The miracle of math

In honor of Pi Day 2025

Yes, this will be on the test

Galileo viewed the universe as God’s mathematical masterpiece, a perspective that resonates with Eugene Wigner’s awe at math’s uncanny ability to describe nature. This article argues that mathematics—from planetary orbits and imaginary numbers to the miracle of Genesis—points to a divine Storyteller behind the laws of nature.

The Enigma of Mathematics in Nature

In 1960, theoretical physicist Eugene Wigner identified a metaphysical mystery for the ages: why are the laws of nature so aptly described by mathematics? It is a deceptively simple question. We think we grasp the answer easily—until we actually try to explain it.

Wigner’s essay, titled “The Unreasonable Effectiveness of Mathematics in the Natural Sciences,” highlights this enigma. The term “unreasonable” captures the bewildering reality that there is no apparent reason why math should so flawlessly mirror the universe’s behaviors. This suggests, whether intended by Wigner or not, that the answer to this mystery lies beyond the universe.

If I had to strip the universe down to its essentials, I would say it is made of space, time, energy, and matter. If the answer to this mathematical mystery transcends these essentials, then what could it possibly be? What else exists outside our concepts of space, time, or physicality except abstract concepts?

For Galileo Galilei, a believing man, the answer was crystal clear: God.

The laws of nature are written by the hand of God in the language of mathematics. – Galileo Galilei

Galileo and the Mathematical Foundation of Science

Galileo is, for better or worse, better known for his epic showdown with the Roman Catholic Church than for anything else. In an ideal world, Galileo would be best known and gratefully acknowledged for something else entirely—his emphasis on mathematics in modern science.

The significance of mathematics in science cannot be overstated. Without them, as physicist Ernest Rutherford quipped, science might as well be “stamp collecting.” Or, to put it kindly, we would be stuck with the approach of the ancient Greeks—lots of clever arguments but no hard data to back them up. Take Aristotle, for instance, who brilliantly argued that if a light stone and a heavier stone were dropped at the same time, the heavier stone would fall faster due to its stronger pull towards Earth. However, he never put his hypothesis to the test. Galileo, on the other hand, did not just talk; he experimented. He ingeniously measured time using his own heartbeat as he watched objects rolling down an incline. Through these innovative experiments, he not only debunked Aristotle’s assumptions but laid bare the mathematical framework that underpins our understanding of the natural world.

Galileo’s pioneering work paved the way for Johannes Kepler, who formulated the three laws of planetary motion. For centuries, humanity knew that celestial bodies orbited each other, but often got tangled in which object was orbiting what. This cosmic confusion was partly why Galileo clashed with the Church. Kepler, who was Lutheran and carefully worked from a more hypothetical framework, took up the baton from Galileo, quantifying the orbits of the planets around the Sun with mathematical precision. His third law tells us:

\(a^3=P^2\)

Here, a is a planet’s average distance from the Sun, and P is how long it takes for a planet to complete its orbit around the Sun.

The Universal Language of Mathematics

My father, who was a math teacher for thirty years, had a knack for making math relatable to teenagers (a minor miracle). To these young people confronted with incomprehensible jumbles of symbols, he taught that math is a language, and equations are just short stories about the world. Take Kepler’s law—it is a concise tale of our solar system. It states that the average distance of a planet to the Sun multiplied by itself three times is equal to the amount of time a planet takes to make one full orbit around the Sun multiplied by itself. This equation does in five symbols what would take me 147 in English, showcasing the sheer efficiency and elegance of math.

The true shock came when Isaac Newton, building on Kepler’s mathematical “stories,” formulated his universal law of gravitation—beautifully predicting Kepler’s laws. To achieve this, Newton had to invent the new mathematical tool of calculus. This has inspired some people to argue that mathematics is purely a human construct. But calculus has since become indispensable in the study of so many disparate fields of science that it is difficult to maintain this view. Calculus is used to describe the physical motion of objects, fluid dynamics, electromagnetic fields, rates of growth and decay in both radioactive materials and living things, chemical reaction rates, the spread of disease, climate events, and even concepts of optimization and elasticity in economics.

It is astonishing that this single “invention” could narrate such diverse stories about nature and society. While it might be tempting to chalk up the widespread use of calculus to mere chance, scientists are inherently skeptical of coincidences, always hunting for a deeper explanation. In my days as a research scientist, ending a paper with “It's probably a coincidence” was unthinkable. Each study demanded a plausible explanation, even for the most baffling observations. From a secular viewpoint, the widespread utility of calculus in so many areas poses a real conundrum. Wigner’s observation suggests no natural, within-the-universe explanation exists for this phenomenon. Scientists, who detest loose ends as much as they hate coincidences, are left pondering: how do we tie up this perplexing thread?

From the Abstract to the Practical

Even more troubling is that we stumble upon mathematical concepts so strange they seem detached from reality, only for them to emerge as indispensable tools for deciphering the world around us. My go-to example is the curious combination of real and imaginary numbers.

Think about square roots. You know that multiplying 2 by itself gives 4, and -2 by itself also gives 4. But what about the square root of a negative number like -4? In grade school, we were told this is impossible, a useful simplification for young minds. Yet, the truth is far more fascinating. Since the 16^th century, mathematicians have embraced “imaginary numbers”—numbers that, when squared, yield negative results. When I first encountered them in university, the term “imaginary” felt out of place in the austere world of mathematics, almost juvenile. Still, I grudgingly acknowledged their utility in abstract math, particularly in the formation of “complex numbers,” which mathematicians of the 19^th century formed from the combination of real and imaginary numbers. I thought of these as intellectual toys for math geeks, nothing more. But imagine the shock—both mine and that of math geeks everywhere—when these so-called imaginary numbers proved pivotal in fields like electrical engineering, quantum mechanics, and signal processing.

Mathematics as Divine Storytelling

For those who crave practicality, the leap from abstract oddities to essential tools in understanding the physical world is nothing short of unsettling. There is no logical reason why these mathematical whims should govern electricity or subatomic particle behavior. This relationship between mathematics and the real world is so strange that Wigner borrowed from the lexicon of the divine to describe it. He called it a “miracle.”

As a university student whose atheism was increasingly found to be on shaky ground, such miracles kept me up at night. I grappled with closing these logical loops, each one extending maddeningly beyond the universe. It was only when I acknowledged God as the master orchestrator of these wonders that the loops finally closed.

For another divine spectacle, flip to the first chapter of Genesis in the Bible. Here, you will find the entire saga of the universe—from the first fiery moments of the universe, through the making of stars and planets, to the dawn of life on Earth and God breathing the animating breath of life into the first human—captured in just a few hundred words. It is a narrative of remarkable economy, especially when you consider the libraries of books it has taken us to merely corroborate what Genesis describes. Modern science has essentially echoed Genesis 1, only with more detail. This realization, which hit me during my doctoral studies, led me to take the Bible seriously—and human wisdom less seriously. Not because we lack intelligence, but because, in essence, science has been a long process of retelling God’s story. Yet it is a worthwhile thing to do, and only made possible by taking advantage of the exquisitely efficient language of mathematics.

Mathematics is about discovering different ways in which symbols in equations can be arranged, revealing intricate relationships between them. Some equations are incredibly intricate and obscure while others cut straight to profound truths. Studying pure mathematics is akin to dissecting languages like English or Mandarin, where you are not just playing by the rules of a game; you are exploring a language that exists because there is something to say.

We may have invented the symbols of mathematics—the letters and signs—but we did not create its grammar. The rules of mathematics remain consistent whether etched on clay, inked on paper, or displayed on a screen. These laws are so fundamental that, with a guide to decode our symbols, we could potentially share them with intelligent extraterrestrials light-years away, and they would recognize the same truths.

Without realizing it, the everyday Christian has already closed the logical loop and solved Wigner’s mystery about the uncanny effectiveness of math in nature. If mathematics narrates the story of the universe, and these narratives are eternal and universal, then they must come from an eternal, universal Narrator. Galileo knew exactly who this Storyteller was, and he would echo Wigner in calling the application of math to science a “miracle.” Not because it represents a baffling coincidence, but because it is God writing his laws into the very fabric of creation.

The profound synergy between mathematics and the natural world is not an unsolvable mystery; it is a testament to an underlying truth. Galileo’s faith that God penned the laws of nature in the language of mathematics explains Wigner’s “miracle.” The harmony we find is not by chance but a clear sign of a universal design, crafted by a divine Storyteller. Through the lens of science, we not only explore but affirm the narrative laid out in the opening verses of Genesis, revealing that our quest for scientific understanding has always been, in essence, a journey back to God.

Scriptural Foundations

“The heavens declare the glory of God; the skies proclaim the work of his hands. Day after day they pour forth speech; night after night they reveal knowledge. They have no speech, they use no words; no sound is heard from them. Yet their voice goes out into all the earth, their words to the ends of the world.” – Psalm 19:1-4

“Where were you when I laid the earth’s foundation? Tell me, if you understand. Who marked off its dimensions? Surely you know! Who stretched a measuring line across it?” – Job 38:4-5

“I was there when he set the heavens in place, when he marked out the horizon on the face of the deep, when he established the clouds above and fixed securely the fountains of the deep, when he gave the sea its boundary so the waters would not overstep his command, and when he marked out the foundations of the earth. Then I was constantly at his side. I was filled with delight day after day, rejoicing always in his presence.” – Proverbs 8:27-30

“Who has measured the waters in the hollow of his hand, or with the breadth of his hand marked off the heavens? Who has held the dust of the earth in a basket, or weighed the mountains on the scales and the hills in a balance?” – Isaiah 40:12