**Authenticity**

The integration of faith, teaching and scholarship obviously flows from the mission of the institution and its holistic vision that all works and vocations relate and answer to a divine purpose. Without that institutional identity, we wouldn’t be doing this exercise.

I do not think, however, that this institutional vision is the ultimate starting point. Faith integration, particularly in the classroom, starts with relationship and authenticity. It’s about building a rapport and a kind of friendship with our students. In the context of that friendship, integration is being able to share, in word and deed, explicitly and implicitly, my full and holistic practice of mathematics.

In my experience, Canadian academic institutions teach reductive mathematics: an isolated and self- contained discipline which rarely examines its own assumptions and foundations. It is a discipline which doesn’t see itself as a spiritual activity. Even before starting at King’s, that secular reductive environment was uncomfortable to me. At the time, I had only sparse language to process my situation; therefore, this concern often remained a semi-conscious uneasiness. I remember, with joy, the rare occasions where we foregrounded the nature and purpose of mathematics.

King’s immediately appealed for the opportunity to find language for my uneasiness—to break away from the reductionism that rules academic mathematics. The task of faith integration is a welcome opportunity to be authentic with myself and my students. It allows me to address the entire reality of mathematics in a holistic vision.

In this context, faith integration cannot be artificial. It cannot be a veneer over a still-reductive ap- proach to the discipline. It can’t be a parallel existence of being Christian and being a mathematician, where I am both and express both in the classroom, but they don’t interact with each other. Integration must arise from honest questions about the activity of mathematics and those question must relate to an honest embodiment of my faith.

Integration starts with the assumption that mathematics, like all human activities, is a spiritual activity. (Throughout this document, I’ll use the term activity, but I mean it in the most general sense. Activities include going for a bicycle ride, researching mathematics, running for political office, knitting, etc.) As a spiritual activity, mathematics expresses the faith of its participants. To understand this, we need to start with faith itself.

**The Faith in Faith Integration**

Before starting on avenues and approaches to integration, I need to understand what it is that is integrated. What do I mean by faith? This starting question is perhaps the most trying part of this whole process.

I’m very skeptical of any simplistic or reductive account of faith (quite possibly due to my years of study of the axiomatic method of mathematics and its significant limitations). To integrate faith, I don’t think I should start with a text, creed or catechism and apply it to an activity. Faith is much more than a starting text, creed or catechism. But defining faith (or religion or worldview or life-philosophy) is a vexing problem.

My best intuition tells me that faith is realized in the patterns of human existence. The term refers, I think, to the complex reality of fundamental assumptions, beliefs, rules and purposes that are demon- strated in embodied human life. As such, faith is not easiliy pinned down: it is dynamic, multifaceted and spontaneous. The thing I’m trying to integrate, in itself, resists description.

This may seem to be a weak starting point, but I intend to turn this weakness into a strength. Instead of throwing up my hands at the impossibility of integrating something I can’t even clearly define, I see integration is an opportunity to realize, investigate and test faith. If faith is a complex, lived and embodied reality, then it is discovered in the context of human activity. It is found in integration.

Integration, therefore, does not start with a known and understood faith which I can apply to an activity. Instead, integration starts with the investigation of an activity to read the embodied faith implicit in the nature of my participation in that activity.

In this sense, faith is always already integrated; indeed, with a holistic vision of faith applying to all activities, it could never be otherwise. The process of faith integration is not to do the integration, but to observe the activity to discover the already-present faith therein. In the process, we certainly learn something about the activity; but we learn as much, if not more, about the faith of the participant.

What, then, are the tools of this investigation? The tools are question asked about the activity which get at the lived, embodied faith realized in the activity. I see two categories: general questions which can be asked about any human activity, and specific questions which relate to the unique character of one particular activity.

**General Questions**

If all works and all vocations have a full divine purpose, then there must be various general approaches to integration: questions which apply in a variety of activities. Some of these questions will likewise have general answers. If we subscribe to a vision where all activities can be forms of worship, we need a general understand that applies to all activities. Some of these questions, however, may have answers specific to the activity: there are different values implicit in knitting as compared to running for political office.

I intentionally included these general questions because I feel there is a pressure, sometimes, to re-do the project of integration from scratch for every activity or academic discipline . I feel that large parts of integration work can be done collectively. We need not feel sheepish that the integration approaches and conclusions are frequently similar across disciplines.

The number of these general question is likely unbounded, but I’ll present a short list of those that frequently occur to me.

- In what way does the activity embody the love that defines God?
- What are the values implicit in an activity?
- What are the ethical standards of behaviour in an activity?
- How does the activity contribute to human flourishing?
- How does the activity build peace?
- What are the idolatries of the activity? How does it seek to command and control the humans involved? Who does the activity serve?
- What is the brokenness in the activity and how it is redeemed and made new?
- How can the activity be part of the divine project to renew all things?
- What is beautiful about the activity?
- What draws people to the activity, or drives them away?
- What is creative about the activity? How does it reflect the original creation?
- What is the ultimate goal of the activity? How does it reflect divine final purposes and eschatology?
- What is transcendent or spiritual about the activity?
- How is the activity a form or prayer, meditation or worship?

**Specific Approaches**

In addition to the very important general approaches of the previous section, there should also be questions of faith integration unique to any particular activity. These reflect the particular nature of an activity. Drawn from my thoughts and experience, the following are some examples of question which are specific to mathematics (or at least to mathematics and a small set of similar activities).

- What are mathematical objects? What is their reality? Are they created? Are they subject to the fall? Are they culturally relative? Are the human inventions
- Mathematics has historically made very strong (even brazen) claims of access to truth. What is the validity of these claims? Is mathematical truth a unique kind of truth? If so, what is its status?
- Mathematicians speak about logical rigor but also about aesthetic beauty and creativity. How can a project whose standards are logical rigor be creative and beautiful? What is the interplay between logical standards and aesthetic standards in the discipline?
- Mathematics appeals to axioms in its foundations. What is the role of belief in these axioms? How are they chosen? What is the scope of application of the axiomatic method for organizing truth?
- Mathematics claims to reckon with the notion of infinity. Does it do so honestly? Can humans, who are finite beings, actually ponder the notion of infinity in a productive and real way? Does mathematics do this? How does the mathematical notion of infinity relate to the divine notion of infinity?
- Mathematics has a unique ability to (quantitatively) describe the world. Is creation made through mathematical models? What is the gulf between the mathematical description of reality and reality in itself? What is the scope of application of quantitative measurement? Can we quantify beauty, goodness, happiness, etc
- Pure mathematics is driven by classification projects for abstract structures. (I.e. what are all the possible finite simple groups.) What’s the value of classifying abstract structures? Why do we need to know this?
- Mathematics, particularly its logical foundations, has been pointed to as a bulwark of truth by certain traditions (some Platonic philosophies, some modern atheisms, logical positivism, etc). Can mathematics be a starting point for human knowledge?

**What About Answers**

The integration approaches listed above, both general and specific, were presented as questions. I haven’t given any answers—that’s intentional. Faith integration, particularly given my understand of it described above, is about finding the already-present faith in our activity. To do that, we need questions. The vast majority of my role in faith integration with my students is to present questions and to argue for their importance. In that process, I will sometimes give answers, or at least suggest answers that fit my experience. But I don’t necessarily want the students to know my answers: I want them to believe that the questions are worthwhile and use them to discover their own faith through how they participate in mathematics.

This reliance on questions circles back to my starting point: none of this integration is remotely possible without authenticity. This kind of activity can only take place in the context of relationship. To that end, the starting point of faith integration is being authentic with my students: specifically asking question that I wholeheartedly believe are important questions.

**How Is Integrated Mathematics Distinctive?**

If I claim to present a classroom or research project involving a holistic, integrative vision of mathe- matics, that holistic vision should be obvious in my classroom or my writing. This naturally leads to the question: what looks different about my mathematics?

When integration is foregrounded, the difference is obvious. If I’m taking time in class to talk about any of the questions listed above, my class becomes something different from most mathematics classes. If I write an opinion piece on integration, or take a few minutes out of a professional talk to foreground perspectives, the disctictiveness is clear. If I include a perspectival question on an assignment, students recognize that something new is happening.

Distinctiveness is much more difficult when integration is not foregrounded (which is the majority of my time doing mathematics). For the most part, my research work, my assignments, my exams, and my lecture materials look very similar to anything you would find at any other institution. What, then, have I accomplished? Any holistic vision of living faces this question: if all interaction is prayer, if all activity is worship, then most of that interaction and activity doesn’t look like prayer or worship. It looks like what everyone is already doing.

I believe this is a tension that must simply be embraced. Integration seeks to enrich and contextualize mathematics, not to destroy it. As authentic people of faith, doing mathematics, in itself, can be cele- brated. The manipulations of calculating a derivative don’t need to look somehow magically different compared to a reductive, secular setting. I don’t have to intersperse bible quotes between the lines of my proofs to make them more spiritual. A holistic, integrative vision of mathematics does the opposite: it sanctifies the prosaic practice of mathematics as a form of worship and prayer, just as it is.

The challenge of integration is to recognize a new reality: the new creation expressed in the activity of ordinary mathematics. In the classroom, the challenge is to share, honestly and authentically, this new reality in ordinary mathematics. It’s not trying to find a new, special, spiritual mathematics that looks radically different. It’s declaring that the activity of ordinary, quotidian, boring mathematics is an activity of human flourishing, a form of worship and prayer.