart.”

From that day, I pay more attention not to miss a single word in math and to remember every definition or theorem the exact way that is written in the textbook. In math, we don’t like to add words that are not important just to make it “sound” better. Everything is so precise, that’s the beauty of Math anyway.