Chaos Work Earns McMullen Fields Medal

Harvard Professor of Mathematics Curtis McMullen received one of the highest honors in the field of mathematics--the Fields medal--this August.

Awarded to four mathematicians every four years by the International Conference of Mathematicians (ICM), the Fields Medal is considered the mathematical equivalent of the Nobel Prize.

McMullen won the medal for his work in the area of mathematics commonly known as the "chaos theory."

More accurately, McMullen says, "My recent research has been in the fields of complex dynamics, Riemann surfaces and hyperbolic geometry."

Although his work has various practical applications, such as providing a better understanding of how earthquakes or heart attacks begin, McMullen says that the purpose of his research does not lie in its applications.

"It is a matter of curiosity and the challenge of wanting to understand," he says.

The gold medal that McMullen received has a profile of Archimedes--the great Greek mathematician who discovered a method of calculating pi--and the quotation "Transire suum pectus mundoque potri" meaning "Rise above oneself and grasp the world," according to a press release from the ICM.

Fields medal winners also receive a cash prize of $15,000 Canadian dollars, which is the equivalent of about $9,500 U.S. dollars, because the medal was established in 1936 by Canadian mathematician John Charles Fields.

Although many people consider the Fields medal the mathematical equivalent of the Nobel Prize, the purpose of the two awards is very different.

While the Nobel Prize is generally awarded to individuals toward the end of their careers, the Fields medal is only awarded to mathematicians under the age of 40.

"I just made it," says McMullen, who turned 40 last May.

According to McMullen, part of the reason for the age limit is to encourage mathematicians to continue and further their research.

McMullen says his work in complex dynamics has lately turned his research in the direction of knot theory--an area that at first seemed unrelated to fractals and chaos.

"Lately I've been thinking about knots, links and braids and how they relate to filling three-dimensional spaces with surfaces," he says.

"If you look at the gallery on McMullen's web page-http://math.harvard.edu/~ctm/gallery.html-you can find an array of graphics generated by computer programs that McMullen has written.

One of these graphics forms the basis for a new solution of fifth degree polynomial equations, which grew out of McMullen's thesis research as a graduate student.

McMullen says that the solution involves iterating a dynamical system on a sphere--more reliable than "Newton's method"--to get closer and closer approximations.

After graduating with highest honors in mathematics from Williams College, McMullen studied at Cambridge University and then earned a doctorate in mathematics from Harvard in 1985.

He taught at MIT, Princeton and the University of California at Berkeley before returning to Harvard as a visiting professor in the 1997-98 academic year.

He joined the faculty permanently this year.