Among the 23 remarkable individuals who won MacArthur Foundation fellowships earlier this week, there was mathematician Maria Chudnovsky, who is married to a violist, and stringed instrument bow-maker Benoît Rolland. Although these two awardees work in completely different fields, they are linked by personal interest and, oddly enough, a kind of scientific artistry. Mathematicians often describe their field as both an art and a science, and bow-making involves a surprising amount of experimentation and engineering.

Maria Chudnovsky: Graph theorist

When Chudnovsky was seven years old, she dreamed of flying the friendly skies. "After I gave up on planning a career as a flight attendant," she says, "math was more or less the next thing." Many years later, as a graduate student at Princeton University, she helped solve a long-standing question in a mathematical field called graph theory. She is now a faculty member in the Industrial Engineering and Operations Research Department at Columbia University.

The field of graph theory deals not with plots of data over x- and y-axes but rather with what laypersons might call networks. A graph consists of nodes, or vertices, and connections between the nodes, represented by lines. For example, attendees at a party could be the nodes, and they could be connected if they know each other. On a larger scale, mathematicians use graph theory to study social networks such as Facebook.

Many of the problems Chudnovsky works on have to do with coloring graphs. This means you use different colors to label the nodes of the graph so that no two connected nodes can share the same color. "You want to avoid conflict," she says. For example, graph coloring can be used to schedule tasks. Each task is a node, and nodes are connected if they cannot be done simultaneously—if, for instance, they require the same tools. A coloring of the nodes corresponds to a way to assign times to tasks: each color is a time interval during which the corresponding tasks can be done. Chudnovsky's work, however, is theoretical rather than applied.

Her first major contribution to the field was as part of the group that proved the "strong perfect graph conjecture." Formulated in 1961 by mathematician Claude Berge, the conjecture states that two different types of graphs, called Berge graphs and perfect graphs, are actually the same. In other words, if you determine that a graph is Berge, you know it is perfect, and vice versa. Their proof shows that there are a finite number of types of Berge graphs, and that all of them are perfect. Mathematically, their take is a bit stronger than the original conjecture. Chudnovsky has also worked on finding efficient algorithms for determining whether graphs are perfect or not.

Chudnovsky says that when she does research her approach is different for every problem. A common technique is to find one small case to play with and see if it can give her any clues about the larger question. She says that the fellowship, which comes with $500,000 over the course of five years, no strings attached, won't change the type of research she does, but that it gives her the freedom to attack problems that seemed too risky before. "Now I'll try them. The biggest advantage of the fellowship is that if I work on something for a year and fail, people won't say, 'she's no good.'"

On a historical note, Maria is not the first mathematician named Chudnovsky to win a MacArthur Fellowship. Gregory V. Chudnovsky, no relation, who works in number theory, mathematical physics and computer science, was selected in 1981, the first year of the fellowship.

Benoît Rolland: Bow-maker

Benoît Rolland
Image: Courtesy of the John D. and Catherine T. MacArthur Foundation

Born in Paris, Rolland started taking piano lessons from his concert pianist grandmother at age four and switched to violin at age nine.

After graduating from conservatory, he switched again—this time from playing music to violin making. "Then one day I saw a beautiful, magnificent bow," he says. "I knew instantly that this was what I wanted to do." After learning the craft, he began innovating. Most bows are made out of an endangered Brazilian wood called pernambuco, or brazilwood. Just like the instruments themselves, they can be prohibitively expensive for students. In 1981 Rolland began working on a high-quality, affordable carbon-fiber bow.

"The idea came to me when I was sailing," he says. He noticed that sailboats are often made of composite materials such as fiberglass. "One day I thought, 'Well, why shouldn't I try to make a bow with those materials?' So I put up my sleeves and I started to research it." He enlisted the help of engineers and ended up with a composite of carbon fiber and glass fiber (distinct from fiberglass, which is plastic reinforced with glass). After many trial runs and prototypes, "in the end I could make a bow that reproduced the best qualities of the best bows of the 19th century."

Rolland has continued to innovate. He made a bow with helicoidal hair, meaning that instead of being parallel with the stick for the entire length, the hair winds around in a partial spiral. To achieve this, the frog (the usually ebony, block-shaped part of the bow, where it is held) is offset by 15 degrees. Rolland says that this bow will improve players' sound quality by allowing more of the hair to contact the string when playing at its lower end. The bow is currently in the prototype stage, and he says it should be available in the next few months.

Rolland speaks of bows with reverence: "The bow has to behave like a human muscle. This bow is a link from the emotion, the personality, the musicality of the musician, to the instrument. Through the bow, all those feelings have to be conveyed" he says. "There can be a world between two bows. It's unbelievable the subtlety of these objects. My goal, of course, is to make the bow ultimately forgotten in the musician's hand. This way the musician can play freely, and go to the end of the world."

Rolland has ideas for several other innovations and says that the grant will help with the labor-intensive process of designing, creating and testing his inventions. "Nowadays with the scientific means at hand we can explain many things—but not all, of course. We cannot explain feeling, playing style." Rolland measures what he can and experiments with new designs, approaching his craft as both a scientist and an artisan.

Among the other MacArthur honorees: Elissa Hallem who studies scent detection in invertebrates to understand and prevent insect- and roundworm-borne illnesses; theoretical computer scientist Daniel Spielman who designs and optimizes algorithms; Sarkis Mazmanian, whose work on the interactions between microbes and human cells could help explain and treat autoimmune disorders; and Nancy Rabalais who studies the "dead zone" in the Gulf of Mexico. Scientific American congratulates them and the rest of this year's winners for earning this prestigious award.

1 Comments

1. 1. zhgart 09:53 AM 10/9/12

   incredible math and art.
   you use different colors to label the nodes of the graph so that no two connected nodes can share the same color
   
   from this recall the question of a map of 4 color problem.
   and m coloring problem.

   Reply | Report Abuse | Link to this