Team Cracks Century-Old Math Puzzle

In a computer generated illustration supplied by the American Institute of Mathematics, the E8 root system related to the Lie group E8, which is 248 dimensions, is seen. A math problem so complicated that its solution would cover the island of Manhattan if written out was cracked by researchers after going unsolved for more than a century. The 18-member team of mathematicians and computer scientists convened by the American Institute of Mathematics in Palo Alto, Calif., took four years to map a 248-dimensional object known as the "Lie group E8." (AP Graphic/John Stembridge, University of Michigan) (John Stembridge - AP)

PALO ALTO, Calif. -- An international team of mathematicians says it has cracked a 120-year-old puzzle that researchers say is so complicated that its handwritten solution would cover the island of Manhattan.

The 18-member group of mathematicians and computer scientists was convened by the American Institute of Mathematics in Palo Alto to map a theoretical object known as the "Lie group E8."

Lie (pronounced Lee) groups were invented by 19th-century Norwegian mathematician Sophus Lie in his study of symmetrical objects, especially spheres, and differential calculus.

The E8 group, which dates to 1887, is the most complicated Lie group, with 248 dimensions, and was long considered impossible to solve.

"To say what precisely it is is something even many mathematicians can't understand," said Jeffrey Adams, the project's leader and a math professor at the University of Maryland.

The problem's proof, announced Monday at the Massachusetts Institute of Technology, took the researchers four years to find. It involves about 60 times as much data as the Human Genome Project.

When stored in highly compressed form on a computer hard drive, the solution takes up as much space as 45 days of continuous music in MP3 format.

"It's like a Mount Everest of mathematical structures they've climbed now," said Brian Conrey, director of the institute.

The calculation does not have any obvious practical applications but could help advance theoretical physics and geometry, researchers said.