By my son’s bedside is an enchanting illustrated volume called The Quiet Book, featuring silent scenes from a teddy bear’s life. My son and I love reading it as a calming activity, because it’s a meditative reflection on the meaning of quiet.

Not all quiets are the same. For instance, you can be “hide-and-seek quiet” (depicted by the teddy bear hiding from a companion), or “coloring in the lines quiet” (our bear concentrating, with crayons), or “right before you yell SURPRISE! quiet” (our bear anticipating, at a party), or “first look at your new hairstyle quiet” (our bear contemplating his reflection at the barbershop). Quietness presents as silence, but it is really an inner state of the soul with varied manifestations.

In a similar way, joy is an inner way of being, and comes in many forms. It may sometimes present as happiness—like the unbridled delight of a toddler squealing in a swing—but, as many writers and thinkers have described, it runs deeper than happiness, which can be fleeting. Joy is more enduring, like the satisfaction of spending time with a lifelong friend.

As a mathematician, I often speak of the joy that math can bring. This strikes most ears as a strange sentiment, even an oxymoron. Math, for many, has been a source of boredom, or worse, anxiety. It conjures drudging memories of memorizing arithmetic facts or algebraic formulas, without enjoying any deeper understanding.

Devoid of joy, though, I wouldn’t call that math at all. Just as literature is more than the grammar or the sentences that comprise it, mathematics is more than the logical rules or the formulas that summarize its truths. Literature captivates us because words convey meaning, and stories move us. Similarly, mathematics can enthrall us because symbols carry meaning, and true understanding evokes feelings of joy. Indeed, joy is central to the mathematical experience. If I were to write a Joy Book to parallel my son’s Quiet Book, math would show up on all of its pages.

For instance, such a book might begin with “toddler-in-a-swing joy.” That’s the adventurous pleasure a child feels as their stomach drops, a gentle breeze rushes past their face, and they squeal in delight at the sensation of flying. I hear the same joyful exhilaration in my 5-year-old son when I count whole numbers—at first correctly and then out of order—and he chuckles in protest. Or, when we play “the opposites game” (what’s the opposite of a given word?) and I ask him for the opposite of “kleenex.” His response, in giggles, shows me that he thinks we’re doing something bold and daring and maybe even forbidden. He knows that I’m playfully messing with him, and yet he still works to formulate a response. He says “sneezing,” and we all have a good laugh. Things that don’t seem to have opposites, actually do! So it won’t be long before we talk about negative numbers, and his stretched imagination now has a way to embrace the new idea.

At his age, my son has also experienced a thrill that might appear in a Joy Book as the “completion-of-a-puzzle joy.” This is the satisfaction he feels after working on a Lego project, studiously following a 100-page instruction book to produce a gloriously intricate model car. That joy comes after much labor, and it is because of this toil that he experiences a euphoria that is correspondingly longer and more enduring. Perhaps you’ve felt this too, after finishing a crossword puzzle or playing a game of Sudoku. It’s the feeling of winning, without being in competition. Notably, your success is not diminished by, nor does it tarnish, the success of others. The winning is both a feeling of accomplishment as well as the prize at the end. That Lego work resulted in something beautiful to behold! That crossword puzzle had a hidden surprise in it, spelled out by answers to several clues! You are trained by the prizes to expect that each new puzzle will bring a similar reward. Unspoiled mathematical joy is like this joy. It follows the hard work of thinking, often resulting in a glorious solution. Not every problem yields such elegance, but glimpses from time to time keep you coming back for more. Such joy is not threatened by the success of others; in fact, you find camaraderie and community with those who scaled the same mountain and beheld the same beauty.

My son has been asking lots of “why?” questions lately. He seems to relish them, which I link to a more subtle form of joy that one might call “chewing-on-an-idea joy,” or contemplative joy. He takes pleasure in asking the same questions over and over, even after I’ve answered them multiple times. “Why does ice float?” “Why does gravity cause things to fall?” Maybe he enjoys hearing me repeat my answer—affirming the truths of the world, like a catechism. Or maybe he likes to see me squirm to answer his question in different ways. I can’t be sure. But he clearly enjoys chewing on ideas. Philosopher Thomas Aquinas suggested that human beings delight in contemplation because we are rational beings, so we desire to know and seek after truth. Furthermore, he says: “more delightful still does this [knowledge of truth] become to one who has the habit of wisdom and knowledge, the result of which is that he contemplates without difficulty.”¹ By this he implies that contemplative joy becomes more available to us the more practiced we are at it. Thus, my son peppers me with a creative variety of “why” questions because for him it is both a source of, and a continued practice of, joy. Similarly, mathematical thinkers, who are practiced at the joys of contemplation, find great delight in continued investigations. They have learned to crave the exercise of the mind. Asking “why” has become second nature.

Aquinas further emphasizes that contemplative delight also follows from the quality of its object, which suggests that our Joy Book should make space for
“beholding-beauty joy.” Picture a teddy bear savoring a spectacular sunset the way that my son beholds Lego creations—with wistful wonder. Surely every person has felt this longing: for a striking piece of art that takes our breath away, for a painting that captures an ineffable feeling, for a person who is our beloved. An object of beauty makes us look closely, and if it has depth, it holds our gaze. We are drawn to study it, because with each look we see something we didn’t see before. Its richness is never ending, timeless. Poet John Keats got it right when he said, “A thing of beauty is a joy for ever.”² Mathematics, too, is like this—it is the joy of grasping enduring truths, whose beauty unfolds in layers and whose depths yield only to persistent contemplation.

The most poignant page in our Joy Book is the one I’d call “painful joy”—like the emotions my son felt about the recent loss of a favorite stuffed animal. His pain was mitigated by the thought that his prized stuffie might now be enjoyed by another child. But painful joy does not necessarily involve sorrow. As the writer C.S. Lewis explained, a telltale sign of this joy is the yearning. Lewis described this joy as “an unsatisfied desire” and “distinct not only from pleasure in general but even from aesthetic pleasure. It must have the stab, the pang, the inconsolable longing.”³ This is the longing we’ve been discussing—the kind that draws us to beauty. Even in mathematics, one encounters it. When I see the same beautiful pattern arise in many places, it’s like an echo of a deeper truth that I have not yet fully understood. I yearn to grasp it, to know it fully. A grown-up version of the Joy Book might call this transcendent joy: a painful longing that anticipates a joyful resolution.

And then, that resolution might have its own page in the Joy Book—an “aha! joy.” This is the joy of understanding, like when a mystery gets explained and everything makes sense. It might not be instantaneous. It could be a slowly growing understanding over time, unfolding in stages, each more revelatory than the last. And an “aha!” moment may still be tied to a longing or a hint of some greater transcendent truth, not yet revealed, causing us to ache for something more. Math is like that, too. As a triumphal project of human ingenuity to grasp the divine order, mathematics is full of this kind of joy, and it is a joy that we should all hope to experience.

So when people think of math as a bunch of things that a calculator can do, they have a crucial misunderstanding. A calculator can’t do math, it can only calculate. Sure, an AI (an artificial intelligence) can do more. But to speculate whether it will someday reason like a human being is to miss a broader point—that by outsourcing our thinking to an AI, we lose something valuable for human flourishing: our own ability to experience joy, to have “aha!” moments that give life texture and richness.

Too many people see math as cold and austere, divorced from human virtues and devoid of the adventurous pleasure, deep satisfaction, contemplative rumination, and the expectant longing that its joyful adherents know. It’s no wonder then, that math is used these days in ways unmoored from deep reflection on its responsible use. It’s just a tool for sorting us and dividing us, rather than a way to bring us together.

That’s why I would end the Joy Book with “sharing-the-joy joy.” This is an outward-facing joy that dignifies others, that shares our bounty with the people around us. I want my 5-year-old to realize that when we experience the delights of joy—whether it’s completion-of-a-puzzle joy or beholding-beauty joy or “aha!” joy—we should want it for others too. I want him to understand what an old Swedish proverb captures well: “A shared joy is a double joy.” I want him to see that the fruit of introspective contemplation is not only a greater grasp of truth and beauty, but also a greater responsibility and care for the people around us.

Math can be a vehicle for a joy that uplifts us and dignifies our neighbors. We need a Joy Book that can remind us of this in the increasingly technological world that my son will inhabit. My earnest hope is that he’d find math on every page of the Joy Book, and so find joy on every page of a math book.