Claire Graber, BS, Mathematics Graduate
- Graduated from Wheaton College with a B.S. in Mathematics and a minor in Geology
- REU student researcher at Lamont-Doherty Earth Observatory of Columbia University (summer 2016)
- Just graduated college
My parents are missionaries in the country of Vanuatu, South Pacific. Although I was not directly involved in the two New Testament translations they worked on, I grew up steeped in theological discussions (and sometimes linguistic puzzles that went right over my head). While at Wheaton, I attended and eventually became a member of Bethel Presbyterian Church, which became my church home.
I was never the sort to really settle on one particular realm of interest. In many ways, I’m the sort of person who enjoys the humanities more than the sciences, and would gladly spend most of my time reading fiction and listening to history lectures. This stems largely from the fact that I like the mystique and fluidity of no particular right answer. The irony is not lost on me that I then turned around and declared a major in Mathematics. When I began at Wheaton, I majored in physics by default. It may seem like an odd default choice, but given that my siblings had both been physics majors, it seemed natural at the time. However, like many freshmen, I quickly found out that my long-term plans for the study of solar physics were not to be: after one semester as a physics major, I decided it wasn’t quite what I wanted to study, and became a math major.
Of course, in college, one of the first questions you answer in conversation with someone new is “What’s your major?” For me, what followed was the ever-present question: “Do you want to teach?” Yes and no. I enjoy teaching, but that’s not the reason I wanted a degree in pure mathematics. What drew me in is the elegance, simplicity, and boggling infinitude of mathematics. Most people think of math majors as people who sit down and “do problems” all day. But the truth of a math major is that much of your time is spent in staring down the implications of an idea. In many ways, math is philosophy that is bounded by a very particular set of rules. There are two ways to find creative ideas: 1) Think outside the box. What limits can be pushed so that something new can be created? 2) Build a box and get in it. This is mathematics. By limiting your options, you can get somewhere interesting.
This method of creativity leads to some extraordinary situations. For one thing, it forces everyone to acknowledge the assumptions of every argument. What kind of box have you built? What shape and dimensions did you design your box to be? What materials and methods did you use to build it? That is standard practice in mathematics. But what happens when you reach a disagreement about the assumptions? Then you have a problem! And a fun one, too.
During my final year at Wheaton, I took a class designed and required for seniors in a mathematics major. Many people in the course were double majoring in something else, or were in athletics or student government. Most apparently had the capacity to work around the clock. I felt a little out of my league. Thesewere the brilliant minds. I needn’t have worried, since everyone was encouraged to speak their mind, everyone else wanted to hear, and I was no exception. As it turns out, even the quietest of these brilliant minds can engage in heated discussion on whether or not numbers do, in fact, exist. These discussions quickly became my favorite component of the course. We all chose material to read independently and bring into discussion, but all of us read the same questions and answers on subjects related to mathematics and faith. The overarching question of the discussion throughout the semester was this: “What doesGod have to do with mathematics?”
At many schools, no one would even think to ask this question, but at Wheaton one of the most prevalent conversations is about the integration of faith and learning. In this discussion, I was not expecting more than an anecdotal explanation of how we can glorify God in mathematics by recognizing his infinitude reflected in the infinities we use in mathematics, or maybe a questionable representation of the Trinity using some geometric figure. I was quite surprised then, to find that there are serious theological implications of more than a few questions in mathematical philosophy.
One of these questions was the debate which has long been held among mathematicians and which centers around the question “Do numbers exist of themselves, or do we imagine them for our own purposes?” Among a Christian community, this translates to “Did God create numbers?” The simple answers to this question, “yes” and “no” are not so simple when you press them for details. These two views are called the Platonic and Aristotelian perspectives, named (as you might guess) for Plato and Aristotle.
Before we discuss the theological implications of these views, we must acknowledge that the question itself is a little odd. The Platonists argue that numbers exist as “forms” (don’t ask me; ask a philosophy major). But what does it mean for a number to exist? The numeral ‘3’ doesn’t just float around space somewhere, and even if it did, it wouldn’t be the essence of “Threeness”. It would just be a written representation of the idea. The same goes for an instance of three objects. Supposing we have three of the most perfect spheres, all made of the same material, and of exactly the same weight. This is not three itself, but an instance of it. In that way, even though there is no variation between the three, it is no different than if we gathered three cows of different size and color and said “Look, I found three!” In both cases, it is not the idea itself which we see or imagine, but an example of it. (See, I told you math is just philosophy wrapped up in some logic.)
Here the Aristotelians have an advantage, because they don’t have to try to describe where these numbers exist. The Aristotelian point of view can even explain whatnumbers are, namely, the most logical invention of necessity. The difficulty then, lies in how people of all different cultures somehow managed to imagine and develop ideas that were, for all their different names, exactly the same. Yes, some cultures found the zero and decimal systems to be useful before others did, but everyone at least can agree that the numbers we count with are standard. No one who is trying to buy four cows will buy three and think he’s gotten the proper deal, even if the transaction happened across multiple languages and cultures. Three is three, no matter the instance, which seems to indicate the existence of the idea before it was named.
As you can see, making a convincing and thorough argument is difficult for both groups. Most of the math majors I met at Wheaton did still fall into one camp or the other, with some bias towards the Platonists. This is where the fun began! When you have two groups of Christian nerds whose fundamental assumptions about numbers are practically opposite, you get into some intriguing discussions. The Christian Platonists argued that to say humans invented numbers by necessity was claiming that God did not create numbers, and that this was an affront to His nature as Creator. The Christian Aristotelians countered that being made in God’s image, we are creators, too, though of a different sort. To claim that we only discover the numbers and their characteristics is to discount the grueling process of mathematical development and creative efforts. And so on and so forth.
The point is that regardless of how they viewed the origin of numbers, both camps were arguing for the sake of God’s glory in his creation: the Platonists arguing for God’s having directly created numbers as an idea, and the Aristotelians arguing for God’s having created creative genius in his image-bearers. This is one of the crucial aspects of integrating faith and learning: whatever you argue for, argue for God’s glory.