The Miracle of Mathematics

“The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning.”

This quote concludes an essay by Nobel Prize winning (1963) physicist Eugene Wigner entitled “The Unreasonable Effectiveness of Mathematics in the Natural Sciences” (published in 1960). In this essay, Wigner draws on examples from both classical and quantum mechanics to support the simple thesis that “the enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and that there is no rational explanation for it.” 

His example from classical mechanics is easier to understand for most readers due to its familiarity.  He describes how Newton applied the law of falling bodies, based on experiments by Galileo and other Italian scientists, to the motion of the moon, and from there “postulated the universal law of gravitation on the basis of a single, and at that time very approximate numerical coincidence.” This simple law (stated mathematically that the gravitational force between two objects is directly proportional to the masses of the objects and inversely proportional to the distance between them squared)  has since been extended to describe planetary motion to an accuracy of less than a ten thousandth of a percent.  The application of the universal law of gravitation to planetary motion illustrates how “the mathematical formulation of the physicist’s often crude experience leads in an uncanny number of cases to an amazingly accurate description of a large class of phenomena.”

More recently, physics in the 20th century, which produced such discoveries as the structure of the atom and Einstein’s theory of relativity (these form the scientific basis of nuclear and even digital technologies), has been mostly advanced by mathematical analysis first, only to be verified by empirical observations sometimes decades later.  Einstein himself marveled that the human mind, relying purely on reason to extend mathematics, could discover truths about the complex structure of the universe, independent of sensory experience of the phenomenon:  “How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality?”

Wigner’s answer is that there isn’t an answer:  “there is no rational explanation.”  Hence, he uses the word ‘miracle’ throughout the essay to describe this correspondence between math and nature.  This implies the need  to add a qualification to his thesis that there is no rational natural explanation.  Perhaps then what is needed is a rational supernatural explanation.  A biblical worldview provides such an explanation.  Galileo believed that the “laws of nature are written in the language of mathematics.”  He was not speaking of ‘language’ metaphorically, but literally.  Some essential characteristics of any language are that it is intentional, rule-governed, and creative – properties that are indicative of intelligence.  That there appears to be a language of the universe suggests that it was ordered by an infinitely intelligent mind, which of course is what the Bible proclaims about the origins of the universe.  Mathematics allows us to discover the blueprint in the mind of God according to which the natural world was made.  Since God endowed humanity with the gift of logical reasoning, having made us in His image, such that we can pattern our thoughts according to His mind,  there exists a kind of pre-established harmony between the structure of the universe and the laws of logic that govern reasoning.  Consequently, when we use our minds as God intended, using rationality to think consistently, we can discover, sometimes through pure reason, unseen truths about the structure of the universe.

 Pope Benedict XVI, reflecting on the legacy of Galileo, discerns the theological implications of mathematics:

Was it not the Pisan scientist who maintained that God wrote the book of nature in the language of mathematics? Yet the human mind invented mathematics in order to understand creation; but if nature is really structured with a mathematical language and mathematics invented by man can manage to understand it, this demonstrates something extraordinary. The objective structure of the universe and the intellectual structure of the human being coincide; the subjective reason and the objectified reason in nature are identical. In the end it is “one” reason that links both and invites us to look to a unique creative Intelligence


The reality of this “creative Intelligence” is not a mere intellectual abstraction to account for the perceived order of the universe.  It also supplies the emotional support scientists need to do the difficult work of unlocking the mysteries of the universe.  Wigner calls this extraordinary correspondence between the human mind and the  laws of nature “the empirical law of epistemology” and concludes “if the empirical law of epistemology were not correct, we would lack the encouragement and reassurance which are emotional necessities, without which the “laws of nature” could not have been successfully explored.”

Indeed, not only is the natural order sustained by God’s power, but it appears that He also sustains the hearts of those who labor to explore this order.  For He is glorified by the unfolding of His brilliant, creative, benevolent design of the universe.  It is no wonder that Wigner marvels,

It is difficult to avoid the impression that a miracle confronts us here, quite comparable in its striking nature to the miracle that the human mind can string a thousand arguments together without getting itself into contradictions, or to the two miracles of laws of nature and of the human mind’s capacity to divine them.

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3 comments on “The Miracle of Mathematics

  1. johnwgunter says:

    Great stuff, Jeremy. . . thanks for sharing.

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