Now, I know I’m a dork, but I’ve seldom been made more painfully aware of my own dorkiness than when I asked my congregation, in the introduction to a sermon, who else found the discovery of solutions to mathematical mysteries to be exciting. I know I should’ve known better. My wife knows better. My small children know better. They all know I’m a dork. And I should too.
But still there’s a part of me that, deep down, truly believes that other people will also get excited to see a mathematical mystery solved. I actually think that other people find elegant proofs to fundamental questions to be thrilling. And I actually am convinced that if a person doesn’t find mathematics beautiful that there’s something wrong with them.
There I said it.
Now, allow me to defend it.
I am no mathematician. But I have studied some advanced calculus and taken my fair share of physics and chemistry courses. I know enough to know I don’t know much, but can appreciate a lot—which is what I’d consider an educated layman. When I have some extra free-time I like to watch informative videos about advanced and theoretical mathematics (dumbed down for popular-level enjoyment). I’m a dork…let us not forget this. I’m not staking my claim to educated-amateur-laity-status to boast—I’m not proud—but simply to say that I actually know something of math and enjoy it.
But, what even is math? I know that that question may sound puerile or abstract—or abstruse—depending on whether or not you like question like “what is math?” But it’s a worthwhile question that will help me to advance my thesis that people should see the beauty in mathematics.
For my money math is nothing more nor less than the description of quantity. Numbers are merely symbolic representations of quantity. There is such a thing as threeness and seveness and fourness. One needn’t fall into some form of mathematical Platonism to avoid the dead-end of Nominalism. No, there is no “form of four” somewhere in the ether, but neither is “fourness” something that is a purely human construct. I grant that there may be some debate here made in good faith by the Nominalists (and the Platonists). But the reality is that while some quantities may seem arbitrary, like looking at 3 trees in a forest and claiming that threeness is therefore an emergent property, that doesn’t mean that ALL quantities are arbitrary and none are self-evident or emergent.
And as a Christian this is a necessary conclusion. Oneness and Threeness are not human constructs, nor are they “economical” in the sense that they only exist because of God’s work in creation. God has always been three in one, therefore quantity has always existed as an ontic category. Or to put it in plain English, because God it triune and was so before He created, no Christian can claim that three or one—or the concept of quantity, in general—is merely an invention. Rather quantity exists as an actual thing…with thingyness.
So, if quantity, and discrete quantity (as in clear-cut quantities possessing clear-cut and self-evident “value”) such as in integrals, has thingyness, then when we use numbers we aren’t JUST playing a game that we’ve made up in our heads. Numbers correspond to real things and real quantities of real things and real concepts of quantity.
And of course, this is true in non-numerical math, too. Geometry was preferred by the ancients because they thought numbers were imperfect, and that the shapes gave more universal proofs. Geometry was considered a fundamental part of theology. And while we may scoff at this, we shouldn’t. Rather, Christians should agree that theology is informed by, enriched by, and emboldened by mathematics.
How?! You ask me. How? I shall endeavor to demonstrate.
So, I just said that when we do math we aren’t JUST playing a game. The “JUST” is important, because we are playing a game. But it’s not a game of pure fantasy. It’s a game because math doesn’t really DO anything. Yes, numbers have a conceptual thingyness—similar to words (more on that later)—but mathematics doesn’t ever give us “new information.” Any mathematical equation that’s solved adds no new data. It may give us a new way of considering a specific quantity, but it doesn’t actually give us a new quantity. The thingyness on the left side of the equals-sign is the same as the thingyness on the right. All math does is say that A is A, but with quantities.
Mathematics is a demonstration of logic. An equation simply says that A is A and that A is not non-A. Indeed one of the great inconsistencies in philosophical history was Kant claiming that mathematics provided predicate statements (that math gives new information).
Now, you might think that I’m crazy. No! you protest, “I do math and I get an answer I didn’t know before.” Sure. You might not have KNOWN that the square-root of 64 was 8, but knowing that doesn’t change anything or give us “new information” because root-64 and 8 are the same thing, they represent the same quantity. They have the same thingyness, but a different description of that thingyness.
Math is a game—it’s a logic puzzle, like Sudoku, or riddles.
But it’s also a very useful game. Because when we solve equations we are able to represent quantity in ways that are useful to us. We are able to observe quantities and changes in quantities and develop theories and formulae that help us describe and predict these changes. Mathematics is an absolutely indispensable tool in human existence—and yet it’s a game that gives us no new information. It is, in a very real sense, just something we’ve invented out of our own heads. Math is elegant and beautiful because it can’t not be. It must be elegant because it always works because it always must. The cleanness and purity of the logic of math is nothing more than the necessary clarity that must come when we say that a thing is what it is! A is A is always elegant because it cannot not be. It must be clean and precise because it cannot be else!
Mathematics is a logical game that humans have invented. Its elegance, precision, clarity, and beauty are all necessary and inescapable. Math is just a man-made game. And yet for all that it’s a profoundly, indispensably, indescribably necessary tool. We could not live in the world we live in without math. And more than that the fact that humans could invent a game that has the power to help us transform the world is a demonstration that we are made in the image of God.
Math only exists in the imagination of Persons. We play a little game with quantity, never changing anything but the way we conceptualize the quantity and yet we can use this fantasy to invent geometry which helps us to build aqueducts, and arches, and cathedrals, and skyscrapers, and computers, and to harness the power of molecules and atoms and particles and save lives and to rule the earth and subdue it. Using the power of imagination we are able to transform the physical world.
This is a testament and testimony to our creation in the image of God. We can create using our imaginary conceptualization of quantity—God creates by speaking.
When we study math we are studying logic at its purest, or nearly purest, form. When we study math we see the breathtaking precision of human thought and its capacity to transform imagination and fantasy into reality. When we study math we encounter mysteries of reality—the reality God created. I pity the person who cannot grow excited to see the Mandelbrot Set or the Prime Number Spiral. I pity the person who cannot discipline their mind to see the beauty of mathematical precision or who cannot find delight in using pure logic to solve a geometric problem. Math helps us to be like God because it allows us to use the immaterial imagination to change the material world.
This is why mathematical education is so theologically important. And this is why homeschool and especially Classical Christian education models must do more than simply put a cross on the cover of the Saxon book or add verses from the Gospels to Euclid’s Geometry. Math for math’s own sake isn’t really math for math’s own sake, but it’s a way to enter into the mind of the Lord—if only in the most frail and paltry way. Math for math’s own sake is about the love of logic and precision and truth. It’s a demonstration of the imago Dei. That’s why we need mathematical education. And not just the kiddies either!