Chapter 16
THE UNREASONABLE EFFECTIVENESS
Mathematics describes reality with uncanny precision—and no one knows why.
16.1 The Puzzle
In 1960, physicist Eugene Wigner published an essay with a striking title: “The Unreasonable Effectiveness of Mathematics in the Natural Sciences.”
His puzzle was simple. Mathematics is a creation of the human mind—abstract reasoning about numbers, shapes, structures. Mathematicians work with definitions and proofs, not telescopes and test tubes. They’re not studying the physical world; they’re exploring logical possibilities.
Yet mathematics describes the physical world with astonishing precision.
Consider quantum electrodynamics—the theory of how light and matter interact. Its predictions match experimental results to eleven decimal places. No other theory in science is so precise. And the theory is expressed in pure mathematics: differential equations, symmetry groups, complex numbers.
Or consider general relativity. Einstein developed it through mathematical reasoning—tensor calculus, non-Euclidean geometry. He wasn’t doing experiments; he was working out what the equations required. Yet the theory predicts phenomena—gravitational waves, black holes, the bending of light—that have been confirmed a century later.
This pattern repeats throughout physics. The universe seems to be written in mathematics. Galileo said as much: “The book of nature is written in the language of mathematics.”
But why?
Mathematics is developed by pure reason, without reference to experiment. Mathematicians prove theorems about abstract structures that need have no physical application. Yet these abstract structures—often developed for purely aesthetic reasons—turn out to describe physical reality.
Wigner found this “unreasonable.” It’s not what we’d expect if mathematics were simply human invention and the universe simply existed. Why should human abstractions match cosmic reality?
16.2 The Candidates
Several explanations have been proposed. None is fully satisfying.
Explanation 1: Mathematics is discovered, not invented.
Perhaps mathematical structures exist independently of human minds—in a “Platonic realm” of abstract objects. Mathematicians don’t invent; they discover. The reason mathematics describes reality is that both mathematics and reality participate in the same underlying structure.
This view has appeal. It explains why mathematics feels objective—why mathematicians talk of “discovering” proofs rather than “inventing” them. It explains why mathematical truths seem necessary, not contingent.
But it raises questions. What is this Platonic realm? Where is it? How do human minds access it? If abstract objects exist outside space and time, how can physical brains interact with them?
Explanation 2: Mathematics is a human projection.
Perhaps mathematics is purely human—a language we’ve invented that happens to be useful for describing patterns. The “effectiveness” is selection bias: we notice the mathematics that works and ignore what doesn’t. We’ve tuned our mathematics to fit reality because mathematics that doesn’t fit isn’t useful.
This view is deflationary. It dissolves the puzzle by denying there’s anything to explain. But it doesn’t quite work. Mathematics developed for pure reasons—with no physical application in mind—repeatedly turns out to describe reality. Non-Euclidean geometry was developed as an abstract exercise; Einstein used it to describe spacetime. Complex numbers were invented to solve algebraic equations; they’re essential to quantum mechanics. Group theory was developed for pure mathematical reasons; it underlies particle physics.
The pattern is too consistent to be coincidence. Mathematicians aren’t trying to describe physics, yet their creations do.
Explanation 3: Evolution explains it.
Perhaps evolution shaped human brains to do mathematics that tracks reality. Brains that could count, predict, calculate had survival advantages. So our mathematics is fitted to reality by natural selection.
This explains some mathematical ability—basic arithmetic, geometric intuition. But it doesn’t explain higher mathematics. Abstract algebra, differential geometry, set theory—these weren’t needed for survival on the savanna. Evolution didn’t optimize us for tensor calculus. Yet tensor calculus describes gravity.
Explanation 4: The universe is mathematical.
Perhaps the deepest structure of reality is mathematical. The universe doesn’t just happen to be described by mathematics; the universe is mathematics—a mathematical structure that exists necessarily and contains all consistent structures as possibilities.
This is physicist Max Tegmark’s “Mathematical Universe Hypothesis.” It’s bold and strange. It implies that mathematical existence and physical existence are the same thing. Every consistent mathematical structure exists physically, and we find ourselves in one of them.
The view is hard to test and perhaps unfalsifiable. But it takes the puzzle seriously. If reality is fundamentally mathematical, no wonder mathematics describes it.
16.3 Mind and Cosmos
Let’s step back and consider what the puzzle suggests.
Whatever the explanation, one thing is clear: there is a deep correspondence between rational thought and physical reality.
The universe is not chaotic. It has structure—regular, lawful, comprehensible structure. And that structure is the kind of structure that minds can grasp: mathematical, logical, rational.
This is not obvious. The universe could have been chaotic—a blooming, buzzing confusion with no patterns, no laws, no structure that thought could penetrate. It isn’t. The universe has exactly the character that makes it intelligible to minds.
And minds—human minds, at least—have exactly the character that makes them capable of understanding the universe. We can do mathematics. We can reason abstractly. We can formulate theories and test them against reality. Our cognitive equipment is fitted to the cosmos we inhabit.
Why?
One answer: coincidence. It just happens that minds can understand the universe. No deeper explanation.
But this answer is unsatisfying. The fit between mind and cosmos is too precise, too productive, too fundamental to be dismissed as accident. Science depends on this fit. If minds and cosmos weren’t matched, science would be impossible.
Another answer: the universe was made to be understood.
This doesn’t mean the universe was made for us—we’ve already rejected that anthropocentric assumption. But it might mean the universe has a rational structure because it has a rational source. Mind and cosmos correspond because both flow from the same ground.
This is where the puzzle touches theology.
16.4 The Suggestion
Consider the traditional theistic claim: the universe was created by a rational God.
If true, we’d expect the universe to have rational structure. We’d expect it to be lawful, orderly, comprehensible. We’d expect mathematics—the science of abstract structure—to describe it.
We’d also expect minds to be capable of understanding the universe. If the same rationality underlies both mind and cosmos—if both are expressions of a rational ground—then the fit between them is explained.
This doesn’t prove theism. The correspondence between mind and cosmos could have other explanations. But theism makes the correspondence unsurprising. On atheism, the correspondence is puzzling—a cosmic coincidence without explanation.
The argument isn’t decisive. It’s suggestive. It’s the kind of consideration that shifts probability without providing certainty.
Einstein’s intuition. Einstein famously said: “The most incomprehensible thing about the universe is that it is comprehensible.” He wasn’t conventionally religious, but he had what he called a “cosmic religious feeling”—awe at the rational structure of reality, a sense that something profound underlies the mathematical order of nature.
He also said: “I want to know God’s thoughts; the rest are details.” For Einstein, “God” was not a person but the rational structure of the cosmos—the deep order that physics reveals.
This isn’t traditional theism. But it’s not atheism either. It’s a recognition that the universe’s intelligibility is itself wondrous, demanding some response even if we can’t articulate what the response should be.
The logos. The opening of John’s Gospel reads: “In the beginning was the Logos.” The Greek word logos means word, but also reason, structure, rational principle. The verse can be translated: “In the beginning was Reason, and Reason was with God, and Reason was God.”
Early Christian thinkers—influenced by Greek philosophy—saw this as affirming what they already suspected: the rational structure of the cosmos reflects the divine mind. The universe is intelligible because it is the expression of supreme intelligibility.
We don’t have to accept this theology to see what it was responding to. The ancient thinkers noticed the same puzzle Wigner noticed: the universe has a rational structure that minds can grasp. They offered an explanation: the universe is grounded in rationality itself.
A modest conclusion. The unreasonable effectiveness of mathematics doesn’t prove God exists. But it suggests something:
The universe is the kind of place where mind and reality correspond. This correspondence is not explained by materialism, which treats mind as an accidental byproduct and has no account of why accidents should track reality. The correspondence is not explained by idealism, which treats reality as a projection of mind and struggles with the objectivity of science.
The correspondence is what we’d expect if both mind and reality are grounded in something deeper—something rational, something structural, something that makes intelligibility possible.
Whether to call that something “God” is a choice. The word carries baggage—anthropomorphic associations, institutional entanglements, historical controversies. Some prefer different language: Logos, Ground, Absolute, Tao.
But the phenomenon is the same. The universe makes sense. Our minds can grasp that sense. This is remarkable. It may even be revelatory.
Coda: The Light of Reason
We began Part IV with a question: why is there something rather than nothing?
We’ve explored what an answer might look like: a ground of being, necessary rather than contingent, simple rather than composite, the axiomatic foundation that makes existence intelligible.
We’ve seen that this ground—call it God or something else—is not the God of folk religion. It’s not a cosmic person with emotions and opinions. It’s something more abstract, more fundamental, more mysterious.
We’ve considered how to read the ancient texts that claim to describe encounters with this ground. Not as factual inerrancy, but as human attempts to articulate something that exceeds human categories. The wisdom survives the death of literalism.
And now we’ve seen one more piece: the universe has a rational structure that minds can understand. This correspondence is not explained by materialism; it is suggested by something deeper.
None of this proves anything. The ground may not exist. The correspondence may be coincidence. The ancient texts may be pure invention.
But the questions are real. The evidence—if “evidence” is the right word—points somewhere, even if we can’t follow it all the way.
Part V will address the darkest question: suffering. If the ground exists and is rational, why does the world contain so much pain? The answer, we’ll see, requires abandoning another assumption—that the universe was made for us.
The light of reason illuminates much. But it also reveals shadows.