When I work with younger students in subjects like mathematics or physics, it doesn’t take much to impress them with my ability to quickly see through a problem and calculate things that would take them minutes. Just like any other student at my level, we often skip the use of calculators because it’s easier to just focus on the work we are doing and do the arithmetic in our head. The most prominent example of this, however, is in algebra.
I’m definitely no expert on the subject, but from my experience with other students, the thing that seems to confound them over and over is algebraic manipulation. Consequently, it takes longer for them to learn any other concept after, because they’re always using the algebra that was already tricky for them.
For example, I’ve worked with some students on the process of factoring expressions. In secondary school, this is usually done with trinomials such as $x^2+5x+6$. The goal is to get from that form to the factored form of $(x + 2)(x + 3)$.
To do this, there is a whole set of instructions that students copy down onto their memory aids for the test. When I worked with these students, the procedure is what they followed.
As they were doing that though, I was solving it in my head. We then compared answers, and I’m fairly sure it was surprising to them how fast I had gotten to the answer, as if I was able to pull it out from the page itself. They, on the other hand, were carefully going through each step of the procedure before getting the correct answer.
Both ways worked, but it seemed as if I had a faster way. I showed them how I thought of the procedure in my head, and I could tell that they probably weren’t confident in their own ability to do that in their heads. To them, they were only ever going to work it out on paper.
What I’m trying to illustrate here is the massive difference only a few years of practice can make. I wasn’t separated from them by that many years, and what was a whole new problem for them to solve was something that I could typically do in about ten seconds or less. It isn’t because I’m brilliant at arithmetic that I can do this. Rather, it’s because of all the work I had done for years to get the hang of it. I can do it all in my head now, but I remember doing countless examples when I was younger, trying to get the hang of it.
In most areas of physics and mathematics that you enter, talent isn’t a prerequisite. Instead, being willing to commit to hard work for a long time is what’s needed. Do that, and you’ll be able to eventually appear “flashy” in front of those who can’t do something as effortlessly as you can.
But be aware: this is true for virtually any domain in life. Athletes don’t pull off amazing plays out of only sheer talent. They have an enormous backlog of hours that were dedicated to improving in their sport, and which culminate to help the player make the amazing play. You will find few examples of people simply having so much talent that they can do everything with little effort. More common is that you will see the hard work that was done by just pulling back the curtain a little on that person and looking at their history.