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# On Understanding, Not Just Memorizing
- URL: https://starikov.co/understand-not-memorize/
- Published: 2017-11-11T19:11:00.000Z
- Updated: 2026-06-09T23:01:29.000Z
- Author: Illya Starikov
- Tags: Mathematics, #u-color-bg-tag-accent, #u-color-text-dark

Throughout my undergraduate studies, I've become good at digging deeper until I completely understand a subject. But when I look around me, I realize I'm in the minority. Often, students only want to know how to get from question to answer without any intermediate thinking. I can't pinpoint a definitive reason why, but I have one hypothesis: encapsulation\[1\].

The most famous example I've encountered is the derivative of any trigonometric function besides \\(\\sin x\\) or \\(\\cos x\\). As any student who's taken Calculus can tell you,

$$\\frac{d}{dx} \\left(\\tan x\\right) = \\sec^2 x$$

However, most students couldn't tell you:

$$  
\\begin{align\*}  
\\frac{d}{dx} \\left(\\tan x\\right) &= \\frac{d}{dx} \\left(\\frac{\\sin x}{\\cos x}\\right) \\\\  
&= \\frac{\\cos x \\cos x + \\sin x \\sin x}{\\cos^2 x} \\\\  
&= \\frac{\\cos^2 x + \\sin^2 x}{\\cos^2 x} \\\\  
&= \\frac{1}{\\cos^2 x} \\\\  
&= \\sec^2 x  
\\end{align\*}  
$$

At first glance, this seems like useless information. You might even think of it as a piece of trivia—until you see how many people miss it on a quiz or test. And entry-level Calculus isn't the only place this matters. This pattern appears everywhere: physics, thermodynamics, mathematics of any kind, computer science, and the like.

You might be wondering: why does it matter? If it's worth a couple of points on a test, is it that harmful? Maybe not—until you realize you don't conceptually understand the subject, only mechanically.

The next time you're learning something, ask yourself: "why?". The outcome might delight you.

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1. The act of enclosing in a capsule; the growth of a membrane around (any part) so as to enclose it in a capsule. ↩︎