PALO ALTO, Calif. – An international team of mathematicians has cracked a 120-year-old puzzle that researchers say is so complicated that its handwritten solution would cover the island of Manhattan.
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.
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When stored in highly compressed form on a computer hard drive, the solution takes up 60 gigabytes — as much as the largest-capacity iPod can hold, or about 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.
The solution was presented by MIT's David Vogan in a talk entitled, "The Character Table for E8, or How We Wrote Down a 453,060 x 453,060 Matrix and Found Happiness."