Augustine was one of the first to suggest that numbers exist eternally in the mind of God, an idea that proved more Platonic than Christian. Nevertheless, at first glance, it’s hard even to make sense of what an alternative description of the ontology of numbers could be. One can’t trek across the world to discover the number one, hiding in a cave like some long-buried fossil. The most common alternative suggests that numbers are creations of our own minds, perhaps ideally expressed as primeval sets (or so one theory goes). This seems to imply that numbers exist only in the human mind. Yet this suggestion seems just as absurd as discovering the number one in a cave. If numbers exist only in the human mind, then why is it that we can all agree on their meaning? If this is the foundation of numbers, then perhaps it’s no alternative to Augustine’s theory after all. Perhaps in this case thinkers in the Augustinian vein, like Descartes and Berkeley, would be right: if numbers do exist in our minds, it’s because God put them there, copies of the eternal numbers in God’s own mind.

My continued search for the foundation of the math superstructure didn’t yield straightforward answers, but it did make the building a lot more intriguing. As I reflect on my studies and compare them to my journey of faith over the years, I’ve noticed that I spent my childhood and early adulthood in a similar search for foundations of faith. For a long time I thought I’d found the answer in the resurrection of Jesus. Like the numbers one and two, Jesus’ death and resurrection seemed as sure a foundation as any for the construction of the Christian faith. Scripture seems to imply as much: the stone that the builders rejected has become the cornerstone.

I was about seven when I asked my parents, “Did Jesus really live on this earth?” When they replied in the affirmative, I was awe-struck. Jesus was a real person in history. Having read the stories about him in the New Testament, this baffled me. Later, I was quickly persuaded by something like C.S. Lewis’ “Liar, Lunatic, or Lord” argument, and frankly I didn’t understand how anyone could think otherwise. It seemed as easy as one, two, three. And from there, as with mathematics, it seemed everything else would come for free. If Jesus died and rose from the dead, then he was Lord; he was right. And if he was right, then one had no real choice but to trust his Scriptures, the Old Testament, however bizarre they might be. And since history had more or less proven that the New Testament was the best witness to Jesus we have, why not include it in the canon, too? From here one can explore historical and systematic theology; just as importantly, one can become acquainted with a church, begin to practice faith, and in general live as a Christian. In this way the resurrection of Jesus was like the foundation of a house. We may quibble about how to furnish this or that room, but that’s not going to stop us from building. Working from the single fact of Jesus’ resurrection seemed as elegant and sure as any mathematical foundation could be.

Not even my philosophy of math course at the University of Edinburgh changed this basic outlook for me. Instead, the intellectual earthquake came in a one-off conversation with my topology professor back on the other side of the Atlantic.

“How do you make sense of whether math is true?” I asked him. He responded, “I think of math less in terms of truth and falsehood than in terms of art.” The rest of his response made his perspective clear: the search for absolute truth in math was a fool’s errand; one would be better off to work as a mathematical artist in pursuit of elegance and beauty.

I didn’t know what to make of his response. But it stuck with me. As I look back at the conversation, I realized it was one moment in a process that slowly changed my epistemology of math and faith alike. Looking back at my studies, what I notice is that, despite its apparent objectivity and sure-footedness, in practice math works a lot like other fields, including theology. Mathematics doesn’t happen in an armchair or in an empty and desolate room, but in a community of practice. After all, the mathematical imperative, prove it, is never meant to imply that anyone could prove it outright or in a vacuum. Instead, this is the task: given the axioms we’ve agreed upon, demonstrate logically that the conclusion follows. In other words, prove it to us, your fellow mathematicians. And at that point, of course, aesthetics assumes paramount importance. The best proofs do turn out like works of art. They are called simple, elegant, beautiful. The resulting picture can indeed take your breath away. In nearly every branch of mathematics, only a handful of axioms has generated a breathtaking amount of math. While to my knowledge consolidations of the field (like the “Theory of Everything” in physics) remain elusive, the elaborate skyscraper of mathematics leaves me in as much awe today as it did when I began college.

While this communal framework may disappoint those in search of absolute truth, it illuminates the function of doubt. On the dull end of the spectrum, a mathematician could doubt a particular proof, identifying an error in its reasoning or ambiguity in its form. More broadly she could wonder whether a more elegant construction of the proof exists that more beautifully illustrates the result. But mathematical doubt can function even more creatively. Some brilliant mathematicians over the years have served as something more like meticulous building inspectors, using accepted axioms to generate outlandish results with the goal of making the mathematical community wonder whether and where the whole construction took a wrong turn. (One need only consider the Banach-Tarski paradox to get the idea.) Such exercises aren’t merely cynical or deconstructive; they can invite the collective to go back to the drawing board, and wonder whether such a strange result implies that we’ve been using the wrong set of axioms, and what the alternatives might be.