Pearls

I was stumped by the following comment from a 14-year-old student: “Why do we need to learn about prime numbers? What’s the point? My grandma never had to learn about prime numbers yet she’s done well in life. She thinks I’m wasting my time learning these kinds of things.”
“It’s a shame,” I replied upon reflection, “that your grandma never had the opportunity to learn about and appreciate the beauty of mathematics. Perhaps nobody taught her maths in such a way.”
And therein lies the problem, I thought. We fail to teach maths properly and therefore condemn the subject to be an abject exercise in solving boring problems. The pure essence of mathematics is thus subtracted from it and its complexity is unnecessarily multiplied. We need to add some other flavour to the way we teach maths. This could divide opinions but I insist: maths should be taught as poetry.
For what is maths but a language? The language of nature, the language of elegance and truth, the language of aesthetics.
It is fair to say that an equation epitomises mathematics. At first sight an equation can be a trivial collection of symbols, no matter how complex their arrangement might be. But  every equation has a story to tell. An equation is a story in its condensed form.
Take, for example, this rather famous equation:
Encapsulated in those 5 symbols is the essence of life; of life on Earth at least. It relates the connections which exists between energy and mass and, by extension, between change and matter. These put together are what make the Sun what it is: a burning ball of gas emanating vast amounts of light and warmth. This light and warmth is what sustains  life on Earth. It is also the combination of the Earth’s atmosphere and the warmth from the Sun that gives rise to the weather. Moreover, going back a few billion years, under certain climatic conditions, primordial life forms arose out of the chemical soup amidst the oceanic hotbeds. But how does the Sun itself generate so much light and warmth in the first place? It’s down to the nuclear reactions taking place at the core of the Sun. The Sun, a giant reservoir of hydrogen gas, is constantly converting this form of matter into nuclear energy which is then manifested as the light and warmth we depend so much on. And the amount of mass converted into energy is described beautifully by Einstein’s equation. Here, E represents energy, m is mass, c is the speed of light (whose value remains constant) and the 2 appended to c simply means that this value, c, is multiplied by itself (i.e. it is squared). The fifth symbol ‘=’ is what connects the mass and energy together stating precisely their immutable relationship. It’s not that some vague quantity of mass could, perhaps sometime or somehow, give you an approximate amount of energy. No. This is an exact definition. The equation tells us exactly how one quantity is related to the other. You cannot be any more specific than this. And this is beauty of maths: it is exactitude “personified”.
This is just one example of how an equation is a concise form of truth. Take any other equation and in it you could extract a lot of information. But maths is not just about equations. Maths is also about shapes, patterns, numbers, groups, chance, etc. It covers a variety of topics. Yet whatever the topic, the truth contained therein is irrevocable as long as the logic is sound.
Maths can also be abstract – i.e. an extrapolation of the real world. It allows us to venture into the unknown without fear; it enables us to explore that which is intangible; most of all, it opens the door to myriads of possibilities. Yet, in spite of its theoretical nature, maths underpins every practical aspects of our lives. It is the language that describes Nature and the physical laws. It is the language of science. And without it, we would not be able to translate any of our theories into technologies.
Take any of these equations below:
Entropy of an isolated system

Entropy of an isolated system

Heat Equation

Heat Equation

Schrödinger's equation

Schrödinger’s equation

Einstein's equation

Einstein’s equation

They each describe something specific our reality. And it isn’t that we ascribe some meaning to these equations in that we assign some definition of reality out of them. But, rather, they actually contain, in a condensed form, the description of reality. But even if it an equation is of such an abstract form,
Euler's equation

Euler’s equation

which so eloquently assemble the basic constants of mathematics, it still has an elegance about it. It is poetry, pure and simple.
On the surface, mathematics might look like a hard, impenetrable shell with no real purpose. But deep inside lies a pearl. Lucky is the one who beholds such beauty for then the world is their oyster…
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2 thoughts on “Pearls

    • Absolutely. It covers every aspect of the real and abstract world. It is both an art and a science. If it is taught in such a way that blends art and science together then it will appeal to a greater audience.

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