The Universe Can Be Understood

Steve had pointed me toward the beginning. Veronica pressed the next question: How could the universe be understood?

A beginning raises the question of cause. Intelligibility raises the question of mind. That difference became important to me.

Veronica saw it clearly. She was not dramatic about it. She did not treat mathematics as a magic trick or a secret code reserved for the gifted. She spoke of it with restraint, as though the subject deserved respect without needing decoration.

That was one of the reasons I listened to her. She also had a habit of straightening whatever was in front of her before making a difficult point—a notebook, a stack of paper, once even a coffee cup that was already straight enough. I noticed it because the gesture usually meant I was about to hear something carefully considered.

She had the rare ability to make mathematics feel both ordinary and astonishing. Numbers are part of daily life. We use them to count money and balance checkbooks, measure lumber and follow recipes. They help us mark time, compare distances, and calculate risk. Beneath those familiar uses, though, is a deeper fact most people rarely stop to consider.

Mathematics works with a consistency that reaches far beyond occasional success, local conditions, or human convenience. The same reliability extends from a kitchen table to the motion of planets, from a child’s counting blocks to the equations of physics, and from a carpenter’s square to the structure of galaxies. It is one of the quiet miracles behind science itself.

What Mathematics Is

Before making too much of mathematics, we should define what we mean. Mathematics is the study of number, quantity, structure, relation, pattern, and form.

It does more than help us count objects. It describes relationships built into reality, allowing us to measure and compare what we observe, predict what will happen, and reason about what we find. Bridges stand, satellites reach orbit, and medicine calculates dosage because mathematics is reliable.

Engineering and architecture depend on that reliability, as do physics, chemistry, and astronomy. Finance, aviation, and computer science make the same underlying assumption: reality has structure, and that structure can be described. If that expectation failed, science would fail with it.

This is why mathematics belongs near the beginning of the investigation. It is one of the conditions that makes the scientific search possible. Science depends on measurement, measurement on mathematics, and mathematics on intelligible structure.

Why is reality mathematical at all?

Discovered, Not Invented

Veronica once explained the point with a simplicity I never forgot.

“People say we invented mathematics,” she said. “But that is only partly true. We invented symbols. We invented notation. We invented ways to write mathematics down. But we did not invent the truths those symbols describe.”

I pushed back.

“So we discover mathematics?”

“Some of it,” she said. “At least the truths the symbols point toward.”

“That sounds more philosophical than mathematical.”

She gave me the smallest smile.

“Mathematics becomes philosophical very quickly when you ask what it is.”

That answer stayed with me because it was exactly the kind of answer Veronica gave. She would not pretend a question was smaller than it was merely to make it easier.

Human beings invented the written symbol “2,” along with the plus and equal signs. We developed mathematical languages and systems, diagrams and proofs, and textbooks to explain them. But the fact that two objects plus two objects make four objects was there to be discovered. So were the relationships between the sides of a right triangle, the ratios that govern circles, and prime numbers.

Long before anyone wrote an equation, the relationships mathematics describes were already present. Pythagoras, Euclid, Newton, and Einstein encountered a reality that already possessed structure. Calculators, chalk, and whiteboards came later still. Triangles and circles did not depend on our understanding or naming them, and the stars moved before we could calculate their motion.

Mathematics draws its power from the structure the mind gradually uncovers in the universe. We did not impose that structure on something meaningless. Knowledge, in this sense, is recognition rather than creation from nothing. We are learning to read a reality we did not invent.

A Simple Theorem

The Pythagorean theorem is worth mentioning because it is simple, ancient, and still true.

In a right triangle, the relationship between the sides is expressed this way:

a² + b² = c²

The squares of the two shorter sides, added together, equal the square of the longest side. If one side is 3 and another is 4, the longest side is 5:

3² + 4² = 5²
9 + 16 = 25

The arithmetic is simple. What is impressive is that the relationship is real. It was real before anyone named it, and it remains true whether a student understands it or not. Carpenters, surveyors, and architects can use it because it describes something stable about spatial reality. The same relationship serves navigation, engineering, and physics.

Its place in this chapter is to show that reality contains discoverable order and that mathematics gives us access to it. A man building a roof or measuring a field relies on that order. So does someone designing a bridge or sending a spacecraft across millions of miles. The universe has structure. It keeps its promises, allowing the mind to find patterns that were already there.

Why should a physical universe be describable by abstract mathematics? Symbols written by a human hand correspond to realities far beyond human scale, and the same mathematical principles function across the earth and in the heavens. Why should that be so?

These are questions about why mathematics fits the world so well, rather than gaps in mathematics itself.

Einstein’s Question

Albert Einstein saw the mystery clearly. He famously observed, “The most incomprehensible thing about the universe is that it is comprehensible.”

Einstein was not saying the universe is easy to understand. It is not. The surprise is that we can understand it at all.

Human beings are small creatures living on a small planet. Our lives are brief, our senses limited, and our minds finite. Yet we can discover laws governing gravity and motion, light and energy, and even time. We write equations describing events no eye has seen. Those equations let us predict eclipses and calculate orbits. They help us split atoms, transmit signals, and peer into the early universe.

If the human mind were merely the accidental byproduct of blind material processes, aimed only at survival, why should it also be capable of discovering deep mathematical truths about the cosmos?

Survival might explain our attention to food and danger, shelter and reproduction. It does not easily explain our understanding of black holes or the expansion of the universe, much less quantum behavior and geometric proofs.

This does not mean every mathematical discovery proves God in one step. That would be too quick. Mathematics adds another layer to the larger case: the universe is intelligible as well as ordered, and human reason is fitted, at least in part, to understand it.

The Reason Science Works

Science has a deeper foundation than many people admit. It assumes a rationally ordered universe in which experiments can be repeated and causes and effects studied. It relies on numbers meaning the same thing today that they meant yesterday, and on the human mind’s ability to follow evidence toward truth.

These assumptions form the foundation science stands on. They are not scientific conclusions.

A scientist does not prove the reliability of reason by using reason. He must already trust reason in order to conduct the proof. Nor does he prove that nature is orderly before doing science. He must assume enough order to begin.

This is a reminder of the deeper realities on which science rests, rather than a weakness in science. The Christian worldview expects those realities.

If God is rational, and if creation reflects His order, then a rationally structured universe is not surprising. If human beings are made in the image of God, then human reason, though limited and fallen, is not an accident. We should expect some meaningful correspondence between the mind and the world.

That is exactly what we find. The universe is not fully transparent to us, and much remains mysterious. But mystery is not the same as chaos. Mathematics often reveals order before we understand its full meaning.

The Limits of the System

For all its power, mathematics has limits. Its formal systems cannot establish everything. Mathematics can measure distance without telling us worth, or calculate force without establishing moral obligation. It can describe patterns with astonishing precision, but it cannot tell us why a pattern-bearing universe exists in the first place.

This became important when Veronica spoke about Kurt Gödel.

Gödel’s work is difficult, and this is not the place for a technical treatment. But one central implication is useful for our investigation: sufficiently powerful, consistent formal systems contain true mathematical statements that cannot be proved from within those systems themselves.

In plain terms, formal proof has limits. A system may be unable to establish every truth expressible within its own mathematical language.

That does not prove Christianity. Nor does Gödel’s theorem prove that the physical universe requires God. To claim either would misuse the mathematics.

But Gödel does challenge the old dream that one sufficiently powerful formal system could close over every mathematical truth and prove everything from within itself. At minimum, it gives us a disciplined warning against treating any formal description as though it were automatically complete and self-sufficient. A given system has boundaries: truths it cannot prove from within its own rules.

That limitation harmonized with a caution already present in the investigation. Cosmology had raised the question of whether the universe could account for its own existence. Gödel raised a different question within mathematics: whether a sufficiently powerful formal system could prove every truth available within its own language.

The arguments were not identical, and one did not prove the other. Together, however, they warned me against confusing a successful description of reality with an ultimate explanation of it.

Reality was intelligible. That did not mean it was self-explanatory.

More Than Utility

One of the errors of modern thinking is to treat mathematics as merely useful. Its usefulness is obvious, but it is not the whole story.

A key is useful because it fits a lock. Its usefulness points to a relationship between the two. Mathematics is useful because it fits reality, and that fit is the mystery.

Why should abstract thought fit the physical world? Equations written on a whiteboard describe the motion of planets. Geometry imagined in the mind corresponds to space outside it. Mathematical reasoning allows us to discover things no person has directly experienced. Why should our minds be capable of this?

The more I considered those questions, the more difficult it became to treat mathematics as a human invention laid over an accidental universe. Mathematics felt less like a tool we created and more like a language we learned.

I do not mean language in the ordinary sense of spoken words and grammar. Dawn would later help me think more carefully about that. But mathematics did seem to function as a kind of rational grammar beneath the physical world. It could be read, even though it did not speak with a voice.

Veronica’s Contribution

Veronica did not push me toward the careless conclusion, “Mathematics exists, therefore Christianity is true.” Her contribution was more precise.

By then I had begun to recognize that precision as part of her character. Veronica rarely gave me the strongest sentence available. She gave me the strongest sentence she believed the evidence could carry. That restraint was becoming part of the method I was trying to build.

She helped me see that mathematics belonged within the larger pattern. Its testimony was distinct, but it did not stand alone. We had considered a universe that began, possessed order, and permitted life. Now we were considering our ability to understand it.

If reality were accidental at the deepest level, intelligibility would be a surprise. If the human mind were only a survival machine, its ability to grasp abstract truths would be difficult to explain. And if mathematics were merely invented, its power over the physical world would be strange.

But if reality is created by Mind, then mathematics begins to make sense. Our understanding is not complete, but it becomes coherent.

Coherence mattered more and more to me. Along with doctrines to believe, Christianity gave me a framework in which the features of reality began to belong together.

None of this removed mystery. It deepened it. But the mystery was no longer empty. It had order and direction, and it seemed to invite pursuit.

The Next Door

By the time I began to understand Veronica’s point, the investigation had moved again. Cosmology had asked why the universe exists; mathematics asked why it can be understood. Another question was waiting.

If mathematics reveals structure, language carries meaning. Human beings speak and name things, interpret what they encounter, and communicate what they think. We use symbols to carry thought from one mind to another.

That ability would matter more than I first realized. From numbers, the investigation would turn to words.