Equations in Stone: A Mathematician Turns to Sculpture to Convey the Beauty of Mathematics

By Peterson, Ivars | Science News, September 8, 1990 | Go to article overview
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Equations in Stone: A Mathematician Turns to Sculpture to Convey the Beauty of Mathematics


Peterson, Ivars, Science News


Equations in Stone

A wild sphere flings its bronzed arms into the sky. A twisted ring pulls itself free from a slab of white Carrara marble. A glistening, silky-smooth knot writhes across the ground. A metallic eye blinks in harsh sunlight.

Each of these creations, realized in stone and bronze by mathematician and sculptor Helaman R.P. Ferguson, represents a concrete expression of a mathematical theorem. Each is an attempt to embody -- in a form that anyone can see and touch -- the special sense of beauty that mathematicians experience in their explorations of abstract realms.

"Aesthetic pleasures are a major motivation [in mathematical research], but we usually don't bring that out," Ferguson says. "I am interested in the adventure of affirming pure mathematical thought in unpredictable physical form."

Compelled to communicate mathematical beauty in tangible terms. Ferguson took an extended leave of absence nearly two years ago from Brigham Young University in Provo, Utah, where he taught mathematics. He now spends as much time as he can immersed in his art at his new home and studio near Laurel, Md. Last month, he exhibited 21 of his sculptures in Columbus, Ohio, at a meeting celebrating the 75th anniversary of the Mathematical Associaton of America.

"Mathematics is both an art form and a science," Ferguson writes in the August-September AMERICAN MATHEMATICAL MONTHLY. "I believe it is feasible to communicate mathematics along aesthetic channels to a general audience." His article describes in considerable detail how he created two of his best-known mathematical sculptures.

Ferguson is not the first to exploit the link between mathematics and art. Aesthetic considerations have long played a role in the development of mathematics, and mathematical ideas continue to inspire the work of both artists and artisans.

Mathematicians have a distinctive sense of beauty. They strive not just to construct irrefutable proofs but to present their ideas and results in a clear and compelling fashion, dictated more by a sense of aesthetics than by the needs of logic. And they are concerned not merely with finding and proving theorems, but with arranging and assembling the theorems into an elegant, coherent structure.

In the words of mathematician and philosopher Bertrand Russell, "Mathematics, rightly viewed, possesses not only truth, but supreme beauty -- a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the trappings of paintings or music, yet sublimely pure, and capable of stern perfection such as only the greatest art can show."

This sense of mathematical beauty remains froreign to most nonmathematicians. Without a well-trained eye, it's difficult to appreciate the bare-bones beauty of a theorem or an equation.

Artists have helped bring some of that beauty out of its cerebral closet. For example, the intriguing drawings of Dutch graphic artist M.C. Escher skillfully convey the illusion of infinitely repeating forms and the strange properties of hyperbolic planes. Other artists have dabbed in representations of four-dimensional forms. And a growing number now use the computer as a tool for creating art.

Ferguson's interest in art emerged early in his life. He learned to work with stone as a young apprentice to a stone-mason, studied painting as an undergraduate and completed several graduate courses in sculpture.

Along the way, he also earned a doctorate in mathematics, later teaching the subject at Brigham Young University for more than 17 years and publishing research papers on a number of mathematical topics. To earn a living and support his artistic efforts, Ferguson currently designs new computer-based numerical recipes, or algorithms, for operating machinery and for visualizing scientific data. He's particularly interested in developing m methods for "sculpting" data into forms that are meaningful and useful to researchers trying to cope with the overwhelming amounts of information that a supercomputer can produce.

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