This is a question that students encounter over and over throughout their education. It crops up when deciding what classes to take, what projects to embark on, and what programs to study. It is a natural question, because we don’t like embarrassing ourselves. Therefore, we want to avoid pursuits that are too difficult if possible.
As a physics and mathematics student, I can only give you my perspective from this small corner of life. How can you tell if you have what it takes to study mathematics and physics?
I don’t want this to turn into a celebration of every person’s ability to do mathematics and physics if they give enough effort. While this may be true, it isn’t exactly helpful. That is avoiding the question, so I want to address it a bit differently.
Work, work, and more work
This is the first thing you should be prepared for. Studying mathematics and physics requires a lot of work. You might get by in the beginning by understanding the “trick” to a problem, but from what I have seen, this doesn’t last forever. At some point, you will encounter problems that confuse you and are not solved in five seconds. When this happens, are you willing to put in the work to understand?
On a practical level, I spend many hours each week doing homework. This is not studying for pure enjoyment. It is studying in order to finish my homework. This often means digging through textbooks and various resources to figure out the essence of a problem. It’s not always fun, and sometimes I spend hours labouring over a specific example that I just cannot seem to get. Perhaps I am slow, but I think it is safe to say that you will encounter your own version of this throughout your studies.
I am not saying the work is always boring. I enjoy a lot of the aspects of solving a problem, and gaining a better understanding of a concept is satisfying. I just think it is worth pointing out that this does not come for free. You will work a lot in a mathematics or physics program, and there is not much you can do to get around that.
Connected to the previous section is the idea of needing to be very smart in order to fare well in these programs. I do think some are better than others, but it’s rare to find someone with zero ability in the subjects. Why is there an initial imbalance? That is probably a question that sociologists can answer better than I can, but I would say that your upbringing can prepare you better or worse for any program. I don’t know if there are any genetic tendencies for people to be better at mathematics or physics, but I do think it’s clear that someone may seem more naturally “brilliant” than others.
Does that mean you need to have an easy time in order to study physics or mathematics? Not at all. In fact, I would say that most of the students I have met do not fall in this category. I would definitely include myself in this category.
Being smart does not automatically mean you are ready to study physics and mathematics. I would put a lot more emphasis on the willingness to do work, because everyone will hit a roadblock. Some people might hit a roadblock later on than others, but each person has their own difficulties. The real question is how you will respond when you encounter a roadblock. Will you quit, or will you persevere?
Memorization and first principles
Throughout our primary and secondary education, the lesson that is reinforced over and over again is that memorization works. We hear teachers and others bemoaning the fact that memorization is all students do, but the simple truth is that it does work.
At least, to a certain extent. When you go further and further into mathematics and physics, you learn that memorization is only part of the picture. The emphasis now is on first principles thinking.
What this means is that, instead of remembering how everything fits together, you start from some bedrock foundation, and build from there. In terms of classical physics, this often begins with Newton’s second law. From that simple equation, you can derive a bunch of consequences that depend on the system. The point is that you no longer worry about the end result. Instead, the emphasis is on understanding the foundations, and building from there.
If you are someone who gets by through memorization (and don’t worry, we all are, to some extent), this shift in mindset will take some getting used to. However, I think it is important to be aware of this, because it is quite different from early education.
My goal with this piece is to remove the fear of not being “smart” enough to study physics or mathematics. If I had to isolate one quality that needs to be built, it is the willingness to work hard. If you can do that (and even find joy in it), you will do fine. You might not be the best researcher who ever lived, but you will be able to understand more than you once did. Therefore, if you enjoy physics and mathematics, I would recommend giving it a shot. With the the right mindset, I think many people are capable of studying these subjects.