“The heavens declare the glory of God, and the sky above proclaims his handiwork.” — Psalm 19:1 (LSB)
There is a language hidden in creation, a language not made of vowels and consonants but of symbols, numbers, and patterns. It is the language of mathematics. From the spiraling arms of galaxies to the delicate branching of rivers, from the ratios that govern music to the curves that describe planetary orbits, mathematics whispers of an order beyond chance.
Among its many voices, the quadratic equation is one of the most surprising. At first glance, it looks plain and unremarkable—something students might scribble reluctantly on a high school exam:
Yet within this small formula lies a depth that has guided architects, physicists, economists, and philosophers alike. It is simple, almost childlike in its expression, and yet profound in its implications. And when we pause to reflect on what it reveals, we may find it pointing us not merely toward patterns in the natural world, but toward the very mystery of existence itself.
The Quadratic Window
The quadratic equation always resolves. No matter what values you put into a, b, or c, it produces two solutions, called roots. These roots are given by the famous quadratic formula:
Sometimes the roots are real numbers—values we can place on the number line, measure, and work with in tangible ways. These are the numbers of our daily lives: the height of a bridge, the arc of a ball, the distance of a journey.
Other times, the roots are imaginary numbers—values that involve the square root of a negative number. At first, this seems absurd. How can you take the square root of “minus four”? It doesn’t fit the world of our senses. And yet, imaginary numbers are as real to mathematics as air is to breathing. Modern science would collapse without them. Electrical engineering, quantum mechanics, digital communications, and fluid dynamics all depend on imaginary numbers.
This means every quadratic equation, no matter how ordinary it looks, contains within it the potential for both the visible and the invisible, the real and the unseen. One solution belongs to the world of concrete measurements; the other often belongs to the hidden architecture of reality, where abstract numbers sustain the very structures of existence.
The equation is both simple and profound. It can be taught to teenagers, yet it can never be exhausted in its applications. Its form is compact, but the worlds it opens are infinite.
Simplicity and Complexity
This duality in the quadratic equation mirrors something deep about God.
Christian theology has always held that God is, in one sense, simple—He is not made of parts or composed of elements. He is one, indivisible, eternal being. The Nicene Creed confesses that the Son is “of one substance with the Father.” The point is clear: God’s essence is not fragmented or divisible. He is whole, without body or form as we know form. The early church fathers echoed this conviction. Theophilus of Antioch described God as “formless, because He is incomprehensible.” Origen spoke of Him as “simple, uncompounded, and without form.” Athanasius emphasized again and again that God’s being is indivisible, simple, and infinite.
And yet within this simplicity lies a profound complexity. God is not an abstract monad. He is triune: Father, Son, and Holy Spirit. He is invisible, yet He has made Himself visible in Christ. He is eternal, yet He enters into time. He is incorporeal, yet in the Incarnation He takes on flesh and dwells among us. God is both utterly simple in essence and infinitely complex in His personhood and revelation.
The quadratic equation whispers of the same pattern. Its form is simple, but its depth is profound. It produces solutions that are visible and invisible, real and imaginary, yet both belong to the same ordered system. Just as the quadratic does not collapse under its own simplicity but expands into layers of meaning, so God’s divine simplicity does not reduce Him to less but reveals Him as infinitely more.
The Harmony of Numbers
This intuition is not new. The ancient philosopher Pythagoras and his followers saw numbers as the foundation of reality. For them, mathematics was not merely a tool of measurement but a glimpse into the harmony of the cosmos. They believed the universe itself was structured according to mathematical ratios, and that to study numbers was to draw closer to ultimate truth.
The quadratic equation belongs in this tradition. It shows us that order is embedded in reality, that solutions exist even when they appear hidden, and that the world is intelligible to human minds. Why should the human intellect, a product of flesh and bone, be able to grasp equations that govern stars and electrons alike? Why should abstract symbols on a page correspond to the movements of the cosmos?
The answer, suggested by Pythagoras and confirmed by Christian theology, is that reality itself is ordered because it flows from an ordered source. Mathematics is not something humans invented but something we discovered, because it was already there, inscribed into the fabric of the universe.
Anselm and Necessary Being
In the eleventh century, Anselm of Canterbury wrote that God is “that than which nothing greater can be conceived.” Many treat this as a mere logical puzzle, the so-called ontological argument. But Anselm’s purpose was pastoral and devotional as much as philosophical. He was responding to the ancient cry of the Psalmist: “The fool says in his heart, ‘There is no God.’”
Anselm reasoned that if we can conceive of a maximally great being, such a being must exist—not as a contingent possibility but as a necessary reality. For if God were only possible, then a greater being could be conceived: one that exists necessarily. Therefore, God must exist as the ground of all existence, the necessary being upon which all else depends.
Here the quadratic equation provides an analogy. Just as the quadratic always resolves—always produces solutions, even when they are invisible—so God is necessary and not contingent. If we deny Him, we are left with infinite regress. But infinite regress collapses under its own weight. If the past were eternal and without beginning, then it would have taken an infinite number of days to arrive at today. Yet here we are. The very fact that we exist in the present moment testifies to a necessary foundation.
Order Against Chaos
Atheism often insists that the universe is the product of randomness. But the quadratic equation challenges that view. Randomness does not produce order that is both simple and profound, visible and invisible, real and imaginary yet consistent. Chaos does not yield harmony.
Mathematics, with its precision and elegance, points us to a deeper truth: the universe is intelligible. And intelligibility suggests an intelligent ground. The quadratic equation does not prove God’s existence in the way a geometry theorem proves a triangle’s angles. But it does whisper of order, symmetry, depth, and necessity. It suggests that behind the numbers is a mind, and behind that mind is the very source of reason itself.
The Nicene Mystery
The Nicene Creed captures this beautifully. God is one substance, simple and indivisible. And yet He is Father, Son, and Spirit—infinitely rich in His reality. He is invisible, yet He reveals Himself. He is beyond form, yet He took on form. He is simple in essence, yet complex in His glory.
The quadratic equation, in its own humble way, mirrors this pattern. Simple in appearance, profound in depth. Producing both visible and invisible solutions. Holding together realities that seem opposite yet belong to the same whole. It is a mathematical parable of divine truth: the simple that contains the infinite, the clear that opens into mystery.
More Than Numbers
The quadratic equation will not lead anyone to salvation by itself. But when we pause to reflect, we see in it a parable of reality: simplicity that opens into depth, order that holds together the real and the unseen, necessity that resists chaos. It is a whisper of the One who is maximally great, the necessary being without whom nothing could exist.
Mathematics is not cold abstraction. It is a lens through which we glimpse the harmony of creation. And when we look long enough, even in the humble quadratic, we may find ourselves caught up in awe—an awe that infers not only order in the universe but the presence of the God who is both simple and infinitely rich, both hidden and revealed, both beyond us and with us.
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