A lot of folks believe math is boring, or terrifying, or impossibly difficult. But guess what? Mathematics isn’t just about adding, subtracting, multiplying and dividing, with a few fractions, decimals and percentages thrown in. And when we put our youth in math class, ask them to memorize the methods of counting that we learned, and then give them timed tests to see how quickly they can perform these operations, we’re doing them a huge disservice. So many intelligent and previously happy human beings end up feeling frustrated — and convinced that they will never understand math.
But there’s a broader, deeper way to view this marvelous science. And from that perspective, we’re all performing mathematical processes every moment of our lives. Because what mathematics actually entails is discovering — and communicating to others — the simple yet delightfully intricate workings of the universe. All of us can do it, because we’re already doing it. You can’t be alive without “doing math.”
And those unique individuals known as “mathematicians” are actually people who are excited by humans’ potential for understanding how the universe works, including both the world around us and the ones inside each of us. Mathematicians spend a good deal of their time stepping back from the tasks of daily life and the social interactions that most of us deem essential in order to immerse themselves in a particular aspect of human consciousness. Within the realm of quiet concentration, they’ve been able to discover — not invent — truths about how things work in our world: that the Earth is round, not flat; that the planets circle the sun, not vice versa; that nature’s patterns and relationships create beauty, efficient reproduction and sustainability; that things in nature work together, helping one another survive; and that mathematics itself is a symbolic, abstract way of understanding and communicating about things we can’t comprehend any other way.
In his book The Math Gene (Basic Books, 2000), Keith Devlin writes: “Because it is abstracted from the world around us, mathematics reflects that world, as well as the mental structure of the creatures that do the abstracting, namely ourselves. Thus, when I say that mathematics is a process of discovery, I mean it is a process of discovery both of the world around us and of ourselves as thinking beings living in that world.”
Discovery, knowing, decision-making and memory are among the mathematical skills that are learned through hands-on, real-life activities and experiential tasks, yielding a deep understanding that supports both lifelong learning and superior test-taking skills.
Take gravity, for instance. You can’t really “take” gravity, of course, because you can’t see or touch or hear or smell or taste it. But Newton’s equations deconstructing motion and mechanics enable us to “see” those invisible forces that keep the Earth revolving around the sun and cause the apple to fall from the tree.
Have you ever wondered, while traveling by plane, why this big, hefty metal object doesn’t simply fall to the ground? When you see a jet aircraft flying overhead, there doesn’t seem to be anything holding it up. Without mathematics, there’s no way you can understand this seeming contradiction of physical reality. But early in the 18th century, the Swiss mathematician Daniel Bernoulli developed an equation that, today, enables us to “see” what keeps a jumbo jet airborne. The mathematics used by both Bernoulli and Newton makes the infinitesimal visible — and measurable.
In contemporary American society, however, mathematics has become a subject to avoid. The mere mention of the word elicits groans and frowns and often stops the conversation cold. This is sad, because human beings are the only species that can understand and communicate about the unseen — about those things that lie beyond the realm of the five senses. Beauty can’t be touched or tasted, yet it sparks a powerful reaction within us. When you see (or even remember) something beautiful, your body responds in a pleasurable way.
And mathematics is a tool that allows us to unlock the beauty lying hidden within our daily routines — and therefore experience more beauty in our lives. Perhaps even more inexplicably (I say that because if you don’t understand that math is beautiful, you won’t believe me), mathematics itself, as it unfolds in one’s mind, is the most beautiful thing there is. It’s a way of literally “bringing into the light” the amazing uniqueness of every universal action. That beauty is always present, but if we don’t know how to pay attention to it, we can’t experience it. A flower displays its incredible colors and scent for its own sake (to attract those creatures that will spread its pollen around and thus help it procreate), yet bees and butterflies and hummingbirds — and yes, even humans — can still find delight in the enticement of it.
I don’t know how the bee or the flower feels, but I know that when I discover something new — whether it’s a thought, a skill, a new place, a new friend, or a new way of thinking about something — I feel a sweetness inside that I want to share with someone. (Actually, I do know that bees dance for their community to show them where to find the best pollen.) If you find a new recipe, for example, your family and friends aren’t likely to get too excited merely hearing you describe how it tastes: You have to cook it and let them find out for themselves.
Of course, part of the reason cooking is enjoyable is that it allows us to anticipate future gratification: pleasing our own taste buds. But it also gives us a chance to share something wonderful with another human being. When we sit down and eat together, the recipient of our hospitality is experiencing both the taste of the food and the joy of an opportunity for deepening friendship. There are also subtler pleasures: remembering the internal tingles that accompanied the discovery of the recipe, knowing that we can bring an abstract notion of food into tangible existence, and deciding to share the results with someone else.
All these skills (discovery, understanding, acting on our awareness, knowing how to replicate an outcome from written instructions — or even enhance it, deciding to share it, and remembering the experience later) are essential aspects of mathematics, based on the mathematical workings of the human brain. This is what enables us to bring abstract symbols into tangible form. The recipe (abstract formula) is not edible; the meal (the result of mathematically applying the formula) is.
Similarly, when I discover a new way of understanding anything in the universe, I need to be able to express it mathematically if I want to be precisely understood. When I try to tell someone about my ideas in words, they fall flat and are often easily dismissed — the person has “missed the point.” Get it? A point is a mathematical term for something so infinitely small that it doesn’t exist, so of course you “miss the point.” But in the next instant, you can “get the point.”
How is that possible? Call me and I’ll show you the math of it — and you may feel as joyful as I always do when I contemplate such wonders. You are a mathematical genius — and I can prove it!
[Joy Harmon owns the Swan Educational Center, Regional Center for Family Learning (4 Eagle St. in downtown Asheville; 252-8215).]