When I was in elementary, learning the basics of arithmetic was an important component of my mathematics education. I participated in various mathematics “challenges”, where I tended to do pretty good. I like the rush of having to beat someone to an answer in a competitive setting, so I became good at it.

In algebra, there is a certain order in which operations must be done. If you’re reading this site, there’s a fair chance that you’re so familiar with this concept that it’s basically subconscious. If not, you’ve probably heard of the mnemonic BEDMAS, meaning brackets, exponents, division/multiplication, and addition/subtraction. These rules are formulated so that there is logical consistency in algebra.

If I wanted you to calculate a bunch of derivatives for me, I could simply show you the algorithmic approach to the process and leave you to do it. With some practice, you’d get better and better at taking derivatives and could even become better than a mathematician.

I once had a mathematics teacher who would say something that bugged me: what we’re doing is easy. I am barely being hyperbolic when I say that this teacher would say this for every single concept we learned. Therefore, I couldn’t help but think that surely not everything could be this easy.