Mathematician David Mumford
Mathematician David Mumford
David Mumford, a part-time resident of Tenants Harbor and one of the leading mathematicians in the United States, was granted the presidential National Medal of Science earlier this month. President Obama will award the medal, which is the highest scientific honor in the country, at a White House ceremony later this fall.

Mumford, a professor emeritus at Brown University who retired from teaching earlier this year after 50 years at Harvard and Brown, is still an active research mathematician.

"Oh, I couldn't give that up," said Mumford. "It's too much fun."

Referring to himself as a science guy in a large family of artists and poets, including his wife, painter Jenifer Mumford, and painters Charles Duback, Steve Mumford and Inka Essenhigh, Mumford speculated that the creative people around him provide a counterpoint to his scientific work in the world of math.

That work has fundamentally changed algebraic geometry and was important in understanding string theory in physics.

"Math is used as a tool and can make unexpected connections between two sets of problems that seem to be unrelated," said Mumford. "It's a link. Math makes the connections possible."

One of the math tools Mumford created, geometric invariant theory, can be used to create mathematical versions of maps. Just as a map has points that stand for roads and hills, but are not the roads and hills themselves, so math can create an equivalent of a map, a bird's eye view of the totality of various mathematical objects, said Mumford.

This tool was later employed in string theory to measure and predict movement across space and time.

"It was a mathematical problem that was beautiful in its own right," said Mumford. "String theory used it later."

Mumford made his name in pure math, but leaned towards applied mathematics, which drew him away from Harvard to Brown University in the mid-1990s.

At Brown, Mumford worked on mathematical models for feedback loops and how they function in computers and in the human brain.

"We had this dream in the 1960s of a powerful computer that was as smart as a human being," he said. "That turned out to be nonsense. It's very hard to duplicate a human being, but we could look at pattern theory and how it works in computers and in the brain."

Feedback loops are essentially return pathways that allow a brain or a computer to loop back and pick up more information or move along one path to the next and share information.

Mumford simply described the analysis in neurobiology that led to a deeper understanding of how the brain processes information.

"A visual signal comes into the back of the brain in the occipital lobe," said Mumford. "The premise was that that part of the brain would distinguish shapes and lines."

But not much else.

Mumford's work helped reveal that the occipital lobe was involved in a much more complicated process: the visual cue would trigger the basic response of shape, but only for a fraction of a second before sending that information back in a feedback loop that would detect more information, such as the direction of the illuminating light and the shadows.

Mumford said that information has not yet been applied in a non-academic way but gave an example of possible applications for this kind of research.

John Donoghue, one of Mumford's colleagues, is in the experimental stages of testing an implant into the motor cortex that would allow paraplegics to turn a thought into an action through the use of electrodes. For example, if the paralyzed person thought "move cursor," the signal would be sent to a computer that is trained to respond to that signal and an action would follow. The same could be true with other cues.

"To go further requires more sophisticated theories," said Mumford. "This is a relatively primitive theory right now, but it has potential."

In contemplating creativity in science and math that can lead to exciting discoveries, Mumford said the process is closer to that of the artist than is commonly recognized.

"The paintings by Jackson Pollock are the classic example, but not the only one," said Mumford, referring to the spatter paint canvases Pollock created in the 1940s. "They seemed random. At the same time, in Los Alamos, John Van Neumann developed the Monte Carlo method to use a random selection of a small number of atoms to predict how the whole atomic bomb would explode."

The mathematical methods for predicting how the blast would disperse and Pollock's paintings both used randomness in revolutionary and constructive ways, said Mumford.

In the late 19th century both math and Impressionist art began to deal with complexity and irregular variations.

"Like the shadows in Renoir's 'Dance at Le Moulin de la Galette,' " said Mumford, referring to the famous outdoor dance scene painted by French Impressionist painter Pierre-Auguste Renoir that captures the play of light, shadow and movement in unexpected ways.

As to the National Medal of Science, Mumford said he was pleased, but that others had made valuable contributions in his field.

"I'm pleased it will bring attention to the important role of science and mathematics in our society," he said.