A Book Review of James Nickel’s Mathematics: Is God Silent?
Mathematics: Is God Silent? is an investigation into the history and nature of mathematics, as well as an extensive study of the question of its ultimate source—that which gives mathematics all its meaning. The author, James Nickel, meticulously demonstrates that this source is, without question, God. Nickel then builds upon his conclusions with a detailed presentation of how mathematics can only be meaningfully taught when it is presented as the language of the “handiwork of God” (p. 226).
“What is mathematics?” Nickel’s answer to this question is breathtakingly exhaustive. He begins by carefully delineating the definition of worldview. Using insightful keywords, such as ‘faith commitments,’ he explains how the facts alone lack meaning and, therefore, must be interpreted through perspectives made up of ‘presuppositions,’ or ‘filters’ (p. 6). Nickel then systematically progresses through a comprehensive study of the history of mathematics, beginning with Adam and relentlessly tracing mathematical thought into the twentieth century, when mathematician Hermann Weyl concluded that, “The questions of the ultimate foundations and the ultimate meaning in mathematics remain an open problem; we do not know in what direction it will find its solution nor even whether a final objective answer can be expected at all” (pp. 192-193).
The aim and scope of Mathematics: Is God Silent? are lofty, yet Nickel masterfully succeeds in demonstrating that the mathematical concept of infinity echoes not a “what,” but a “Who.” The ultimate foundations and meaning in mathematics find “its final solution in the infinite, personal God revealed in Holy Scripture…[and the] reason that mathematics is…effective [is]…because the biblical God, the creator of the real world with its mathematical properties and the human mind with its mathematical capabilities, upholds and sustains it…” (pp. 193-194). Nickel concludes that mathematics is the human reflection of nothing less than the Logos of God, producing and maintaining creation. Man is able to grasp that Logos—to ‘translate’ it via mathematics, if you will—because man is made imago Dei.
Nickel points out that secular mathematics has erred in jumping to the conclusion that creation is chaotic—the so-called ‘uncertainty principle’ (pp. 203-205)—because man’s mathematics is imprecise in its measurements, particularly at the quantum level. In reality, the imprecision of man’s measurements reflects a shortcoming in humanity’s ability to measure, not in any inherent shortcoming in creation. “It may be that behind the physics of quantum mechanics lies a higher degree of unity and harmony that our current instrumentation cannot yet measure…” (p. 205). Nickel’s book contains an implicit warning that, if we do not abandon the faulty conclusion to which modern science has come, so aptly stated by Weyl above, our own mathematics—and science and technology with it—will decline.
In addition, Nickel observes that it is only through understanding mathematics in the context of the biblical worldview that we can account for its seemingly mysterious properties. For example, only the Trinity provides a resolution of the dilemma of the ‘one and the many’ (p. 231), the apparent paradox of the universals versus the particulars. In addition, it is only this view of mathematics which gives justification to the mystery of why mathematical conventions—which so many argue are simply ‘linguistic conventions’ (p. 231) created wholly from the mind of man—are actually so practical and useful in the physical world. Finally, it is only in the biblical worldview in which man’s use of mathematics in creation is given an ethical basis: “God has always purposed for man to take dominion over the earth…by understanding, observing, classifying, and taking pleasure in God’s works…” (p. 233).
Furthermore, Nickel demonstrates that, historically, it is only through the biblical worldview that significant leaps in mathematical progress have been made. Other civilizations, such as the Babylonians and Egyptians, experienced stagnation in their mathematics because their worldviews did not include pursuing precision and perfect order as priorities. “Animistic in nature, each ancient culture worshiped the creation rather than the Creator. The flow of time occurred in cycles, not in terms of a linear beginning and end…With a treadmill view of history, no meaningful advance could be confidently made in any aspect of human endeavor” (p. 15).
The ancient Greeks, Nickel points out—although they shared the cyclical view of history—took a new perspective, attempting “to seek answers to the basic questions of life…in the power of human reason alone” (p. 16). Nevertheless, the Greek culture as a whole, though it advanced further than those before it, ultimately decayed as well. By the time of Christ, it was in decline because, as Stanley L. Jaki said, the Greeks failed “to go resolutely one step beyond the prime heavens to a prime mover absolutely superior to it…Needless to say, a world not governed by its divine pilot is a largely irrational world which discourages…science” (p. 53).
Muslim influence, based upon Arab access to Greek manuscripts and Hindu concepts of the number zero, negative numbers, and the idea of positional notation (p. 83), helped to pave the way through the Middle Ages in Europe for a time when, in fact, biblical theology became “the match that lit the fires of the Scientific Revolution” (p. 129). Nickel notes that although the Hindu culture produced significant advances in numerical concepts, it did not advance to the “formulation of quantitative laws and systems of laws” (p. 141) because, again in the words of Stanley L. Jaki, “Hindu culture…was obsessed with the perennial recurrence of cosmic cycles. In this context, man is no more than a senseless product of an all-pervading biological rhythm” (p. 141).
It was “the conviction that the biblical God had designed the universe in a rational and orderly fashion; in fact, so orderly that it could be described mathematically” (p. 129) that spurred the incredible advancements in mathematics, science, and technology to which we have since been witness. Nickel quotes evolutionary anthropologist, Loren Eiseley: “We must also observe that in one of those strange permutations of which history yields occasional rare examples, it is the Christian world which finally gave birth in a clear articulate fashion to the experimental method of science itself” (p. 143).
Nickel begins his book with a profound observation: “…professional mathematicians are in a quandary as to the ultimate foundations and meaning of mathematics” (p. xix). In addition, he asks, “Why does a mere product of man’s autonomous mind accurately model the workings of the physical world?…Humanistic mathematicians and scientists answer using terms like ‘incredible, unreasonably effective, and mysterious’” (p. xix). For the Christian, however, the crystal clear answer to this lies in the “biblical doctrine of creation. Man’s mathematical constructions and the workings of the physical world cohere because of a common Creator” (p. xx). In fact, “since mathematics deals with things visible (the structure of the physical world) and things invisible (the structure of human thought), it would be reasonable and befitting to deduce that the person of Jesus Christ is the ‘cohesive’ that holds the structure of mathematics together” (p. 5). The cohesive—the ‘Logos,’ which Nickel specifies as “a lawfulness or wisdom or logic” (p. 8)—is centered in none other than the person of Christ himself.
Thus, mathematics must be understood to be built upon the bedrock of the biblical worldview, or else it becomes meaningless—a mystery and an uncertainty. Furthermore, when viewed properly in this way, the teaching of mathematics becomes imbued with meaning and purpose. In contrast, if it is taught from the humanistic worldview—a worldview which denies God—it is emptied of meaning, and is reduced to mere “chicken scratches” on a blackboard (p. xix), leading to apathy as well as outright rejection of the subject amongst students. This is a development which we are perhaps seeing come to fruition today, and it bodes ill for the future of our civilization’s mathematical and scientific endeavors.
Nickel makes it patently clear that the sole context in which mathematics can be meaningfully taught is that of the biblical worldview, leading to the final section of the book entitled (so as to be purposefully evocative of Francis Schaeffer’s How Should We Then Live?): “How Should We Then Teach?” In answer, Nickel asserts that the biblical worldview must be all-pervasive: “God [must be] seen as the foundation of all knowledge, not just ‘spiritual’ knowledge…To God, every item of His creation, invisible and visible, reflects back to Him the beauty, wonder, and infinity of His attributes…Since mathematics is a unique…description of God’s creation, we must expect to find, upon reading it, the invisible things of God” (p. 234).
Nickel identifies four integrated curriculum objectives in teaching biblical Christian mathematics. First, mathematics describes the wonder of God’s creation; as such, it should be emphatically connected to the phenomena in creation. Second, it reveals the invisible attributes of God himself. Third, it is a tool to aid man in fulfilling God’s mandate of dominion; man may only hold dominion if he fully understands and can assess creation. Finally, mathematics assists God’s people in fulfilling the Great Commission. It achieves this last objective not only by allowing technology to become a powerful tool in the spread of the gospel, but also as it strives “to confront false philosophies head to head…False philosophies must be confronted with robust, comprehensive, and systematic faith, a faith wide enough to speak to all of life” (p. 278). In the words of Rousas J. Rushdoony, this faith proclaims “…a gospel…as wide as life and creation, as wide as time and eternity” (p. 279).
The final portion of Nickel’s book deals with pedagogy and resources. While secular mathematics “divorces itself from the concrete, physical world” (p. xxvi), Nickel lays out a picture of what it is like to teach mathematics in its “true perspective” in which “abstract principles have been derived from concrete, physical, and scientific foundations. The power of mathematics is that its methods can be applied to these abstract principles and produce new insights that can be returned to the concrete in extremely fruitful applications” (p. xxvi). Thus, Nickel discusses, among other things, music, trigonometry, and wave motion, drawing the connections between the abstract mathematics and the mathematical language of physical creation.
Nickel concludes with a discussion of pedagogical principles and an extensive list of resources to which instructors can turn. Laid out methodically (including introductory summaries, in-depth information about the history of mathematicians and scientists as well as philosophies and worldviews, clearly articulated pedagogical objectives, text resources, a thorough timeline, a Scripture index, and questions for review, research, and discussion at the end of every chapter), Mathematics: Is God Silent? is a rich labor of love in the service of God’s kingdom. It is an invaluable book for any Christian, and especially for one who wishes to teach mathematics with purpose, understanding, and efficacy.
Mathematics: Is God Silent? answers the question posed in its title with a resounding ‘No, God is not silent!’ and is a call to vigorous action: “We need scientists and mathematicians who boldly confess, ‘How great is the Creator who has made both the mind and nature so compatible!’ We need scientists and mathematicians who see the universe, not as a mere mass of mechanistic and impersonal laws, but as the handiwork of God…May God in His mercy add to this tribe and may the reader of this book be one of them” (pp. 225-226).
As we turn our faces to the Son in our journey toward the Quadrivium, Classical Conversations wholeheartedly embraces Nickel’s understanding of mathematics and the way in which it must be taught in order to have meaning and purpose, and thereby, in order to bear fruit. Classical Conversations encourages the mastery of mathematical and scientific factual knowledge in the Foundations program and expands it at every level in the Challenge programs in order to encourage the dialectical integration of subjects and to foster the understanding of all created things as the ‘handiwork of God.’ The ultimate goal of all the Classical Conversations programs is to facilitate, through the classical Trivium, a Christian education that recognizes that “we do not live in a ‘multi-verse’ but in a ‘uni-verse’” (Classical Christian Education Made Approachable, p. 18). Proceeding through clearly defined goals associated with each stage of the Trivium, and combining that tried-and-true educational model—which is biblical in its basis (see Proverbs 24:3-4)—with a “governing biblical worldview, classical Christian students will be prepared for doxology as they ‘echo in celebration’ of God’s creation” (Classical Christian Education Made Approachable, pp. 30-31). Classical Conversations students will, by the grace of God, be equipped to continue studying the ‘handiwork of God’ through the Quadrivium.
