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Barack Obama went full math in Brooklyn in 2013.
THE REAL BEAUTY

Two new books will transform your everyday understanding of math

By Ephrat Livni

Perfectly smart adults feel intimidated by numbers and aren’t ashamed to say, “I hate math.” Two new books could help change that by making the dreaded topic relevant and accessible to naturalists, artsy types, the philosophically inclined, and committed calculators alike.

Both Math Art: Truth, Beauty, and Equations, by Stephen Ornes, and Eight Lessons on Infinity: A Mathematical Adventure, by Haim Shapira, illuminate an old lesson your math teachers probably tried to convey when you were a kid: Math dominates our lives even while we try with all our might to ignore it.

Creative works inspired by math

In Math Art, released in April, science writer Ornes examines creative works inspired by math. It’s an aesthetically pleasing book with a delightfully tactile cover and satisfyingly thick and glossy pages that make it as fun to flip through as a fashion magazine. Chapters are dedicated to different concepts like pi, the golden ratio, equations in nature, and hyperbolic geometry. All of which may sound scary to the uninitiated but gain appeal when illustrated through sculpture, crochet, and painting.

As Ornes explains in the introduction, math art isn’t new. Since ancient times, humans have visualized math in creative works. He argues that what is new is the mutual recognition that mathematicians and artists now show each other, increasingly gathering together at events dedicated to the intersection of aesthetics and numbers. “This is art by way of math and math by way of art, beauty at the crossroads,” Ornes writes.

His exploration begins with pi, the irrational mathematical constant 3.14159, plus some, ad infinitum. Pi, the ratio of the circumference of a circle to its diameter, represents mystery itself. Because the sequence never repeats, pi hints at the vastness of the universe. “It speaks to a world without bounds, since its digits go on forever,” Ornes explains.

Pi is used for calculations in math and physics, and employed by math artist John Sims to make music, videos, drawings, paintings, quilts, clothing, and stories. Sims created and taught a math curriculum for students at the Ringling College of Art and Design in Sarasota, Florida, and has spent much of his career at the intersection of math and creativity. In Ornes’ book, he explains how he’s also used this fascination to connect with other people he might not otherwise meet, such as the Amish quilters who joined him to make pi quilts with each colored panel representing a number in the mathematical sequence.

Choose it all

Stony Brook University
Umbilic torus: math in stone and bronze at Stony Brook University in New York.

In a chapter entitled “The Consequences of Never Choosing,” Ornes examines the sculptures of Helaman Ferguson, who makes math art designed not just to be admired from afar but to be physically explored. Ferguson was warned at an early age to separate his passion for making things from his love of numbers. He was a math professor for 17 years at Brigham Young University in Provo, Utah, where he helped develop a new algorithm that finds the relationship between numbers. He refused to choose between math and art and ultimately reconciled the two fields (which he never saw as separate) in massive granite works shaped into graceful multi-ton toruses—a twisted donut-like shape—and more.

His designs highlighting the relationship between negative and positive space are based on mathematical considerations. For Ferguson, the goal is to engage people physically and intellectually. He delights in the notion of kids climbing his sculptures, getting inside, and bringing them to life through tactile interaction.

Daina Taimina
Hyperbolic geometry in craft.

Ornes also shows the work of Daina Taimina, “a visionary pioneer in crochet.” Taimina visualizes abstract calculations through craft.

As Ornes puts it, “Some people crochet hats and scarves; others produce thick sweaters and warm blankets, fuzzy smartphone cases, and stuffed animals. Taimina can do all those things, of course. But over the last two decades, she’s earned fans and followers among craftspeople and mathematicians alike for decidedly less practical pursuits; fascinating, multicolored, soft, warm floppy blobs built according to the rules of hyperbolic geometry.”

Taimina’s works are all about curvature. She began exploring math through craft in the 1990s when she was assigned to teach a hyperbolic geometry class at Cornell University in Ithaca, New York. As a student, Taimina loathed the topic and hoped never to encounter it again. When she brushed up again to teach it, she realized that abstract concepts could be rendered visually and become much more comprehensible through crochet. She took to demonstrating how curvature works in space by crafting models for students. Her approach has since spawned a whole math craft movement. To Taimina this has been amusing: She was warned as a child that she had no artistic talent and should just focus on math for which she had an obvious aptitude.

Ornes’ book is as much about breaking false barriers between seemingly disparate topics as it is about math and art. The artists he features have all ultimately unified and enriched their fields by refusing to choose.

Grab a pencil

In Eight Lessons on Infinity—released in April—Shapira, an Israeli author and math, psychology, and philosophy professor, works with a related theme. He contends that math is fun and accessible and is determined to bring mathematical thinking to the masses. The fact that we choose to see ourselves as math types or art types is a mistake, Shapira argues, and his book shows that solving problems with numbers is an entry way to philosophical exploration.

Unlike Ornes’ book, Shapira’s text is chock-full of math problems he challenges the reader to solve, all with the goal of attempting to make sense of infinity (which can’t really be conceived by anyone). Shapira avoids frightening formulas, walking readers through the questions gently. It’s a funny, playful work, best read with a notebook and pencil nearby as he is not shy about making readers do the math.

The problems can be challenging (this reader did not manage to solve them all) but the discussions are amusing and illuminating. Shapira offers a history of math, stories about great mathematicians, jokes, and an encouraging tone that really does make it easier to contend with math.

To explore the topic, with all its challenges and abstractions, is to embrace the universe’s greatness, to make sense of the real and explore the mysterious, to dip our toes in the infinite and recognize that many of our limits are self-imposed. Luckily for us, with these works to guide us, we don’t have to go on this bold adventure alone.