by Keaton Stubis

If you asked me what the one thing is that I truly love to do, I would answer without any hesitation: mathematics.  In general, however, I am not such a decisive person. When faced with a multitude of choices at a restaurant or when asked for a few words to describe myself, I am at a total loss. To be honest, I consider myself very lucky to know something so fundamental about myself. Still, there remains the question of why mathematics is what I enjoy so much, as well as why it is the answer to one of the few personal questions I know with certainty.

It all goes back to my first year of middle school. Before then, I had always been a very logical person, but nothing seemed to be just right for me. Science was interesting, but it just wasn’t what I was looking for, and mathematics was nothing more than an endless supply of seemingly arbitrary multiplication problems. I did recognize that there were many possible interests around me, all tugging at other people with their own gravitational forces, but I felt immune to it all.

Then, during the second week or so of middle school, someone came up and asked me if I had taken “the math test”. I was startled and somewhat worried that I had missed a class, but they reassured me that it was only an optional test. It spanned two days, and you had to solve a bunch of questions during allotted times on those days. Unfortunately, I had missed half of the test time already, so I told them no and went home. I wanted to take it, but it just seemed too late.

The next day, however, I found myself in the cafeteria joining everyone else, in some crazy attempt to finish two days’ worth of problems in one session. After some encouragement from my mother the night before and a short talk with the proctors, I had been able to obtain a question packet. I had no idea what the outcome would be, but I figured that giving it a try couldn’t do any harm. When it was over, I was pretty surprised to find I had finished everything; but I was even more surprised later when I learned that I had passed, and could join an advanced math class that didn’t simply consist of doing arithmetic problems over and over and over.

On the first day of that class, I discovered that mathematics didn’t simply involve mindlessly following procedures. You sometimes have to think about things and use what you know in less direct and obvious ways. For instance, suppose you have a pond with algae growing in it. The amount of algae doubles each day, and the pond is full after 60 days. How many days did it take for the pond to be a quarter full? I, along with many other people, answered 15, because 15 is a quarter of 60. However, when the correct answer of 58 was explained, I felt quite silly. You can’t just take the words you have been given and try and combine them to get an answer. It all revolves around a much deeper ability to understand and analyze situations. I had been introduced to a whole new style of thinking, and I was amazed by it. The next day, I learned my first “theorem”, the four fours theorem. It simply states that every number from 1 to 100 can be expressed using four fours and some tricky mathematical operations. For example, one can obtain the number 2 as follows: 4/4 + 4/4. I was astounded that someone could prove such a thing and didn’t realize at the time that the proof was to simply find an expression for each number. However, even if I had known that, I don’t believe it would have mattered. The important part to me was learning that deep patterns could exist in the numbers, which allow you to make such general yet completely unobvious claims. It was soon after that that I decided mathematics was my true interest.

After I chose mathematics, the first thing I had to do was develop a whole new type of intuition. Real world intuition can tell you, for example, not to touch a glowing hot object, but it can’t tell you whether a number is prime. I didn’t mind having to acquire this new type of intuition because, unlike real world intuition, mathematical intuition can also help you think logically in many real-life situations.

Since that experience in middle school, I have continued to do mathematics. What especially appeals to me is that mathematics can be done anywhere and it’s not difficult to come up with an interesting idea (although it isn’t always easy, without paper, to see where that idea may lead!). At one point, I had a notebook that I would fill with all of my ideas. I would just be sitting down, when suddenly an idea might pop into my head, and I would quickly get my book and write it down before I forgot it. The end result of this work was a whole lot of interesting ideas. Some became math problems, and others were turned into my own little theorems. I would often find out that “my” theorems had already been discovered, and that did dampen my excitement. On the other hand, I realized that it meant I was on the right track.

Still, I was never doing a lot of actual solving, and I found this out when I joined my high school math team. Suddenly, tricky math problems became much more common, and everything was clearly a step up from where I was before. It was quite an experience to see many other people who also liked math, taking everything this step further. I just had to cling to my love of math and the intuition I had developed over the years and dive in. At first, I couldn’t do anything, but I eventually realized that it wasn’t because I was incompetent, but because I was using the wrong mindset for those problems. I think of that situation as similar to a tree and a point in space to the side of the tree. The tree’s difficulty in reaching that spot isn’t because the tree is too short, but because the tree may not have any branches in that particular area.

Like that imaginary tree, I was missing a lot of branches. Luckily, I wasn’t daunted by my limitations.  I enjoyed math enough that I took it all as an opportunity, and I eventually developed those branches. And I kept trying to grow more, even if I didn’t need them. There is so much out there, and I felt that anything I learned could only lead to more possibilities. I wasn’t quite sure what I was reaching for, but my eyes had been opened.

By my second year on the math team, I had gotten significantly better at solving problems, and by my third year, I could even write problems that could stump my teammates. It was all a lot of fun.

Now that I’m at MIT, I’m not sure what to expect, except that I know I’ll need to take a step up again. What I also know is that, although my view of math has changed over the past several years, my reason for liking math has not: It helps us find hidden order in this chaotic world.

Keaton Stubis is a member of the class of 2015 and plans to double major in math and physics. Originally from Great Neck, NY, he has recently moved to Bethesda, Maryland.  At MIT, he resides at Next House. Although not entirely sure what his future holds, he continues to follow his mathematical ideas and will often sit down at a whiteboard to work them out. He also enjoys playing his clarinet as well as games like ping pong, tennis, and badminton.