Helaman Ferguson's sculpture blends the artistic, mathematic

The marriage of two disciplines, mathematics and art, may seem an unlikely union given an artist’s innate desire for free expression. Meet Helaman Ferguson, whose sculpture is known for its root in mathematical design.

Ferguson, of North Laurel, recently completed a massive undertaking: a 2 1/2-story, 9-plus ton bronze and granite sculpture, Umbilic Torus SC. Commissioned by the Simons Foundation, a private institution committed to the advancement of science and mathematics, the torus is being donated to Stony Brook University, in Long Island, N.Y.

Ferguson, 72, who holds a doctorate in mathematics, designed umbilic torus, a three-dimensional doughnut-shaped figure with a single edge. The edge travels around its surface three times before returning to its starting point. He celebrates his 1970s mathematical brainchild by creating it in physical form, sculpture. His first bronze torus was exhibited at a computer art exhibition in 1989 at the Computer Museum in Boston.

"Math is my design language, and my inspiration is in observation,” says Ferguson. “Anything, or anyone, I see may turn up as art."

Patricia Weisenfeld, vice president of Family Giving at the Simons Foundation, says the sculpture’s allure lies in its rich mathematical detail. “With an intrinsic appeal to differential geometry, the Umbilic Torus displays the notions of curvature — an area of keen interest for mathematicians, physicists and artists.”

Dual nature

To understand Ferguson’s dualistic approach, it is helpful to know his earlier years. Orphaned in childhood, he was adopted by an Irish immigrant in upstate New York. Young Helaman grew up with a natural proclivity for art and science, with his biological parents both based in art, and a familial background in science. His adoptive father was a carpenter and stonemason by trade. From him, Ferguson learned to work with his hands in an old-world style with earthen materials.

In school, Ferguson found a kindred spirit. “I had a really great math teacher in high school who also liked art and appreciated my dual nature. When I was raised, parents would say, ‘If you can do science, do science, not art. Everyone knows an artist will starve.’ But that’s not true,” he continues. “We are living in a golden age of science, but it’s also a golden age for art.”

Adult life has been kinder to Ferguson.

Forging his own path, he created sculpture and theorems at Hamilton College, a liberal arts school in New York. He taught math and earned his doctorate from the University of Washington, Seattle, in 1971. Later the same year, he and his wife, Claire, moved to Utah, where he continued to teach math and she studied art at Brigham Young University. The couple raised their children — seven in all — while Ferguson was tenured at BYU for 17 years.

In 1977, during his BYU term, Ferguson and another mathematician, Rodney Forcade, developed an algorithm, the Integer Relation Detection Algorithm. Computer scientists Jack Dongara and Francis Sullivan named the algorithm one of the Top Ten Algorithms of the 20th Century in the January 2000 issue of Computing in Science and Engineering magazine.

Ferguson’s artistic work flourished as well. “My art was growing, and it was time to move from the Rocky Mountains, — East Coast or West Coast. East Coast won.” He and Claire moved their brood, in 1988, to Howard County.

Among their seven adult children there are mathematicians, musicians, a software developer and a potter.

Claire and Helaman, who will celebrate 50 years of marriage next spring, collaborated professionally in Claire’s 1994 book, “HELAMAN FERGUSON: Mathematics in Stone and Bronze,” a pictorial that includes a 30-piece selection of her husband’s earlier sculpture and intimate commentary on his abstracts and philosophy. Together, they continue to travel to symposiums, sharing his work and lecturing on art and mathematic integration.

Ferguson doesn’t keep track of how many sculptures he’s created. “I don’t count such things. I just make them, and they go out into the world and tend to stay where they are put,” he says. “Now our seven children, I count them so I can keep track of them, and they aren’t so many.”

Birth of a torus

For the Stony Brook piece, Ferguson supersized his umbilic torus figure. To forge such a large work, he needed a gantry robot — so he built one.

The 16-foot-by-20-foot device resides in his studio, a local hideaway akin to a construction work yard. He wrote a program consisting of 25,000 movements — communicating shifts to the robotic arm and its affixed attachment, a foot-long industrial diamond-encrusted cutting tool.

The precision tool, working perpendicular to a sandstone surface, rotates counterclockwise and speedily — at 1,740 rpm — indenting an intricate pattern.

Delighted with the material for the molds, Ferguson declares, “This batch is quality sandstone — really, really good stuff.” The blocks were supplied by Danko/Arlington Inc., a sand-casting foundry located in Baltimore.

Silicon bronze is then poured into each numerically marked mold, creating bronze panels. Set free of the sandstone, the 144 bronze panels are welded adjacently by Ferguson and iron-masked assistants, amid showering sparks. After construction and welding are complete, an antique verde finish is applied to the bronze surface by nimble workers atop stretched ladders.

Looming large, at 24 feet, the sculpture is placed on a 24-foot-wide deltoid and circular base, made of Lake Superior green granite, and quarried in Elizabeth, Minn. The raised pattern on the torus’ surface is stroke-worthy, and the wide granite base may very well beckon university students in their own medium — skateboarding. Ferguson, undisturbed at the notion, chuckles, “Granite lasts billions of years.”

Weisenfeld, of the Simons Foundation, says the sculpture will be a fitting way to welcome students, faculty and visitors to Stony Brook’s Simons Center for Geometry and Physics.

“We hope the Umbilic Torus will serve as an inviting symbol of the beauty and power of mathematics,” she says.

The sculpture is to reside just outside the office window of Stony Brook mathematics professor Tony Phillips, who met Ferguson in 1989 at a university symposium. Phillips recalls, “I remember walking the campus a long time with Helaman, trying to find a good place for a math sculpture. The campus here is expansive, and now, all these years later, it’s come to fruition.”

For Ferguson, the Umbilic Torus SC represents “three exhausting years of my life, well spent” but also a celebration of mathematics, “the Queen of the Sciences.”

Helaman Ferguson sculpture nearby:

• American Center for Physics, College Park, Md.
• National Council of Teachers of Mathematics, Reston, Va.
• United States Congress, former office of Technology Assessment, Washington, D.C.
• Mathematical Association of America, Washington, D.C.

Farther afield:
• Center for Communications Research, La Jolla, Calif.
• University of California at Berkeley, Mathematical Sciences Research Center, Berkeley, Calif.
• Springer-Verlag Publishing, Heidelberg, Germany
• Daiichi Pure Chemical Corp., Tokyo

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