Mathematics Through the Eyes of Faith.
A Certain Ambiguity: A Mathematical Novel
David B. Klanderman is Professor of Mathematics and Director of Education Programs at Trinity Christian College, and Sharon K. Robbert is Professor of Mathematics and Dean of Academic Planning and Effectiveness at Trinity Christian College.
In our experience, preaching to the choir is a necessary but insufficient pedagogical strategy. At Trinity, faculty members seek to help students integrate their Christian faith with their discipline. We have found that the most effective strategy in mathematics for this faith integration issue uses both direct and indirect approaches. One such melding of approaches assigns the book Mathematics Through the Eyes of Faith in tandem with A Certain Ambiguity: A Mathematical Novel.
The preface to Mathematics Through the Eyes of Faith reminds the reader that most people consider the discipline of mathematics and matters of Christian faith to be located on parallel, nonintersecting planes. James Bradley and Russell Howell counter that “many thought-provoking questions require an understanding of both mathematics and religious perspectives” (vii) and offer ten such questions as evidence that the intersection is a nonempty set. This book explains why these questions are important and challenging and provides both the historical context and potential answers for the reader to consider.
During the past several decades, other authors have engaged similar issues with various levels of success. One provided a brief and well-written overview of rival philosophies of mathematics in the context of three significant developments of mathematics, with implications for both the discipline and underlying beliefs in certainty and truth.1 Another made a link between God and mathematics throughout history, with limited success.2 In an earlier collaborative work with colleagues, Bradley and Howell compiled a broad but helpful overview of underlying philosophical, historical, cultural, and aesthetic issues within mathematics that can engage a Christian worldview.3 Regular contributions to the intersection of mathematics and Christian faith can be found in the online Journal of the Association of Christians in the Mathematical Sciences (ACMS).4
Mathematics Through the Eyes of Faith revisits some of these issues but extends the dialogue and offers readers references for additional investigation along with discussion questions. The text was written collaboratively with a writing group of ten mathematics professors with common membership in ACMS, under the leadership of writers/editors Bradley and Howell, whose editing gave a cohesive structure and highlighted occasional cross references between chapters.
The ten “Big Questions” of the text are introduced in the initial chapter by way of a dialogue between four fictitious college students with majors in art, biology, mathematics, and religion. This creative starting point, which might have been easier to follow if the first letter of the student names and the discipline names had matched, is not continued through the main chapters of the book. Neverthe-less, the questions do provide a framework for the rest of the book. The questions range from philosophical (“How can we be sure about what we know?” or “What is truth?”) to the place of mathematics in general revelation (“Do mathematical concepts … point beyond themselves to a higher reality?”). After a brief foray into the historical context for the questions, the next eight chapters blend mathematical ideas, examples, and arguments with a Christian view of the world and the place of humans in it. Some chapters unfold a topic commonly linked to mathematics, such as infinity, dimension, chance, or proof. Others focus on issues of a more general nature but with special attention to mathematics, such as beauty, effectiveness, epistemology, and ontology. A final chapter provides a justification or apology for the overall purpose of the book.
The text contains several features that are helpful for Christian college classrooms, including the aforementioned suggestions for additional reading and discussion questions. All chapters start with a contextualizing quote; most of these are scripture passages. Other scripture references flow naturally in support of answers to the “Big Questions.” Some chapters contain text within a shaded box that augments the flow of the chapter; these boxes contain a brief mathematical biography (80-81) or provide a more detailed description of an application such as a golden spiral linked to Fibonacci numbers (148). The chapters also include a selection of interesting exercises that extend the mathematical content of the chapter.
The book’s construction process helps explain the variation in chapter density and in writing style; since the chapters are written by eight different author groups, one would expect readability to vary from one portion to the next. This is also true of the mathematical expositions. While it may be true that the previous mathemati-cal experience of the reader plays a role in ease of understanding, the density of exposition regarding fractal dimension in chapter four is likely to be a challenge to all new readers of the subject, while the pace of presentation regarding infinity and the “Hilbert Hotel” in chapter three is accessible yet thought-provoking.
The mindset and worldview of the authors are not hidden in the text but are identified from the start and reviewed periodically to keep the reader in tune with the viewing of mathematics through the lens of faith. For example, in the first chapter, the authors identify that they will follow the “broad framework histori-cally affirmed by Orthodox, Roman Catholic, and Protestant believers” (11). They go on to say that they will seek “to interpret mathematics from a faith perspective, not to create a distinctively Christian mathematics” (11; italics in original). Later, they acknowledge that enthusiasm for mathematics is not universally shared by readers, saying, “[W]hy did we bother to try to make the case that there is beauty in mathematics? . . . Well, we’re mathematics professors. We love this stuff, and we hope you will too!” (165).
Finally, it is apparent, especially from the exercises, that the audience of this book is intended to be as broad as possible among the mathematical and academic communities. Target student audiences span from those in general education mathematics classes to those completing an undergraduate mathematics major. Some exercises are creative extensions of the chapter content: “Find a triangle on the surface of a sphere whose angles add to more than 270°” (140). Others prompt additional topical research: “What aspects of Aristotle’s thought did Galileo object to and why?” (36). Repeat users of the book as a course text may need to supplement the exercises from other sources.
Although the Bradley and Howell book provides an excellent and detailed discussion of many issues at the intersection of mathematics and Christian beliefs, it assumes that the reader starts with a mindset that is either overtly Christian or open to Christian ideas. While understandable, this may limit the usefulness of the book without additional sources that deepen the reader’s understanding of alternative viewpoints. One suggestion would be to add A Certain Ambiguity: A Mathematical Novel to the reading list. Gaurav Suri and Hartosh Singh Bal wrote a mathematical novel that created a plausibly historical but fictional account of an atheist mathematician who is eventually challenged in his reliance on mathemati-cal reasoning for certainty and truth.
The authors center the story on Ravi, an undergraduate economics and finance major who signs up for an elective course, “Thinking about Infinity.” While in this course, Ravi wrestles with vocational direction and unravels a mystery involving his grandfather, Vijay Sahni, an Indian mathematician. Ravi discovers that Sahni became entangled in a controversy over religious expression and freedom of speech in a conservative town in New Jersey in the early twentieth century. The mystery unfolds when Ravi learns that a Christian judge must decide whether to recommend that the atheist Sahni be put on trial for blasphemy or be released by the governor on free speech grounds (64-65).
The novel alternates between two threads. The first thread documents Ravi’s rekindled love of mathematics through his encounters with infinity and proof. The second describes his investigation of the New Jersey legal controversy via interview transcripts of jailhouse mathematical discussions between his grandfather and the judge. In both threads, characters move from an elementary understanding of the content to a deeper acknowledgement that certainty requires a foundation. Initially, the judge is impressed by Sahni’s ability to provide mathematical certainty through geometric proofs that rely solely on a minimal number of axioms that seem beyond question. However, difficulties later arise when attempting to explain the truth of the parallel postulate and this evidentially leads to a discus-sion of non-Euclidean geometries. At this point, Sahni’s belief in mathematical certainty comes under attack.
As in Mathematics Through the Eyes of Faith, Suri and Singh Bal write about the intersection between worldview and mathematics. They introduce several additional characters who embody several other worldviews or “isms” addressed in the Bradley and Howell book. For example, a classmate of Ravi seeks absolute truth through the use of Aristotelian logic and embodies the logicism of Bertrand Russell. Other characters include a finance major who values the pursuit of wealth over the pursuit of truth, a professor who embraces the ambiguities within both mathematics and life, and a fellow student whose pragmatism overrides any need for absolute certainty. The authors also introduce several foundational concepts in mathematics, including the infinitude of the prime numbers, infinite sums, the countability of the rational numbers, different sizes of infinity, and deductive proofs within both Euclidean and non-Euclidean geometry.
The parallel plot lines of the novel make for an engaging story, suitable for readers with a mathematical background or with a mathematical curiosity. Among the students enrolled in Trinity’s senior math seminar, one remarked that it is an “entertaining book about the history of math,” including links between the present day and historical events. Another noted that the book is “valuable because of the different worldviews. It brought up questions that I never considered before in depth.” Yet another remarked that the novel is a “thought-provoking story that questions your worldview and certainty about life.” Some readers will find the different type fonts to be irritating, especially the relatively small font used for transcript entries, newspaper articles, letters, and journal entries. However, these stylistic choices delineate the different sources of information, helping the reader remember the current context within the larger narrative.
Based upon our own experiences, as well as those of our senior mathematics majors, we conclude that the novel deepens a Christian reader’s appreciation for the richness of her own faith-based perspectives on mathematics, truth, and certainty. At the same time, readers with limited exposure to other (non-Christian) worldview lenses will gain an appreciation that these different lenses exist. Equally important, readers of this book can be prompted to explore critiques of certainty while personal faith commitments are affirmed through the characters of the judge and a rural pastor introduced at the end of the novel.
The authors present the mathematics in this novel in a way that meets the needs of readers. The mathematically trained reader will appreciate the flow, ac-curacy, and detail of the mathematical content. Novice mathematicians will benefit from the scaffolding provided; the surrounding story and dialogue are engaging enough to motivate the effort by these same readers. One example explores the summation of an infinite series, complete with an initial insight containing a mathematical flaw (22) and later, a corrected version based upon partial sums (55-57). Fictitious but historically plausible written correspondence among famous mathematicians provides additional context for both sets of readers.
Both of these books are good choices for those who wish to talk about the intersection of faith and mathematics in their classrooms. Mathematics Through the Eyes of Faith could function as a supplementary reader in a general education mathematics survey class with careful choice of assigned chapters. For mathematics majors, reading selections of this book in their first year could spark initial curiosity about links between worldview and mathematics that could mature with a second reading in their senior year, after the student is equipped with intervening mathematical coursework. On the other hand, A Certain Ambiguityis an entertaining novel for the mathematically curious, but it is especially valuable as a teaching tool in counterpoint to Mathematics Through the Eyes of Faith for students with a sufficient background in both mathematics and a Christian worldview. Tandem use of the two books satisfies the necessary and sufficient criteria and hence is optimal.
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Footnotes
- Robert Brabenec, “The Impact of Three Mathematical Discoveries on Human Knowledge,” Journal of the American Scientific Affiliation 30.1 (1978): 2-6.
- James Nickel, Mathematics: Is God Silent? (Vallecito, CA: Ross House Books, 1990).
- James Bradley and Russell Howell, Mathematics in a Postmodern Age: A Christian Perspective(Downers Grove, IL: InterVarsity Press, 2001).
- Journal of the Association of Christians in the Mathematical Sciences. Accessed January 10, 2012, http://www.acmsonline.org/journal/index.html.
