“WHY DO we have to learn all these complex formulas? Are we ever going to use them?” Under a curriculum in which math classes are mandatory, students who plan to pursue a career completely unrelated to mathematics often express such complains. True, people could manage to live their life knowing no more math than what is needed to let them know how many bills and coins to pull out of their pocket at the counter. Yet, this does not mean that math has little to do with our lives. Mathematical concepts and formulas exist not only in the classroom but also in the real world. The Yonsei Annals hopes to draw Yonseians’ attention to math with three books that show the often over-looked connection between the mathematical world and the world we live in.

Is God a Mathematician?, Mario Livio

   In the book Is God a Mathematician?, the author Mario Livio takes note of many instances in which mathematical formulas describe the world around us more precisely than anything else. Providing the evidence that mathematics can often explain physical phenomena, Livio guides the readers into a mystery: whether mathematics is a human invention or the discovery of an already existing order in the universe.
   Some mathematicians have developed the argument that the universe is formed according to mathematical patterns and that humans have only to discover such patterns. Archimedes of Greece described forces in the real world by using mathematics. Galileo Galilei saw math as a tool with which humans could look into the secrets of nature. Descartes even thought that all human knowledge follows the logic of math.
   Yet, the author provides some counter-examples to the belief that math is an absolute order that pre-exists humanity. A primary one is the birth of non-Euclidean geometry, which challenged the Euclidean geometry that had been considered as the absolute system of physical space for a long time. Non-Euclidean geometry has no physical representation in a scale that humans can perceive. Yet mathematicians proved in the 19th century that it is just as valid as Euclidean geometry. The fact that a mathematical system does not have to coincide with human perceptions of the world suggests that math could be an invention as well.
   The author does not take either side in answer to the question “Is math an invention or discovery?” Instead, he explains that, through the process of evolution, humans’ logic had to coincide with the world around them, and mathematics, developed from such logic, inevitably reflects how physical space is shaped and operates. Rather than giving a definite answer to the initial question, this book gives the opportunity for the readers to contemplate the nature of the relationship between mathematics and the physical world.
*Available in Korean at the Central Library

Broken Symmetry, Jack Ridl

   Broken Symmetry is a collection of poems written by Jack Ridl. The poems seem just to deal with common activities, such as walking a dog and raking leaves, but they are, quite unexpectedly, sorted through a mathematical context. The poet approaches every little thing with great specificity, allowing the readers to see the things around them in a new light. For example, in “Broken Symmetry,” the opening poem of the collection, the common act of looking at oneself in the mirror has inspired the poet to contemplate the symmetry in our universe and the invisible inner structure of life.
   The author groups his poems into three chapters: Fractals, Quantum Theories, and Differential Equations. At first glance, these mathematical terms seem totally unrelated to the poems, but each of them metaphorically represents the common theme in the chapter. For example, the poem “Fractal” depicts how the poet observes his surroundings and recalls moments in other times and places. Every small thing recalls different memories, which is similar to the structure of a mathematical fractal, a geometric shape made up of parts that resemble the whole, yet are of smaller and smaller sizes. The title “Fractal” seems to represent how the poet’s life is built upon little moments, just as a fractal is constructed of small pieces. Using abstract mathematical concepts in categorizing poems about daily life, the poet suggests a commonality between mathematics and our lives. As such, the author sees that mathematics can be used in delivering our thoughts, just like human language.
*Unavailable at the Central Library

...Go deeper. All the cells split
into identical ice dancers, all
the electrons spin the same bacchanal.
Only the broken reveals, gives
the universe its chance at being
interesting ...
-From the poem "Broken Symmetry"-

Flatland: A Romance of Many Dimensions, Edwin Abbott

    Flatland is a satirical work of fiction describing a world of shapes, written in 1884 by the English educator Edwin Abott. The main character is Square, living in Flatland, a two-dimensional world. While providing knowledge about concepts of dimensions, Flatland is also a stinging satire on English society at that time. For instance, in the chapter “Concerning the Women,” Square describes women as just straight lines, like a needle, and as therefore invisible from certain angles. This is a satire on how women did not have a voice in English society. In the second half of the book, Square describes other worlds: Lineland and Spaceland. Lineland is a one-dimensional world. Square attempts to explain the nature of Flatland to the inhabitants of Lineland, but they are unable to grasp it. Similarly, Square has a hard time understanding the mysteries of Spaceland, a three-dimensional world. In order to help Square’s understanding, Sphere finally takes him to Spaceland, where Square becomes shocked, yet enlightened upon experiencing a higher dimension. He realizes the limits of his previous knowledge and desires to learn more about higher dimensions. Then he tries to spread his newly discovered knowledge to the rest of Flatland, but this attempt only comes under censure and ridicule from the Flatlanders.
   The mathematical concept of a “dimension” is parallel to the conventional way of thinking by which we confine ourselves. Square gets thrown into confusion upon his encounter with a whole new world, which is similar to how humans experience a shock when their fixed ideas are challenged. He also faces denunciation from his own society, representing how innovators throughout human history have so often been considered as mad by their ignorant and closed-minded contemporaries. However, the novel implies that it is through such experiences that humans become able to overcome their limits and develop a wider and more sophisticated view of the world.
*Available in Korean at the Central Library
*Available in English at the Dept. of Mathematics Library

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   Now, in college, students not in math or science related majors do not have to take mathematics courses. As a result, students are bound to become more and more distant from math. Still, do not forget that even though we are often unaware of it, mathematics always has its place in the world we live in. It is fundamental to the understanding of the universe, and can provide us with a different way of thinking and of expressing our thoughts. Starting with the three books introduced in the article, the Annals hopes that Yonseians will find more books that can promote an interest in finding unique approaches to mathematics and discovering its close relationship to the real world.