The (Un)Reasonableness of Mathematics

Reasonable Faith and Avoid Project team up another cinematic short film. This time, Dr. Craig explains the baffling universal framework that is "mathematics."
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The book of nature is written in the language of mathematics. Throughout human history, man has discovered a universal framework that provides him with a window into the nature of our universe. Mathematics not only informs the curious, revealing some of the deepest mysteries of our universe, but it remains our best avenue to solve real-world problems.
Math lies at the foundation of transformative technologies like the personal computer and the color photograph. Its theorems led to the discovery of Einstein’s General Theory of Relativity. The Laws of Physics are all represented in surprisingly elegant mathematical equations. Every invention, every advancement, owes mathematics a debt of gratitude. In fact, all of science relies on the assumption that we live in a mathematically imbued universe.
But mathematics is so accurate, so effective at describing nature, that it presents us with a puzzle.
In 1960, the Nobel prize winning physicist and mathematician Eugene Wigner published a paper that stunned the scientific community. He called it, “The Unreasonable Effectiveness of Mathematics.” Wigner realized that the universe did not have to exhibit the mathematical structure that it does. His awareness led to a question that continues to baffle philosophers and mathematicians. Why does mathematics work?
The realm of mathematics is nonphysical and abstract. Yet for some reason, the physical universe operates mathematically. Perhaps even more puzzling, a mathematical framework not only exists in the natural world, but in the minds of human beings as well. How is it that a mathematical theorist like Peter Higgs can sit down at his desk and, by pouring over mathematical equations, predict the existence of a fundamental particle? The idea that this universe should be imbued with a mathematical structure that makes science possible cries out for some sort of explanation. Why is mathematics so effective?
Wigner concluded, “It is difficult to avoid the impression that a miracle confronts us here,” For on his worldview, the effectiveness of mathematics is inexplicable. His account had to be a purely physical, scientific one. As a result, the unreasonable effectiveness of mathematics seems to the naturalist to be just an amazing coincidence.
But naturalism doesn’t tolerate cosmic coincidences. For if mathematics exists solely in the abstract, nonphysical realm, its ability to illuminate the mysteries of the physical realm is just too improbable. The more the naturalist has to postulate happy coincidences, the less plausible his worldview becomes. Appealing to chance to explain the effectiveness of mathematics provides yet another example that an atheistic worldview is explanatorily inadequate.
But the dismissal of the Divine was never the initial target of scientific inquiry. For it was the faith of early scientists that inspired the very project of modern science. Because there is a rational creator, they thought, you could study the universe mathematically. Subsequent discoveries unveiled its elegant mathematical foundations. The universe, indeed, had a logical structure. Mind seemed to be at its center.
The theoretical physicist Paul Dirac rightly said that “God is a mathematician.” It turns out that the unreasonable effectiveness of mathematics provides powerful evidence for the existence of God. While atheism shrugs its shoulders, theism easily explains why mathematics is so effective. Both the human mind within and the universe “out there” are ultimately the product of the same divine mind. If God exists, the effectiveness of mathematics is actually something we should expect. And on atheism, there just isn’t any explanation.
As Albert Einstein famously said, “the only incomprehensible thing about the universe is that it is comprehensible.” If God does not exist, then the applicability of mathematics to the physical world truly is incomprehensible. Yet, we find ourselves in a world with a deep, mathematical underpinning that defies probability.
It turns out that Wigner was more right than he realized: the effectiveness of mathematics in describing the physical world is quite literally a miracle and thus evidence for the existence of God.