HOW TO FALL IN LOVE WITH MATH

It’s difficult for me to discuss why I love math. I’m always worried about coming across as pretentious, weird, or high-strung, but I think Andrew Wiles describes how I feel accurately and humbly: “when doing math there’s this great feeling. You start with a problem that just mystifies you. You can’t understand it, it’s so complicated, you just can’t make head nor tail of it. But then, when you finally resolve it, you have this incredible feeling of how beautiful it is, how it all fits together so elegantly.” This statement works in tandem with an anecdote in Edward Frenkel’s Love and Math: The Heart of Hidden Reality, which essentially stated that the way they teach math in school is like teaching an art class how to paint a white fence every year. There’s breathtaking things like “Starry Night” and the Sistine Chapel ceiling, but the class is only exposed to a boring, white fence. I think more people would love math if they reached out and looked at problems beyond their coursework.  There is a great feeling that comes with the singular moment of understanding that follows hours, weeks, or years of grappling with a problem, or a proof. It is wih that feeling that the connection between beauty, human curiosity, and math appears. 

I’ve always loved proofs, and Fermat's Last Theorem, the problem I began my Capstone with, can appropriately be called The Proof. As one might guess from the dramatic name, the theorem went unsolved for quite some time—over three hundred years, in fact. Amazingly, the theorem posed is quite simple: while the Pythagorean Theorem yields real answers, for no power higher than two does the statement remain true. Such a deceptively straight-forward idea required a one hundred and fifty page proof, and was not solved until 1994.

Mr. Ertl introduced me to this problem at the end of Pre-Calculus over a year ago, through the PBS NOVA documentary based on my summer reading book. Now, this was no ordinary experience; all of the juniors had left for interim, and it was only me, Mr. Ertl, and a comprehension packet in the room while the movie played. He had to pause the movie multiple times for me to find the correct answers amidst the haystacks of mathematics, and it was by far the worse movie date of my life. 

I began my capstone with Fermat's Last Theorem because it is one of the most important mathematical discoveries in the past century, and because I am fascinated as to how such a simple-sounding question could connect to something as complex as modular forms. To put it simply, Fermat’s Last Theorem is my “Starry Night.”