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Tag: art

Anyone Can Be a “Math Person”

Dr. Francis Su, a mathematician and professor at Harvey Mudd College and the author of “Mathematics for Human Flourishing,” wants you to know that math can be beautiful. As these “infinitely quartered” squares show, 1/4 + 1/(42) + 1/(43) + … = 1/3. Image attribution: Tdadamemd, via Wikimedia Commons, under Creative Commons CC0 1.0 Universal Public Domain Dedication

Francis Su, Ph.D., visited Duke to talk about math. He began by talking about art.

Su, a mathematician and professor at Harvey Mudd College, displayed “Hope,” an 1886 painting by George Frederic Watts. He asked the audience to look at it, really look at it, and think about what’s happening in the painting. At first glance, it shows a blindfolded woman holding a wooden object. She seems to be in pain. But the more time we spend looking, the more we notice. We might notice that there’s a single star above her. We might notice that the wooden object is a lyre with only one string left attached. We might notice, too, that the woman is plucking that final string and straining to hear its music. 

If we take the time to explore the history of the painting, we might learn that Martin Luther King, Jr., talked about the same painting in a sermon. Su quoted a line from that sermon: “Who has not had to face the agony of blasted hopes and shattered dreams?” We find beauty in art, and often we find it relatable as well. Art invites us to look closer, to wonder, to feel, to ask questions, to imagine.

“Why,” Su asks then, “don’t we approach mathematics the way that we approach art?”

Professor Francis Su’s book, “Mathematics for Human Flourishing.”

Whether we consider ourselves “math people” or not, we rarely if ever hear mathematics discussed as an affirmation of human virtues and desires—love, beauty, truth, the “expectation of enchantment.” Su wants to change that. In his book “Mathematics for Human Flourishing” and in his talk at Duke, he envisions mathematics as beautiful, inclusive, and accessible to anyone.

Along with the painting “Hope,” Su’s first slide shows a quote by Simone Weil: “Every being cries out silently to be read differently.” Simone Weil, according to Su, was a “French religious mystic” and “widely revered philosopher,” but she also had a deep interest in math. Her older brother, André Weil, was an influential mathematician whose mathematical achievements often overshadowed her own. In a letter to a friend published posthumously in the book “Waiting for God,” Simone Weil wrote: “I did not mind having no visible successes, but what did grieve me was the idea of being excluded from that transcendent kingdom to which only the truly great have access and wherein truth abides.” Su sometimes wonders how Simone’s relationship to mathematics would have been different if André had not been her brother. Again, “Every being cries out silently to be read differently.” According to Su, when Simone Weil speaks of “reading” someone, she means “to interpret or make a judgment about them.”

Su has a friend, Christopher Jackson, who is an inmate in a high-security prison, serving a thirty-two year sentence for involvement in armed robberies as a teenager. When you think about people who do math, Su asks, would you think of Chris?  “We create societal norms about who does math,” and Chris doesn’t fit those norms. And yet he has been studying mathematics for years. After studying algebra, geometry, trigonometry, and calculus while in prison, he sent a letter to Su requesting help in furthering his mathematics education. The two men still correspond regularly, and Chris is now studying topology and other branches of mathematics.

“Every being cries out silently to be read differently.”

Why do math in the first place? Just as you can take your car to a mechanic without fully understanding how it works yourself, we might think of math as “only for the elite few” or perhaps as “a means to an end,” a tool “to make you ‘college and career ready.’” Su sees it differently. He views math in terms of human flourishing, “a wholeness of being and doing.” He points to three words from other languages: eudaemonia, a Greek term for “the overarching good in life”; shalom, a Hebrew word often used as a greeting and roughly translated as “peace”; and salaam, an Arabic word with a similar meaning to shalom.

The pattern on Romanesco broccoli is a fractal, common in both math and nature. Image credit: Francis Su

“What attracts me to music,” Su says, “isn’t playing scales over and over again.” But once you “experience a symphony,” you might see the value in playing scales. Can we learn to think of math the same way? Here, Su quoted mathematician Olga Taussky-Todd: “The yearning for and the satisfaction gained from mathematical insight brings the subject near to art.”

Beauty and awe probably aren’t the first words that come to mind when most of us think of math, but Su believes math can unlock “transcendent beauty.” He references a quote by C.S. Lewis: “the scent of a flower we have not found, the echo of a tune we have not heard, news from a country we have never yet visited.” That is what math at its best can do for us. It can help us see the big picture and realize that we’re “just scratching the surface of something really profound.”

“Math is not a single ‘ability,’” Su says. “In reality, math is a multi-dimensional set of virtues.” When learning or teaching math, we often focus more on skills like recalling facts and algorithms, factoring polynomials, or taking a derivative. But Su believes more important lessons are at play: virtues like persistence, creativity, a thirst for deep knowledge, and what he calls the expectation of enchantment. And, he says, employers are often much more interested in virtues than in skills. “If you want to be really practical about this—and I don’t, with mathematics, but if you do—then it’s actually the virtues that are more important than the skills,” Su says.

One basic human desire that Su believes math can help fulfill is the desire for truth, which, in turn, can help build virtues like a thirst for deep knowledge and the ability to think for oneself, which can help us figure out what’s true instead of just blindly trusting authorities. “Truth is under attack,” Su says. “Misinformation is everywhere.” Su wants to teach his students “to think, to be ‘that person who doesn’t need to look at the Ikea instructions.’” But he also wants them to view math as more than just a means to an end. “It’s my responsibility to help my students remember the beauty” in math and to understand that their dignity as human beings isn’t dependent on their grades.

Along with truth and beauty, he believes math can and should bring opportunities for exploration and discovery. “My role isn’t to be a teacher,” he says. “My role is to be a co-explorer.” He recalls his own excitement when he first saw a Menger cube, or Menger sponge, cut along its diagonal. The resulting cross-section is beautiful and, yes, enchanting. “What would it look like for classrooms to be like that?” During the pandemic, Su started adding more reflection-focused questions to his exams, questions like “Consider one mathematical idea from the course that you have found beautiful, and explain why it is beautiful to you.” Even more traditional math questions can be phrased in an “exploratory” way. Su gives the example of a question that asks students to make two rectangles, one with a bigger perimeter and one with a bigger area.

A visual representation of Nicomachus’s Theorem.
Image from Cmglee, via Wikimedia Commons, licensed under Creative Commons Attribution-Share Alike 3.0 Unported.

Another desire or virtue important in the field of mathematics is justice. Su wants math to be accessible to all, but not everyone has had positive experiences with math or feels like they belong there. As an analogy, Su talks about receiving dishes from a “secret menu” when visiting certain Chinese restaurants with friends who are fluent in Chinese. When he goes there on his own and requests the “secret menu,” however, he is sometimes turned away or told that he wouldn’t like those dishes. “Are people side-by-side in the same restaurant having different experiences” in math, too? “Who are you to say they do or don’t belong in mathematics?”

Even Su himself hasn’t always had wholly positive experiences in math. One of his professors once told him he didn’t “have what it takes to become a successful mathematician,” and he almost quit his Ph.D. program. Instead, he switched to a different advisor who had encouraged him to stick with it. Meanwhile, he surrounded himself with people who could remind him why he loved math. Math as a field can be competitive, but “if you think of mathematics as human flourishing… then that’s not a zero-sum game anymore.” 

In Su’s words, “we’re all math teachers” because “we all pass on attitudes about math to others.” He says studies show that parents can pass on “math anxiety” to their kids. But Su encourages people to “believe that you and everyone can flourish in mathematics.” Simone Weil. Christopher Jackson. And you. 

Who will you read differently?

Post by Sophie Cox, Class of 2025

Combining Up-Close Views of Science, Nature With the Magic of Light

Zinnia stamen by Thomas Barlow, Duke University

Thomas Barlow ’21 finds inspiration in small everyday things most people overlook: a craggy lichen growing on a tree, a dead insect, the light reflected by a pane of glass. Where we might see a flower, Barlow looks past the showy pink petals to the intricate parts tucked within.

The 20-year-old is a Duke student majoring in biology. By day, he takes classes and does research in a lab. But in his spare time, he likes to take up-close photographs using objects he finds outside or around the lab: peach pits, fireflies. But also pipettes, pencils.

A handheld laser pointer and flitting fireflies become streaks of light in this long-exposure image in Duke Forest. By Thomas Barlow.

Barlow got interested in photography in middle school, while playing around with his dad’s camera. His dad, a landscape architect, encouraged the hobby by enlisting him to take photos of public parks, gardens and playgrounds, which have been featured on various architects’ websites and in national publications such as Architecture Magazine. But “I always wanted to get closer, to see more,” Barlow said.

In high school he started taking pictures of still lifes. But he didn’t just throw flowers and fruit onto a backdrop and call it art. His compositions were a mishmash of insects and plants arranged with research gadgets: glass tubes, plastic rulers, syringes, or silicon wafers like those used for computer chips.

“I like pairing objects you would never find together normally,” Barlow said. “Removing them from their context and generating images with interesting textures and light.”

Sometimes his mother sends him treasures from her garden in Connecticut to photograph, like the pale green wings of a luna moth. But mostly he finds his subjects just steps from his dorm room door. It might be as easy as taking a walk through Duke Gardens or going for one of his regular runs in Duke Forest.

Having found, say, a flower bud or bumblebee, he then uses bits of glass, metal, mirrors and other shiny surfaces — “all objects that interact with light in some interesting way” – to highlight the interaction of light and color.

“I used to be really obsessed with dichroic mirrors,” pieces of glass that appear to change colors when viewed from different angles, Barlow said. “I thought they were beautiful objects. You can get so many colors and reflections out of it, just by looking at it in different ways.”

In one pair of images, the white, five-petaled flowers of a meadow anemone are juxtaposed against panels of frosted glass, a pipette, a mechanical pencil.

Another image pair shows moth wings. One is zoomed in to capture the fine details of the wing scales. The other zooms out to show them scattered willy-nilly around a shimmering pink circle of glass, like the remnants of a bat’s dinner plate.

Luna moth wings and wing scales with dichroic mirror, Thomas Barlow

For extreme close-ups, Barlow uses his Canon DSLR with a microscope objective mounted onto the front of a tube lens. Shooting this close to something so small isn’t just a matter of putting a bug or flower in front of the camera and taking a shot. To get every detail in focus, he takes multiple images of the same subject, moving the focal point each time. When he’s done he’s taken hundreds of pictures, each with a different part of the object in focus. Then he merges them all together.

At high magnification, Barlow’s flower close-ups reveal the curly yellow stamens of a zinnia flower, and the deep red pollen-producing parts of a tiger lily.

“I love that you can see the spikey pollen globules,” Barlow said.

Stomata and pollen on the underside of a tiger lily stamen, by Thomas Barlow

When he first got to Duke he was taking photos using a DIY setup in his dorm room. Then he asked some of the researchers and faculty he knew if there was anything photography-related he could do for their labs.

“I knew I was interested in nature photography and I wanted to practice it,” Barlow said.

One thing led to another, and before long he moved his setup to the Biological Sciences building on Science Drive, where he’s been photographing lichens for Daniele Armaleo and Jolanta Miadlikowska, both lichenologists.

“A lichen photo might not seem like anything special to an average person,” Barlow said. “But I think they’re really stunning.”

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