Article About Ferguson

more drawn to painting. After finishing high school in 1958, he wanted to study art as well as math. He chose Hamilton Col- lege, a liberal arts school in upstate New York near where he had spent most of his childhood, where he could do both. After getting his math degree, he enrolled in a doctoral program in math at the University of Wisconsin, Madison. He paid for some of his living expenses by selling paintings. He also met and began dating an undergraduate art student, Claire. The couple married in 1963 and had their first child (of an eventual seven) in 1964. Ferguson dropped out of school for a couple of years to work as a computer programmer, then resumed his math studies. He obtained his master’s degree in mathematics at BYU and PROFILE: HELAMAN FERGUSON a doctorate in group representations—a broad area of math that involves algebra, geometry, topology, and analysis—at the Carving His Own Unique Niche, University of Washington, Seattle. In 1971, he accepted an appointment as assistant In Symbols and Stone professor at BYU. As a mathematician, Ferguson is perhaps By refusing to choose between mathematics and art, a self-described “misfit” has best known for the algorithm he developed found the place where parallel careers meet with BYU colleague Rodney Forcade. The algorithm, called PSLQ, finds mathemati- BALTIMORE, MARYLAND—Helaman (BYU) in Provo, Utah. What is unusual is cal relations among seemingly unrelated Ferguson’s sculpture studio is set back how successfully he has pursued a dual real numbers. Among many other applica- from the road, hidden behind a construc- career as mathematician and artist and the tions, PSLQ provided an efficient way of tion site. Inside, pieces of art line shelves ease with which he blurs the categories. computing isolated digits within pi and and cover tabletops. Ferguson, clad in a Math inspires and figures in almost all of blazed a path for modeling hard-to-calculate yellow plastic apron and a black T-shirt, Ferguson’s artistic works. Through particle interactions in quantum physics. serenely makes his way through the them, he has helped some mathe- In 2000, the journal Computing room. The 66-year-old is tall and white- maticians appreciate the in Science and Engineering haired, his bare arms revealing a strength artist’s craft and aesthetic. named it one of the top requisite for his avocation. And he’s persuaded per- The most striking work in the studio is a haps even more artists Function-al form. The more than 2-meter-tall, 5-ton chunk of gran- that math may not be Fibonacci Fountain at ite. When it is finished, it will stand in the as frighteningly elu- the Maryland Science entry to the science building at Macalester sive as they believe, and Technology Center College in St. Paul, Minnesota. Right now, it or even if it is out of was inspired by the is a mass of curving surfaces sloping in dif- their reach, it’s as “golden ratio.” ferent directions, its surface still jagged beautiful as any with the rough grains left by the diamond- work of art they 10 algorithms of toothed chainsaw Ferguson uses to carve might imagine. “The the 20th century. through the stone. way he has brought Meanwhile, “I’m in my negative-Gaussian-curvature together the worlds Ferguson’s artistic phase,” Ferguson says. “Say we’re going to of science and the career also developed shake hands, but we don’t quite touch. OK, arts—this is an admirable apace. When he married see the space between the two hands?” That thing,” says Harvey Claire, a painter, the two saddle-shaped void, he explains, is a perfect Bricker, Ferguson’s former struck a deal: “I get the example of negative Gaussian curvature. college roommate. floors, she gets the walls,” he Our bodies contain many others, he adds: says. He began focusing more on the line between the first finger’s knuckle Twin callings sculpture. The art department at BYU and the wrist, for instance, and where the Ferguson himself finds it hard to say which allotted him some studio space, and he SCIENCE neck meets the shoulders. calling came first. As a teenager in upstate turned out a regular stream of work. He’s The topological jargon is no surprise: New York, he learned stone carving as an done commissions for the Maryland Sci- Ferguson spent 17 years as a mathematics informal apprentice to his adopted father, a ence and Technology Center, the University professor at Brigham Young University stonemason. Artistically, however, he was of California, Berkeley, the University of CREDITS: J. MOGLIA/ 412 20 OCTOBER 2006 VOL 314 SCIENCE www.sciencemag.org Published by AAAS NEWSFOCUS St. Thomas in St. Paul, and many other insti- water to wash down the fine parti- Twisted. Braids and tutions. He has also designed small sculp- cles of stone that could otherwise knots turn up in many tures for awards presented by the Clay Math- become deposited in his lungs. For of Ferguson’s works, ematics Institute in Cambridge, Massachu- some of the work, he dons gloves including these small setts, the Canadian Mathematical Society in made of woven stainless steel and metal sculptures Ontario, and the Association for Computing a positive-pressure facemask. Machinery in New York City. A large sculpture can take sev- says Ferguson. He has worked to keep a foot in each of eral months to complete, People he interacts the “two cultures.” While at BYU, he taught working flat-out. with, new information a course each year for honors students Granite is Ferguson’s he obtains, mathematics called Qualitative Mathematics and Its favorite medium. “Math- he has had on his mind— Aesthetics. Both art students and math stu- ematics is kind of time- all of these become “part of dents enrolled: the artists looking for a less,” he says, “so incor- the design consideration.” palatable way to take in a math require- porating mathematical As an example, he cites ment, and the math students lured by the themes and ideas into geo- an architectural-scale promise of higher level mathematics. Fer- logically old stone—that’s sculpture recently installed guson delivered on both ends. He taught something that has great aesthetic outside his alma mater Hamilton concepts mathematicians don’t normally appeal to me.” He also likes the idea that his College’s new science building. The work, encounter until graduate school, such as sculptures will be around for millions or made of 10-centimeter-thick granite, cen- braid theory. Artists could relate to braids even billions of years. ters on a pair of massive disks representing as physical objects, rope or hair that can be The finished sculptures vary widely in the planets Mars and Venus. “Venus” is woven into a specific form. But students appearance. Some are delicate, with exactly 161 centimeters in diameter—the were also asked to write down an algebra to looped projections or intricate imprints, height of the average female Hamilton stu- go along with how the braid was formed— and are small enough to hold in one’s hand. dent, taken from the records of one of the a noncommutative algebra. Others are massive, meant to be touched, college’s psychology professors. “Mars” is “Some of these folks were in there even climbed on (as many children have 174 centimeters in diameter—the average because they were either afraid of or hated discovered). As a rule, they also contain male student’s height. The disks are inlaid math,” says Ferguson. At the end of the much more detail than meets the eye. “My with tiles in a pattern defined by the semester, however, “quite a few art students work generally involves a circle of ideas,” Poincaré and Beltrami-Klein models of wanted a follow-on semester— plane hyperbolic geometry. more math, more art.” Ferguson’s admirers say his artwork goes far beyond academic exercises. David Bridging Broadhurst, a physicist at the Open Univer- Ferguson, who left BYU in 1988, sity in Milton Keynes, U.K., learned about now devotes most of his time to Ferguson’s sculpture after using the PSLQ his art. For his large-scale or algorithm in his research in quantum complicated pieces, he uses mechanics. He compares Ferguson’s artistic computer programs such as renderings of math to Fournier playing the Mathematica to form and refine Bach cello suites, “giving expression to the shape he wants the finished abstract forms, whose beauty is preexistent piece to take. “With sculpture, to the interpretation, yet recreated in a you want a piece to be a unit so it widely accessible medium.” has direct impact as a form,” he For his part, Ferguson says his lifelong says. “Sculptures are compli- project to embody mathematics in mass and cated enough already.” With form is very much in the spirit of the times— computer programs, he says, and he credits technology with making it all before even putting hand to stone possible. “We’re living in the golden age of “you can walk around [the piece] art, we really are. But it’s also the golden age and see a different view; you can of science,” he says. “Today, young people touch it and reshape it to make it have seen more art and science in, say, their simpler and more direct.” first 25 years of life than anyone in the years Once the design is in place, before that.” With the collaborations between Ferguson turns to the task of computer scientists and artists, and tools for carving the stone.

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