"Good at Math": What Counts?

Sunday, March 23, 2008

Recently, I was asked “What does it mean to be ‘good at math’?” I thought it through, and here is an edited response. Even if you don't like mathematics, it is a good exercise to go through for anyone. What does it mean for someone to be good at what you do? There are a few points that I would address in being “good at math”:

  1. The proficiency of the student in the narrowest sense of mathematics,
  2. The student’s reasoning ability in dealing with philosophical arguments, and
  3. The religious motivation behind the student’s study.

At the most superficial (disregard the negative connotation) level, being “good at math” is about knowing the language of mathematics. The student who is good at math will begin to have both a competency with the tools of mathematics and an intuitive understanding (a “gut feeling” if you prefer) of what will work. These appeal to those situations where the student sees a theoretical result developing from the material and where the student models mathematically a physical phenomenon. In other words, the student sees the ramifications of the learned theory with regard to (a) the broader scope of the theory and (b) is able, if it is possible, to handle the theories and applications in the physical sciences. I do believe that the second (b) is of lesser importance relative to the first (a). The student should be able to write clearly, concisely, and logically to express the theory.

Next, we deal with a philosophical understanding of the math. The student who is good at mathematics is able to see into the world of philosophy. The student, able to navigate through arguments, can think critically through the philosopher’s logic and develop an opinion (given an appropriate amount of time). This view comes from an understanding that philosophy and mathematics have been intertwined throughout history. In fact, Plato inscribed over the door of the Academy, “Let no one who is not a geometer enter.”

Finally, while the other two are based in skill and intellectual adeptness, this one is based on motivation. I mentor a mathematics student, and my focus in our meeting time is not ultimately on the mathematics; though, we both appreciate it. Instead, our shared passion for mathematics and the beauty of reason provide a springboard to worship God as revealed in the Bible. The following is a sampling of passages that deal with this particular topic:

a.) “Whatever you do, work heartily, as for the Lord and not for men...” (Colossians 3:23).

b.) “So, whether you eat or drink, or whatever you do, do all to the glory of God” (1 Corinthians 10:31).

c.) “The heavens declare the glory of God, and the sky above proclaims his handiwork. Day to day pours out speech, and night to night reveals knowledge. There is no speech, nor are there words, whose voice is not heard. Their voice goes out through all the earth and their words to the end of the world” (Psalm 19:1-4a).

d.) “In the beginning was the Word, and the Word was with God, and the Word was God. He was in the beginning with God. All things were made through him, and without him was not anything made that was made” (John 1:1-3).

e.) “He [Jesus] is the radiance of the glory of God and the exact imprint of his nature, he upholds the universe by the word of his power” (Hebrews 1:3a, emphasis mine).

This is the ultimate reason why I study mathematics. This is the characteristic I want to see in myself when I desire to be “good at math”. If the student is to be good at mathematics, the student must understand from where math comes. Math is part of the way that God has revealed himself to creation, and students miss something crucial when they (a) ignore it and (b) do not use it to contemplate joyfully the manifold beauty of God as revealed in the complexity of his handiwork through the providence of Christ’s word of power. Because biblical Christianity teaches that there are no rogue molecules in all of existence, it is rebellion against the Creator not to consider the beauty of Christ when studying the laws, i.e. the mathematical principles, that govern creation which find their root in the Creator. Therefore, I do not encourage people to be good at math for math’s sake; that would be meaningless, absurd even. In the truest definition of good, it would not be good to deny the fundamental truth that undergirds all the truths you are analyzing. I would encourage them to see why there is meaning in studying math. There are two immediate quotes that come to my mind:

a.) “For he loves Thee too little who loves anything together with Thee, which he loves not for Thy sake.” – Augustine in his Confessions, writing to God

b.) “If we consider the unblushing promises of reward and the staggering nature of the rewards promised in the Gospels, it would seem that our Lord finds our desires not too strong but too weak. We are halfhearted creatures fooling about with drink and sex and ambition, when infinite joy is offered us, like an ignorant child who wants to go on making mud pies in a slum because he cannot imagine what is meant by the offer of a holiday at the sea. We are far too easily pleased.” – CS Lewis in The Weight of Glory


Chelsea said...

To be good at what I aspire to do seems very complicated to me right now. One must be a language expert. One must be dedicated, but not emotionally attached. One must be thorough but concise. It's overwhelming as I am still learning.