A Christian Mathematician's Apology

By Matt Lunsford, Ph.D.

This article first appeared in the 2020-21 edition of The Journal of the Union Faculty Forum

The idea of writing about my goal of living an integrated life as a Christian mathematician grew out of a desire to respond to G. H. Hardy’s autobiographical essay A Mathematician’s Apology, originally published in 1940. While my experiences as a mathematician are similar in many ways to Hardy, I must acknowledge that I am not a research mathematician at one of the most prestigious institutions in the world. Even so, since being a mathematician has many universal similarities, I can relate well to most of Hardy’s comments. However, one significant distinction is that Hardy was a self-declared atheist. While many may believe that this distinction makes little to no difference in the professional life of a mathematician, I disagree, and that is my main purpose for writing this essay. It is my hope that by doing so, I might encourage fellow mathematicians, and possibly even academicians in other fields who hold to the Christian faith, to pursue the integrated life.

I have always had a natural ability to do mathematics. Throughout my school years, I was very good at arithmetic, algebra, and geometry. As an undergraduate, I did not select mathematics as a major until I took my first Calculus course. There was something about that course, with its epsilons and deltas, limits, derivatives, and integrals that I found fascinating. I recall being intrigued by the mathematical notion of the infinite. That was a new idea. However, most of my undergraduate mathematics career was simply thinking that mathematics was like a game of chess: just follow the rules and get the correct result. Near the end of that time, I was introduced to the idea of a mathematical proof. This was the next new idea, and it thrilled me. By this time, I was ready to try my luck at postgraduate education in mathematics.

Something dramatic happened in my first-year graduate courses in mathematics. My professors introduced me to abstract algebra, and in particular, to an area of algebra known as Galois theory. I already knew that I loved mathematics, but I fell head over heels in love with abstract algebra. Even today, I find the subject beautiful. I believe that passion, after ability, is probably the most important quality for becoming a mathematician. Passion was and continues to be the driving force for my becoming and remaining a mathematician.

Hardy and I agree that pursuing mathematics as a career is a noble goal, assuming that you are gifted and passionate about the subject matter. As for me, a career in mathematics was further confirmed by vocatio, a sense of calling. In my early years of college, I floundered. I was wrestling with a call to ministry, but I really did not know what that ministry would be. Now, after teaching for more than 25 years, I realize that my ministry is in undergraduate mathematics education, teaching students to love the discipline that I love. My vocation has been rewarding and fulfilling, but incorporating the integrated life into my career has remained a challenge.

Circa 1996, I embarked on a journey to discover and then to live out the integrated life. I realize that I have not arrived at the final destination. As with most journeys, a guide is invaluable. I found my mentor in a most unusual place – not among the living. English language scholar and Christian writer C. S. Lewis died before I was even born. Even though Lewis was not a mathematician, I have found him to be a marvelous guide and a kindred spirit. He was a first- rate academician who sought to live a life fully faithful to Jesus. Reading Lewis convinced me that I was on the road less traveled, but that I was not on this journey alone.

Let me begin unpacking my thoughts on the integrated life. Hardy asked two fundamental questions in his essay: First, is mathematics a worthwhile pursuit, and second, why would someone become a mathematician? He dispenses with his answers to the second question rather quickly and then spends most of the rest of the essay discussing his first question. Taking my cue from Hardy, I want to ask two questions that will guide the remainder of this essay. What is mathematics? What makes a Christian mathematician different from a secular mathematician?

What is mathematics? That question has been pondered by humans for at least two millennia. First of all, the term mathematics is derived from the ancient Greek word mathematos, which literally means “that which is to be learned.” So, historically, mathematics has been associated with those areas of knowledge that were deemed worthy of study. For the Pythagorean sect, this specifically meant the natural numbers and their properties, geometry, astrology (including astronomy), and music. These four subject areas formed the original quadrivium of the liberal arts. I do not know of a universally accepted definition of mathematics, but here is my current working definition: mathematics is the discovery, creation, proof, and rigorous communication of logical theories, encapsulated within a prescribed and mutually agreed upon axiomatic system. The ultimate goal of this activity is both the acquirement of results, known as mathematical truth, and the rigorous dissemination of those same results. This mathematical enterprise, which has been operational for over two thousand years, exists, at least in part, to enhance humanity’s understanding of the created order (reality) in which we find ourselves. While my definition might sound exotic, rest assured that I am describing the same well known discipline – the one which explores the properties of right triangles and provides formulas for solving quadratic equations and so forth.

What makes a Christian mathematician different from a secular mathematician? For me, it is not the mathematics. What I call the “kernel” of the discipline is exactly the same. By “kernel,” I mean the core of the discipline as it is understood and practiced by contemporary mathematicians. The content of the papers I write for scholarly journals and the talks I give at professional meetings is remarkably similar to that of a secular mathematician. However, as I am contemplating my discipline, I feel the freedom to explore whether ideas that emerge from my Christian faith commitment might enrich my understanding of mathematics, and alternately, whether the mathematical ideas I am pondering might enhance my understanding of the Christian faith. For example, Christian mathematicians might contemplate how the mathematical concept of infinity amplifies the meaning of eternal life. They might also investigate the relationship between mathematical truth and absolute truth. This freedom, I believe, is a substantive difference between the Christian and secular mathematician, but it is not the only one.

Another distinction is the source of our motivation. Why do we, as mathematicians, continue to learn, practice, and teach mathematics? Hardy asserts that the dominant motivations for the mathematician are intellectual curiosity, professional pride, and ambition. Christian educators like Parker Palmer have offered a partial retort to this mindset (6-9). Pursuing mathematics primarily for curiosity equates to seeking knowledge for the sake of knowledge itself. Pursuing mathematics primarily for recognition equates to seeking knowledge for vanity. Pursuing mathematics primarily for utility equates to seeking knowledge for its power to control. (Hardy, who argued that his contributions to number theory were both useless and harmless, never sought to exploit his mathematical abilities in this way.) If, however, we pursue mathematics primarily for love, then we seek knowledge to heal a fallen world; that is, we seek knowledge to serve and edify others, to bring reconciliation and restoration to humanity, and also to glorify the Creator. Therefore I, and hopefully many other Christian mathematicians, strive to be motivated primarily by love.

While freedom of exploration and source of motivation are clear distinctives for the Christian mathematician, I do not believe that either is the core distinction. Christians are called to live their lives under the Lordship of Christ. This call is for an integrated life, where both piety and intellectual activity are accountable to Christ. As academicians, this means that even our scholarly pursuits should be subject to the Lordship of Christ. In the preface of On Stories, Walter Hooper, the custodian of C. S. Lewis’s works after his death, writes this about Lewis:

“Whether the reader of Lewis’s books is or is not a Christian, it ought to be said here that Lewis’s conversion just was the chief watershed in his life. There was no nook or cranny of his being that it did not eventually reach and transform” (xiv).

This provocative quote goads me to ask a question of myself. Have I allowed the Lordship of Christ to penetrate and transform all areas of life, especially that prideful area of expertise I achieved in mathematics? I find this to be the core of it all.

So the integrated life is a personal journey. It is not formulaic. One size does not fit all. The question of “how do I live an integrated life?” is not just another academic problem to be solved. It cannot be answered solely by reading the “right” books, or by asking the “right” questions, or even by hearing the “right” speakers. The answers to this question will be spiritually deeper than that. On the journey, seekers uncover who they are now and who they are becoming under the Lordship of Christ. The destination is clear: Jesus as Lord over all of my life, even over my area of expertise.

Now, let me address the elephant in the room. Practically, how does living an integrated life, being both a professional academician and a faithful follower of Christ, manifest itself in a Christian mathematician? In attempting to answer this question for myself, I will use two phrases that are often heard in Christian higher education: “redeeming the discipline" and “thinking Christianly.” First of all, does “redeeming the discipline” entail changing or altering the content of the discipline? For the discipline of mathematics, I would argue no. Altering the discipline has not been part of my calling as a Christian mathematician. I conjecture that Christians in other disciplines may respond differently to this question. However, I want to argue that “redeeming the discipline” of mathematics could have at least two meanings for the Christian mathematician.

Firstly, “redeeming the discipline” of mathematics involves reinvigorating and prioritizing certain subareas within the discipline. These subareas (e.g. algebra, analysis, probability, geometry) are categorized by the contemporary mathematical society. Just as clothes can be either in or out of vogue, these subareas have received varying degrees of importance during different periods of time. My work involves the training of future Christian mathematicians, both teachers and researchers. Realizing that both of these groups lack a broad understanding of the human story of mathematics, I prioritize exposure to the history of mathematics for undergraduates. In a similar manner, regardless of current trends, another Christian mathematician might emphasize a different subarea of the discipline, accomplishing, at least in part, the mission of Christian higher education. Thus, we have one powerful method for “redeeming the discipline.” But there is another.

Secondly, I propose that “redeeming the discipline” of mathematics entails a return to the original source and purposes of this knowledge. Hardy equated intellectual curiosity with the desire to know the truth. I would argue that intellectual curiosity alone is insufficient and will lead to, at best, an incomplete version of the truth. The missing piece is context. First of all, the ability to do mathematics is a gift from God, and this should be acknowledged in our professional lives. We can debate until the end of time whether God is the author of none, some, or all of mathematics, but we as Christians cannot deny that God is our creator. So, regardless of one’s opinion on the origin of the discipline, God deserves the ultimate credit for the existence of mathematics. Then, responding to our God-given ability, we engage in the mathematical enterprise and become stewards and co-creators of knowledge in this world. This mathematical knowledge allows humans to comprehend aspects of the creation, to make predictions about the creation, and even to engage in thoughts we believe to be similar to, yet wholly different from, the Creator. Using the gifts of ratiocination and imagination, we can prove mathematical truths not only about this created order (reality), but also about abstract, idealized worlds that exist only in our minds, all to the glory of God.

What about the phrase “thinking Christianly”? As an educator and a scholar, I want to ensure that my Christian faith impacts both my pedagogy and my scholarship. Let me begin with scholarship. Ideally, my faith commitment would both influence and inform all of my scholarly pursuits. Many academicians would cry foul at this last statement, believing that in order to preserve complete objectivity, any hint of a religious conviction must be wholly excluded from the arena of scholarly activities. C. S. Lewis, in a short essay entitled Meditation in a Toolshed, addresses this critique. Lewis asserts that there is a bias in the academy that “looking at” something (a detached observer) is always superior to “looking along” that same thing (a partisan observer). Lewis uses the imagery of standing in a dark toolshed where a beam of light is streaming through a small hole in the toolshed door. Detached observers see something when they look at the light beam (e.g. dust particles floating in the beam) but partisan observers see something quite different when they move to look along the beam (e.g. the tree swaying in the wind outside the toolshed door). Lewis concludes, “We must, on pain of idiocy, deny from the very outset the idea that looking at is, by its own nature, intrinsically truer or better than looking along. One must look both along and at everything” (God in the Dock 215). Lewis’s conclusion is obvious: complete objectivity is unattainable.

In mathematics, “thinking Christianly” necessitates both looking at and looking along the discipline, hopefully in harmonious collaboration. I won’t elaborate further on “looking at” the discipline, since this is the current academic practice. However, what exactly might “looking along” the discipline mean? Here are a few questions that have prompted discussions with my colleagues and my students.

Is mathematics eternal or a temporal human construct?
Why does mathematics require both reasoning and imagination?
Does mathematics, in any way, satisfy your longing for beauty?
Is the effectiveness of mathematics to comprehend aspects of the creation something “miraculous”?
In mathematics, is truth the same as provability?
How does mathematics enrich your understanding of order and chaos?
How does mathematics enrich your understanding of chance and determinism?

Academic papers addressing these and similar questions generally do not appear in scholarly mathematics journals. However, there are journals that publish scholarly papers addressing meta-mathematical ideas. So, in my own career, I have had academic seasons when I pursued and published primarily meta-mathematical papers and other academic seasons when I pursued and published only conventional mathematical papers.

Now, let me address pedagogy. What can “thinking Christianly” contribute to the teaching and learning enterprise? Consider the question: How does a person acquire knowledge? A biblical response would assert that knowing, at least in part, comes from abiding in a personal relationship with another being, either divine or human. In my context of higher education, that personal relationship is realized by the roles of teacher and student. Hence, I am compelled by my faith commitment to create within my classes a community of learning in which caring platonic relationships are prioritized. Most often, I will occupy the role of teacher. Yet, if it is truly a community of learning, there will be times when a student will assume the role of teacher, even though the content being shared at those times may not be from the kernel of the discipline. At all times, the members of the community should aspire to love and care for one another. The ultimate goal of this learning community is the formation of students who also will “think Christianly” about mathematics and whose primary motivation for learning mathematics will be love.

Hopefully the elephant in the room has been addressed: signed, sealed, and delivered. If not, I invite readers to join the conversation by articulating their thoughts on how to live an integrated life as academicians and followers of Christ. Hardy believed that because mathematical truths (theorems) were permanent, a mathematician, much like a painter or poet, could achieve eternal prominence from his scholarly work. Of course, the Christian mathematician is also concerned about eternity, but not in the interest of renown. I know that my legacy will not be the theorems I have proven or even the meta-mathematical papers that I have written. The legacy I desire to leave will be in the relationships I have formed, with both colleagues and students, who love God, love each other, and strangely enough, love that discipline which is called mathematics.

Works Cited

Hardy, G. H., and C. P. Snow. A Mathematician's Apology. Cambridge U.P, 1967.
Lewis, C. S., and Walter Hooper. God in the Dock: Essays on Theology and Ethics. Eerdmans, 1970.
Lewis, C. S., and Walter Hooper. On Stories, and Other Essays on Literature. Harcourt Brace Jovanovich, 1982.
Palmer, Parker J. To Know As We Are Known: Education As a Spiritual Journey. HarperSanFrancisco, 1993.

Posted Aug 19, 2021