The following essay is actually my class assignment for GP. It is one of the essays that I am most proud of. Wish myself all the best for the upcoming GP Exam! Note that the question is adopted from Singapore-GCE A’Level 2012 General Paper P1.
Consider the view that Mathematics possesses not only truth, but supreme beauty.
How can you expect those alien-looking equations, tedious proofs and frightening collections of numbers to possess something beautiful, something that inspires awe, pleasure and imagination? While Mathematics is often praised for unlocking the underlying patterns and properties of the universe, its aesthetic value is largely questionable. It is commonly believed that dealing with those inanimate, cold numbers is a highly intellectual activity that has little beauty as people may easily get bored or frustrated. However, in my opinion, one has to be clear that the beauty of Mathematics is less explicit than the beauty of the arts or any natural landscape. The beauty of Mathematics lies within the creative approaches of problem-solving, the exceptional artwork which integrates Mathematics principles, and, most importantly, the insightful understanding of the universe that people gain from Mathematical theorems. It is in fact precisely because Mathematics contains truth, people are able to understand, utilise, and experience supreme beauty.
Unfortunately, in the contemporary pragmatist world, people often perceive Mathematics as a useful tool that solves real-life problems while very few of them actually bother to appreciate the beauty of Mathematics. Ever since the Industrial Revolution, Mathematics has been serving as the foundation for many practical disciplines like engineering and accounting. Mathematics has also become a discipline devoid of aesthetic pleasure, not to mention the supreme beauty. In China, where the education system heavily emphasises standardised tests, Mathematics is mostly taught as an examinable subject that only involves problem-solving skills. Teachers seldom mention the beauty of Mathematics simply because that will not effectively improve the scores of their students. Most of the brightest math students in China actively participate in Mathematics Olympiads because they wish to raise their competitiveness in the admission processes of their dream courses. A profession in pure Mathematics will probably not bring them a high material standard of living. Driven by pragmatism, students tend to learn Mathematics as mechanical problem solving. They may rely heavily on the accuracy and objectivity brought by Mathematics in their work, but simply not aware of the beauty of the subject.
In addition, there is no denying that dealing with inanimate numbers does not stimulate the five senses of people, making it very difficult for them to appreciate the beauty of Mathematics. In order to evoke awe, pleasure and imagination, it is commonly believed that the object, mainly an art piece or a natural landscape, should occupy people’s five senses to engage them. That process is crucial for the perception of beauty. This can be illustrated by the innumerable visitors of the Louvre who are willing to spend hours queuing just for a glimpse of the world’s most mysterious smile. The master piece, Mona Lisa, successfully stimulates the imagination of its visitors regarding the reasons for her smile and her life in Italy during the Renaissance. In contrast, fewer people would want to read the books written by Andrew Wiles, who offers a proof for Fermat’s Last Theorem, one of the most difficult Mathematical problems that have troubled Mathematicians for centuries. Unlike Mona Lisa, the proof is so intellectual and rigorous that people have to follow every step closely and pay fullest attention. Those numbers and reasoning cannot consistently engage their readers who may easily get lost along the way. Once they are lost, Mathematics may be very boring and frustrating. Therefore, it is understandable for many to claim that the beauty of Mathematics, which is too implicit and intellectual, can only be appreciated by Mathematicians. The rest may just feel that the subject is very boring and dull.
However, if people are willing to explore further, Mathematics can also be exceptionally beautiful. One cannot doubt the existence of such beauty just because it is too intellectual to get access to. In fact, the world is surrounded by the beauty created by Mathematics. Many of the greatest artists have adopted Mathematical principles to create many of the most brilliant artwork we enjoy today. The well-known and long-standing Golden Ratio is the best example. It is so surprising and yet somehow expected to discover the fact that the mysterious Pyramid of the Ancient Egypt, the Parthenon of Greece, Vitruvian Man from the Renaissance and the design of modern instrument Pearl Drum all exhibit the same ratio 1 : 0.618. Throughout history, artists from different cultural backgrounds and beliefs are fascinated by the same ratio which is believed to be visually beautiful and aesthetically pleasing. In other words, the Golden Ratio, and the beauty of Mathematics, unites people all around the world. This can be achieved because as compared to the unpredictable modern fashion trends and the rapidly changing perceptions of beauty, the beauty that Mathematics contains is superior and able to stand strong against time. That is probably why countless artists are attracted by those seemingly boring Mathematical patterns and principles. As a source of inspiration for artists throughout history, Mathematics itself does contain supreme beauty.
Moreover, there is often creativity involved in the actual practice of Mathematics, and that often triggers aesthetic pleasure among Mathematicians or even ordinary people who engage themselves in Mathematical discussions. The creativity is raised essentially because there are many different methods to be explored in order to solve a problem or prove a theorem. Mathematicians often describe a particular method as elegant when it uses a minimum number of assumptions, adopts a succinct approach and reflects one’s original insights. The classical example is the Pythagorean Theorem which can be proved in many different ways. The ancient Chinese attempted to prove it using a visual method. They even named the integers fulfilling the theorem to be “Gou Gu” numbers. The most well-known proof is offered by Greek Mathematician Pythagoras, who creatively proved this theorem by re-arranging the square tiles from his neighbour. Even in the modern world, long after the theorem was proved, people are still trying to offer alternative proofs using new discoveries in algebra, geometry and technological advancements. Every new method of proving or solving involves one’s innovative thoughts and unique expressions of his thinking. Therefore, dealing with those inanimate numbers does involve a sense of aesthetic pleasure comparable to the artistic pleasure when creating an art piece. The beauty is in fact accessible to everyone, even those who do not know much about Mathematics, as long as he is courageous enough to offer his original thoughts. There is indeed beauty, or aesthetic pleasure, in the world of Mathematics, and it is the profound beauty that caters to people’s curious and creative nature.
Furthermore, it is precisely because Mathematics contains accuracy and precision, the discipline also contains supreme beauty. Truth and beauty, in other words, are two integral elements of Mathematics. Mathematical theorems and principles are crucial for people to understand the beauty of the universe because they articulate quantity, structure, shape and movements with the highest precision. With Mathematics and the accuracy is provides, people are able to perceive and systematically analyse the rules and codes of musical harmony and rhythm that resonate deeply across different cultures. People are also able to realise what equations produce the perfect dome shape of soap bubbles and trucks of snowflakes falling from the sky. Essentially, Mathematics is the subject that helps the world define beauty in a logical, systematic way. It fuels appreciation as well as discussions of the arts or any natural landscape. Being the theoretical foundation of what people generally perceive as beautiful, Mathematics itself is, of course, exceptionally beautiful.
According to Betrand Russell, the British philosopher, logician and Mathematician, Mathematics constructs a world that is perfect and true. The discipline has the combination of characteristics of the great arts and freedom. As for the beauty of Mathematics, it is so cold and austere, like that of a sculpture. Admittedly, not all people can appreciate the beauty described by Russell since they often perceive the subject to be merely a useful tool devoid of beauty, and they easily get bored by it. However, we should not reject Russell’s perspective. In fact, truth and beauty are two inseparable parts of Mathematics. With the accuracy, precision and objectivity it contains, Mathematics inspires artists to create enduring artwork, helps people discover their inner creativity and systematically defines the idea of beauty. As such, those alien-looking equations, tedious proofs, and frightening collections of numbers not only possess truth, but also something exceptionally beautiful, something that inspires awe, pleasure and imagination in its unique way.