Year after year, ambitous college-bound high-school seniors tackle the infamous University of Chicago application essay questions. Here’s Ben Cho‘s answer to U Chicago’s question…
What is so odd about odd numbers?
Odd can mean strange or indivisible by two.
Intuitively, I always thought odd numbers are odd. Imagine you are sitting around the campfire enjoying s’mores and find out there is an odd number of crackers! You could throw the odd cracker away, but the oddness remains in the emptiness of your mouth. You could split the odd cracker into two, but the oddness still remains in the small, uneven size of the last s’more.
However, wondering why the word odd has two seemingly unrelated definitions, I consulted with the etymology dictionary. According to the dictionary, “odd” came from the Indo-European root “Uzdho”, meaning pointing upwards. Later, the Old Norse modified this root into a new word “oddi”, which was initially used to refer to a triangle. Like a point of land or angle, oddi was recognized to have two paired angles and a third anglethat stood alone. Overtime, the Old Norse used “oddi” to refer to something unpaired, as in “odda martha”, the one who gives a casting vote. The Middle English adopted oddi’s definition of “something unpaired” as “odd”. In 1580s English, the notion of “the odd man out” gave rise to the modern meaning “strange”.
As a math enthusiast, I contemplated on whether odd numbers are actually odd.
How many times even numbers are added together does not affect the parity of the outcome. Even numbers are consistently themselves no matter how many times they meet other even numbers. However, how many times odd numbers are added together does affect the parity of the outcome. Odd numbers added an odd number of times equals an odd number. Odd numbers added an even number of times equals an even number. Odd numbers are capricious; the parity changes every time they meet another odd number.
The sum of consecutive odd numbers starting from one equals a perfect square. The phrase “square pegs in a round hole” seems to coincide with, even effectively illustrate, this property. Like the square pegs, the community of all odd numbers is so perfectly square that it hardly fits anywhere else.
Metaphysically, I concluded. As can be seen in both nature and philosophy, the world is full of symmetry: the exterior of many organisms, the shape of earth, and the concept of good and bad. This symmetry adds to the oddness of odd numbers, which cannot be evenly divided into two groups. In the community of odd numbers, there are always winners and losers: no ties, no peace. Odd numbers are very black and white. One way to bring harmony is to place some members of the community on the symmetry line or take them out of the community. Doing so may not bring true harmony, as it is to make an odd group of rulers or misfits. Another is to give up being an odd community and combine with another odd community to become even. In other words, there is no way for an odd community to maintain peace and identity simultaneously. If odd numbers are not odd, then what else can they be?
–Ben Cho