Why Is Mathematics So Successful?
The success of mathematics in describing the universe is a fact that most of us, even scientists like me, take for granted. Yet it is actually extremely surprising. Nobel Prize–winning physicist Eugene Wigner wrote an article over fifty years ago entitled “The Unreasonable Effectiveness of Mathematics in the Natural Sciences,” in which he repeatedly used the word “miracle” to describe this phenomenon.1 Why, he asked, do the same beautiful mathematical equations apply uniformly across all time and space? We could easily conceive of a universe that is wholly haphazard and chaotic, described by no underlying mathematics at all. Or we could conceive of a universe that is sporadically chaotic, where the laws of physics are occasionally suspended or altered every few years. Or we could conceive of a universe in which the laws of physics are not universal; they could vary from planet to planet or from galaxy to galaxy. Instead, we observe a universe with a deep and beautiful underlying mathematical structure that appears to be universal in space and time. Wigner asked why this should be the case; what is the explanation for this phenomenon?2
In addition to the mathematical structure of the universe, Wigner called attention to another unusual and “miraculous” phenomenon: that human beings are able to perceive and understand this structure. This fact is also quite surprising. After all, while one might argue that evolution would produce organisms with enough intelligence to flee from tigers or to avoid falling off cliffs, why are human beings unique in their ability to comprehend quantum mechanics or molecular biology? Surely, these activities didn’t confer any reproductive benefit on hunter-gatherers foraging for fruit and fending off predators. Why should we expect human beings to understand science and mathematics any better than other intelligent animals like chimpanzees or dolphins?
Atheistic Explanations for the Success of Mathematics
“The universe’s mathematical structure is necessary.” With regard to the first phenomenon, I think the atheist’s best response is to say that the mathematical structure of the universe might be necessary; that is to say, there is no possibility that the universe could not have possessed a deep, mathematical structure. But this idea strikes me as odd. Why think that irregular or unpredictable universes should be impossible? We normally do not make the assumption that there is a necessary connection between mathematical beauty and truth. For example, most physicists insist that even very mathematically beautiful theories like string theory must be certified by evidence. Unlike Keats, we do not simply assert that “beauty is truth, truth beauty” and call it a night. We fairly ruthlessly demand that beautiful theories withstand the scrutiny of empirical testing.
Neither do we reject successful theories purely on the grounds that they are mathematically inelegant. Consequently, we should not insist that the “ugliness” of a nonmathematical universe renders it impossible. Mathematical beauty and structure certainly exist, but they do not appear to be necessary. So why do they exist?
“Language explains our mathematical ability.” Explaining the second phenomenon—that humans can perceive and understand the mathematical structure of the universe—is also challenging. It is objectively true that we human beings are unique in our capacity for abstract mathematical and scientific thought. Furthermore, these abilities don’t directly contribute to our ability to produce offspring; early humans didn’t use particle physics to escape from hyenas. So we can’t appeal to the idea that these capacities were evolutionary adaptations. How, then, can we explain their existence?
I believe that the best option for an atheist is to argue that our highly advanced cognitive faculties are an accidental by-product of our ability to use language. The evolution of language, an atheist could argue, allowed human beings to mentally process abstract symbols, which, in turn, led to the development of our mathematical and scientific abilities even though they didn’t directly increase our chances of survival. Language was an evolutionary adaptation, and mathematics was an accidental evolutionary by-product.
Unfortunately for the atheist, human beings are just as unique in their ability to use language as they are unique in their ability to understand mathematics.3 Worse still, the evolution of language is extremely mysterious. In a 2014 review article co-written by numerous renowned evolutionary psychologists, biologists, and linguists, including Marc Hauser, Noam Chomsky, and Richard Lewontin, the authors state:
In the last 40 years, there has been an explosion of research on this problem [of the evolutionary origin of language] as well as a sense that considerable progress has been made. We argue instead that the richness of ideas is accompanied by a poverty of evidence, with essentially no explanation of how and why our linguistic computations and representations evolved.4
After describing in their paper the various obstacles facing research into the origins of language and outlining possible ways for research to proceed in the future, given certain advances, they conclude: “These are all big IFs about the nature and possibility of future evidence. Until such evidence is brought forward, understanding of language evolution will remain one of the great mysteries of our species.”5
If God is a rational, infinitely intelligent Being, it is no surprise that the universe he created reflects his reason and intelligence.
Appealing to the acquisition of language as a solution to our mathematical abilities only moves the problem back one step: rather than asking why we are uniquely able to understand math and science, we are left asking why we are uniquely able to use language in a way that also allows us to uniquely understand math and science.6 Because scientists currently have no clear answer to this puzzle, it is difficult to insist that the answer—whatever it is—must be atheistic.
Theism’s Explanation for the Success of Mathematics
In contrast, both of these phenomena—the mathematical beauty of the universe and our unique ability to understand it—fit quite naturally into a theistic universe. If God is a rational, infinitely intelligent Being, it is no surprise that the universe he created reflects his reason and intelligence. And if, as the Bible teaches, men and women were uniquely created in the divine image to understand and appreciate the universe that God has created, our capacity for mathematics and science is similarly explained. A rational God gave us our rational cognitive faculties to understand the rational universe he created. At least this one piece of the puzzle seems to fit more readily into a theistic picture of reality than into an atheistic picture.
- Eugene Wigner, “The Unreasonable Effectiveness of Mathematics in the Natural Sciences,” Communications on Pure and Applied Mathematics 13, no. 1 (1960): 1–14.
- Physicist Paul Davies echoes this sentiment. He tells the story of a classmate who, when Davies said that he could predict the motion of a projectile using Newton’s equations, asked incredulously, “How can you possibly know what a ball will do by writing things on a sheet of paper?” Davies reflects: “Over the years I came to see that her impulsive response precisely captures one of the deepest mysteries of science: Why is nature shadowed by a mathematical reality? Why does theoretical physics work?” Davies, The Goldilocks Enigma: Why Is the Universe Just Right for Life? (London: Allen Lane, 2006), 11.
- Martin A. Nowak, Evolutionary Dynamics: Exploring the Equations of Life (Cambridge, MA: Harvard University Press, 2006), 249–51. Nowak writes: “The emergence of language was the last in a series of major events in evolution, comparable in significance only to the origin of life, the first bacteria, the first higher cells, and the evolution of complex multicellularity. Language is the biggest invention of the last six hundred million years” (249); and “Language is the one property that sets us apart from all other animal species” (250).
- Marc D. Hauser et al., “The Mystery of Language Evolution,” Frontiers in Psychology 5, no. 401 (2014): 1; emphasis added.
- Hauser et al., “The Mystery of Language Evolution,” 10.
- See also Fiona Cowie, “Innateness and Language,” The Stanford Encyclopedia of Philosophy, ed. Edward N. Zalta, January 16, 2008, https://plato.stanford.edu/.
This article is adapted from Why Believe?: A Reasoned Approach to Christianity by Neil Shenvi.
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