Short answer: Yes

Long answer: No. Well, at least I hope not. Maybe I am not studying correctly, or I am not polishing my understanding as often as I thought. Did I understand what I just read, or did I mindlessly copy and paste the highlighted phrases into my notes, hoping I could do the same on my exam paper? Or am I too scared of facing my fear of being wrong? . . .

. . . the list of possibilities could go on. One may think this is a cherishable experience, as it lights the way down from the peak of "Mount Stupid" on the Dunning-Kruger Effect Curve. But some of us, like myself, would rather slit our throats in the hope of reincarnating as a pebble on the fiery banks of Mustafar.

Earlier today, I was tutoring my 6-year-old brother on the basics of geometry, like finding the area of a square or rectangle. He was struggling, so I asked if he knew his multiplication tables. He said yes. Indeed he did, and he proved it to me by solving every question I drafted in less than a minute. When I asked him how he came to that solution or what it means to multiply two integers, he couldn't answer me. I asked him to map his thoughts on paper while he solved 8 × 10. He started to mumble, "8, 16, 24, 32, ..." A nostalgic learning technique that relies purely on memory: it can only get you so far, not beyond the scope of basic geometry, but just enough. For some people, that is sufficient. But it may not be for my brother, who might one day like the same things I do.

I, too, started learning maths this way. It got me through high school and maybe a few first-year maths units in my undergraduate degree. My learning after that was like driving a car in the dark without headlights, or baking cookies in the middle of the night without glasses (assuming your vision is terrible). You don't know what you are cooking, and you don't know what you are looking at, but you know damn sure that you are baking some good old cookies. If you don't know what you are looking at, then how would you know the cookies were baked perfectly? Or how would you know if you actually liked maths? These questions prompted me to do many things, from attempting to change degrees to revisiting high-school maths textbooks.

Relearning my fundamentals made me realise that mastering higher maths depends on how strong your fundamentals are. In other words, how fast you can complete a large puzzle depends on how fast you can solve the smaller ones. Curiosity, consistency and frequent practice definitely come into play in building your problem-solving skills. However, what I found most important was mastering patience and resilience.

Much like my younger self, my brother is clearly more comfortable memorising the solutions than taking the time to reason. In an economic sense, I guess he is better off, since it takes less time. The point is, if he understood how addition and multiplication work, then solving for the area of a rectangle or square would become second nature.