PHILOSOPHY OF MATHEMATICS
Mathematics is beautiful. Yet those of us privileged with the capacity to comprehend math often find ourselves frustrated by the fear and contempt expressed towards it by others. It is regarded by many as little more than a baffling collection of arithmetic operations, useful only as a classroom survival skill. But the sentiment that math is so narrow and lacks application beyond the confines of an academic setting could not be further from the truth.
Imagine an observer in an art gallery, admiring a painted portrait. One’s initial reaction might be to dismiss the situation as something far-removed from the realm of mathematics; after all, math is associated with the more logical left side of the brain, while art is a function of the spontaneous and creative right hemisphere. But closer attention reveals that the portrait adheres to several specific properties rooted in mathematics. The size of the subject’s body parts, for instance, must be in proportion to one another if the portrait is to accurately resemble a human being. The positioning of this person likely obeys what is known as the “rule of thirds,” which advocates that prominent features of a painting or photograph should fall along specific imaginary lines. These lines divide the work into three equal sectors on both the horizontal and vertical axes — if illustrated, they would intersect to form an obvious Cartesian plane.
Next, consider the paint used to create the portrait. Each hue was painstakingly mixed by the artist, until the different primary colors reached an ideal ratio to represent part of the person or object they were depicting. Understanding the chemistry involved would be impossible without the aid of mathematics, but there is more still we can learn from this scenario. Somewhere in the room, there is a source of light — likely set to a specific, measurable brightness (determined by the light wave’s amplitude) by the curator and positioned at a carefully-calculated angle relative to the pieces on display. It is only due to this precision that the observer is fully able to appreciate the artwork. As light hits the portrait, each paint molecule absorbs some of it and reflects the rest; every beam of reflected light has its own calculable wavelength, and its path and shape can only be understood using equations. The sine and cosine functions used here (along with other more complex formulas involving infinite series summations) describe not only the nature of the waves, but the oscillations of the matter comprising our Universe.
Finally, the light reflected by the painting reaches the human eye, where the individual wavelengths are perceived by cones that are carefully calibrated to specific segments of the visible spectrum. The cones convert this information into nerve impulses that take the form of waves not dissimilar to those by which the image was transmitted. In a fraction of a second, the brain receives this information, and the viewer is able to enjoy the masterpiece before them — although they may not understand the laws of craftsmanship and nature which made it possible.
Looking at a painting — something that seems like a simple act — is dependent on principles of art, chemistry, physics, biology, and even psychology. But the common factor shared amongst all of these studies is their dependence on mathematics; without it, we could not fathom any of them. Mathematics defines our understanding of the Universe, underlies the code in which it is written — it is the very backbone of our existence. I therefore hope to dedicate my professional life to the exploration of its numerous fields. Uncovering the mysteries of pure mathematics and finding their links to the physical world is surely the fastest way to advance the body of human knowledge!
Imagine an observer in an art gallery, admiring a painted portrait. One’s initial reaction might be to dismiss the situation as something far-removed from the realm of mathematics; after all, math is associated with the more logical left side of the brain, while art is a function of the spontaneous and creative right hemisphere. But closer attention reveals that the portrait adheres to several specific properties rooted in mathematics. The size of the subject’s body parts, for instance, must be in proportion to one another if the portrait is to accurately resemble a human being. The positioning of this person likely obeys what is known as the “rule of thirds,” which advocates that prominent features of a painting or photograph should fall along specific imaginary lines. These lines divide the work into three equal sectors on both the horizontal and vertical axes — if illustrated, they would intersect to form an obvious Cartesian plane.
Next, consider the paint used to create the portrait. Each hue was painstakingly mixed by the artist, until the different primary colors reached an ideal ratio to represent part of the person or object they were depicting. Understanding the chemistry involved would be impossible without the aid of mathematics, but there is more still we can learn from this scenario. Somewhere in the room, there is a source of light — likely set to a specific, measurable brightness (determined by the light wave’s amplitude) by the curator and positioned at a carefully-calculated angle relative to the pieces on display. It is only due to this precision that the observer is fully able to appreciate the artwork. As light hits the portrait, each paint molecule absorbs some of it and reflects the rest; every beam of reflected light has its own calculable wavelength, and its path and shape can only be understood using equations. The sine and cosine functions used here (along with other more complex formulas involving infinite series summations) describe not only the nature of the waves, but the oscillations of the matter comprising our Universe.
Finally, the light reflected by the painting reaches the human eye, where the individual wavelengths are perceived by cones that are carefully calibrated to specific segments of the visible spectrum. The cones convert this information into nerve impulses that take the form of waves not dissimilar to those by which the image was transmitted. In a fraction of a second, the brain receives this information, and the viewer is able to enjoy the masterpiece before them — although they may not understand the laws of craftsmanship and nature which made it possible.
Looking at a painting — something that seems like a simple act — is dependent on principles of art, chemistry, physics, biology, and even psychology. But the common factor shared amongst all of these studies is their dependence on mathematics; without it, we could not fathom any of them. Mathematics defines our understanding of the Universe, underlies the code in which it is written — it is the very backbone of our existence. I therefore hope to dedicate my professional life to the exploration of its numerous fields. Uncovering the mysteries of pure mathematics and finding their links to the physical world is surely the fastest way to advance the body of human knowledge!