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Usefulness

Author: Youngjin Kang

Date: 2022

"But... is it useful for anything?"

This is a common question which arises among school students when they confront a seemingly obscure theory, such as an abstract concept in mathematics. Whenever a teacher presents the students with a new idea that is not obviously applicable to real-life examples, some of them even deny the authenticity of the education they are receiving because of this.

Some educators answer this question by providing their students with the most down-to-earth type of examples, so as to demonstrate the usefulness of the theories that they are trying to convey. American math textbooks, for instance, are usually covered with images of roller coasters, industrial robots, and other "useful" cases of mathematics in our daily life. This creates a sense of: "You must eat these vegetables in order to get healthy".

Taking pragmatic necessity as a hostage is a valid short-term strategy, and it does work in cases where a student is particularly interested in real-life applications whilst showing particular disdain towards pure theory. However, this approach introduces two major problems:

(1) Emphasis on "usefulness" hides the true beauty of the theoretical subject. By treating geometry as a mere tool for industrial design and optimization, the educator is downgrading pure theory into some kind of "technical cookbook" for specific use cases instead of preserving geometry's original source of fascination which did not rely on practical applications (e.g. Ancient Greek notion of the essence of space, as well as its implications regarding the structure of the universe).

(2) It encourages students to learn the subject in a superficial manner, oftentimes by memorizing technical rules and exercising some kind of puzzle-solving dexterity. This mode of learning has its own benefits, yet it deters students from really trying to understand the essence of the knowledge by burying them in a heap of specific case-by-case scenarios which are nothing more than reiterated versions of the same old concept. This tendency further enhances when students are exposed to a highly competitive environment, in which memorizing a bunch of problem-solving recipes is considered a far more efficient way of outperforming one's competitors than reasoning with fundamentals.