Teachers make the difference

When I was learning electrical engineering at the university, we've been told to model AC circuits with complex numbers. The professor said that is how we do it. The textbook did not say anything more. That's how we roll, kids!

I did not understand why we use complex numbers there. It felt like something random. No one explained why we use them. At the same time, I did not ask why we use them there. I just used them.

Years later, I found myself on YouTube getting lost in the rabbit hole of YouTube's constant stream of recommended videos. Math videos were served on that particular day. One of them was explaining Euler's identity.

And then it hit me. I understood why AC circuits are modelled with complex numbers. It was about the cyclic nature of both complex numbers and AC circuits.

It took me 10 years to finally get this. For 10 years I felt like an idiot that can't understand basic concepts. The truth is I can understand them. I just needed the right teacher. Someone who phrases the problem in such I can get it straight away.

I've had a similar experience when I started to learn linear algebra from 3Blue1Brown's excellent Essence of Linear Algebra series. I was taught how to multiply vectors and matrices but they were for me just formulas to memorise. Grant's videos explained those concepts in such a way that I was blown away how intuitive and beautiful they are. I was in this state of intellectual euphoria that culminates with the words "I get it" followed by a small smile.

I'm not an idiot. I don't need to beat myself when I don't get some concept. Neither should you. We all can get them. Sometimes we just need someone who can explain the same thing in a different way.