MAth + loGIC = MAGIC: Let’s talk about logic, math, and college

On one weekend afternoon in sixth grade, my father presented me with a classic thinking-out-of-the-box problem: given 9 dots in a 3×3 grid, draw four lines through all 9 points (the lines can cross each other), without lifting up the pencil. He promised me the solution would be very satisfactory, that it was an embodiment of the saying “thinking outside the box”. With the problem presented in front of me, the pencil on my hand, and an eraser, I tried countless different possibilities, but all of them involved drawing at least five lines to connect all the dots. After 20 minutes of defeat, I asked my father for the hint. He simply said: “The lines do not have to be contained within the grid.” His hint was so simple it seemed magical; after the hint, I got the solution nearly instantly.

These mind-wrenching problems initiated my interest in logic, the world in which every problem has in it a (or even multiple) beautiful yet elusive solution. The sequence of gathering information about a problem, putting forward assumptions, and making logical inductions to reach a result, seems at first glance straightforward. Yet the brainpower required to mentally navigate through this process is immense. Though tiring and sometimes frustrating, the process of getting to the final solution of a hard logical problem is highly mentally rewarding.

Working my way through secondary and high school, I carried this mindset over to mathematics, and it worked just as well. The clever use of math rules, rigorous arguments to justify such use, and sometimes a bit of trick and creativeness, validate math as a subject of logic. However, math is much more than crude formulas on cheat sheets for exams. Instead, one aspect of it that makes it even more practical and beautiful than pure logic is that many mathematical concepts arise from the need to explain natural phenomena.

There is a long history to the formulation of today’s calculus, but many have credited Sir Isaac Newton (known to college students with his Three Laws of Motion) and mathematician Gottfried Leibniz for establishing the foundations of modern-day calculus. That’s why Physics is a huge bulk of calculus

My most profound realization of the wide applicability of math in real life occurred in tenth grade when I first encountered calculus on a Physics problem. I was surprised how calculus can be used to such a broad extent, from the description of the motion of projectiles to celestial bodies, from calculating the area and volume of objects to the complex motion of fluid flow… My second large realization was when I read about Statistics and Probability in my senior year of high school, as I understood its importance in clinical trials, biomedical research, data science and machine learning, and so many more fields. I was so enthralled by the power of math that I believed it to be an intrinsic language of Nature, not an invention by humans.

As I continued learning math in college, I shifted my attention to exploring how math is used to create the technological world we are living in today. Literally, every modern-day device requires precise calculations to operate, which all arise from solving mathematical equations. This desire led me to pursue Engineering because I hope to bridge my mathematics and logic knowledge with practical engineering problems to come up with novel device designs or methods.

The introduction slide to my presentation in the English Speaking Club in my high school. The main content of this presentation was that I attempted to discuss views from different scholars about whether math was an invention by humans, or a discovery of Nature’s language

Right now, in college, I have an opportunity to learn about many advanced mathematics concepts through my courses at UC. Even though I struggled at times to grasp and memorize more advanced math techniques and meanings, I usually reminded myself, that math is designed by mathematicians and engineers to idealize much more complicated practical problems. College math is a preparation for me to deal with the challenging engineering problems I will face later on. This shift of perspective allowed me to study college math better and with a growth mindset.

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