Apologetics · Creation & Science — the tool science cannot work without, and cannot account for
In 1915 Albert Einstein finished the field equations of general relativity using a branch of geometry Bernhard Riemann had developed sixty years earlier for no reason at all. Riemann was not trying to describe gravity. He was doing pure mathematics, following an idea because it was beautiful. Six decades later the universe turned out to be built that way.
That is not a one-off. It happens constantly. Group theory, invented to study the solvability of equations, later turned out to describe the family structure of subatomic particles. Complex numbers, invented as a bookkeeping trick for roots that “do not exist,” sit at the heart of quantum mechanics. Non-Euclidean geometry, conic sections, knot theory — abstractions chased for their own sake, later found waiting inside physical reality.
The physicist Eugene Wigner wrote a famous paper about this in 1960 and called it a miracle. He did not mean it religiously. He meant it as a confession: we have no idea why this works, and we did nothing to deserve it.
Here is the question I want to put on the table, and I want to put it fairly. If everything that exists is matter and energy in motion, what is a number?
Three Things That Do Not Fit in a Material World
Consider the number seven. Not the numeral — the ink shape is obviously physical, and so is the neural firing in your head when you think about it. I mean the number itself, the thing that both the ink and the neuron are about.
It has three properties that materialism has no shelf for.
- It is not located anywhere. You cannot point at it. It has no mass, no charge, no position, no duration. There is no experiment that finds it.
- It does not change. Seven was prime before there were minds to notice, and it will be prime after the last star goes out. Physical things decay. This does not.
- Its truths are necessary, not contingent. Every physical law could conceivably have been otherwise. But there is no possible universe where seven is even. That is a different kind of truth than “water boils at 100 degrees.”
So a worldview that says only matter exists is in an awkward spot. Its most reliable instrument — the one it uses to describe matter with astonishing precision — is not made of matter.
The Answers a Materialist Can Actually Give
This is where a cheap apologetic would declare victory. Let us not. There are serious answers here, and they deserve to be stated at full strength before they are examined.
First: mathematics is a human invention — a language, nothing more. We made up the rules the way we made up chess. There are no numbers “out there”; there are only conventions and the marks we use for them.
That is coherent as far as it goes, but it collides with how mathematics behaves. In chess, we can change the rules. In mathematics we cannot. Mathematicians consistently describe themselves as discovering results, and often ones they did not want. Nobody voted for the irrationality of the square root of two — the Pythagoreans reportedly found it appalling. A game we invented should not be able to tell us things we hate and cannot overrule.
Second: fictionalism. The most rigorous version, argued by Hartry Field, says mathematical statements are strictly false but useful — numbers are like fictional characters, and science could in principle be reformulated without them.
Give that its due; it is a genuine philosophical project, not a dodge. But the reformulation has never been carried out for real physics, and the cost is severe: it asks us to say that our single most reliable body of knowledge consists of falsehoods that keep landing on the truth. That is not simpler. That is stranger.
Third: evolution explains it. Brains that counted predators survived. Our mathematical intuitions are just fitness-tracking equipment.
This one is partly right and is the strongest of the three — but it explains the wrong thing. Natural selection can plausibly account for small-number arithmetic and rough geometry, because those had survival value on a savanna. It has no purchase on why a hominid brain shaped by predator avoidance should be able to derive tensor calculus, prove theorems about infinite sets, or produce — centuries in advance and with no feedback from reality — the exact structures the interior of an atom would turn out to require. No selection pressure was ever applied there.
Fourth: selection bias. Of course the math that fits gets used; the rest is forgotten, so the “miracle” is an artifact of counting the hits.
Fair point, and it does trim the wonder. But it does not touch the cases that matter, where the mathematics was completed long before any application existed and then turned out to fit with unreasonable exactness. You cannot select in advance for something nobody knew would be needed.
Fifth — and most honest: platonism without God. Numbers exist as abstract objects; they simply do, as a brute fact.
I respect this position more than the others, because it takes mathematics at face value. But notice what it has done. It has abandoned materialism outright. It now affirms a realm of non-physical, immaterial, eternal, necessarily existing realities — and then has no account of why that realm and the physical realm should have anything to do with each other. Two unrelated kingdoms that mysteriously match.
What Theism Says, and Why It Is Not a Patch
The Christian answer is not “God did it, stop asking.” It is a specific claim about the kind of thing a rational order is: mathematical truths are not free-floating abstractions but features of the mind of God, and the universe is the work of that same mind.
If that is true, three things follow immediately, and they are exactly the three things we observe. Mathematical truths are necessary and unchanging, because God is. The physical world conforms to them, because the same Mind authored both. And human beings can find them, because we are made in the image of that Mind.
“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 came into being through Him, and apart from Him nothing came into being that has come into being.”
John 1:1–3
The word John chose is Logos — a word his Greek readers already used for the rational principle holding the cosmos together. John’s claim is that the rational structure of reality is not an accident or an abstraction. It is a Person, and everything that exists came into being through Him.
Which is why order shows up where nothing had to be orderly at all.
“Lift up your eyes on high and see who has created these stars, the One who leads forth their host by number, He calls them all by name; because of the greatness of His might and the strength of His power, not one of them is missing.”
Isaiah 40:26
By number. Written twenty-seven centuries before anyone catalogued a star.
Scripture goes further and says the regularity itself is covenanted, not incidental — God speaks of the fixed patterns of heaven and earth as something He established (Jeremiah 33:25). And Proverbs pictures wisdom present at the founding of the world, when He inscribed a circle on the face of the deep and set a boundary for the sea (Proverbs 8:27–29). A measured world, measured on purpose.
Where the Believing Scientists Themselves Land
It is worth saying that this argument runs cleanly across an in-house disagreement. A young-earth creationist and an old-earth creationist will argue hard about Genesis 1 and the age of the world — and both hold, without any tension at all, that mathematical order reflects the character of the Creator. Nothing in this line of reasoning depends on settling that debate. It is a point about the rational structure of reality, and the whole believing camp holds it together.
It is also, historically, why the scientific enterprise got started where it did. Kepler said he was thinking God’s thoughts after Him. Newton wrote more on Scripture than on physics. These men expected the universe to be mathematically intelligible because they believed it had an Author — and that expectation, more than any single experiment, is what launched modern science.
The Question Underneath the Question
None of this will convert anyone by itself. Arguments clear ground; they do not raise the dead. But an argument that clears ground is worth making, and this one clears a lot.
Because the person who says “I only believe what science can show me” is standing on a floor science did not lay. Every equation he trusts is written in a language made of nothing, obeying rules nobody set, describing a world that had no obligation to cooperate. He is using the invisible to study the visible and calling only one of them real.
“For since the creation of the world His invisible attributes, His eternal power and divine nature, have been clearly seen, being understood through what has been made, so that they are without excuse.”
Romans 1:20
Understood through what has been made. The order in the equations is not a proof handed down from a lectern. It is a signature, sitting in plain sight, on every page of every physics text ever written.
And the Mind whose signature that is did not stay behind the mathematics. The Logos who ordered the world entered it, took on flesh, and died to bring the men He made in His image back to Himself. That is the part no equation predicts — and it is the part that changes everything.
Teaching the Word. Watching the Times.
— SmithForChrist