Well,
They said it couldn't be done and this explains why.....Joe
Team Cracks Decades-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. John StembridgeFrom Associated Press
March 20, 2007 11:42 PM EDT
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.
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.
bc, whose VW bug's license plate was: SU 3, and is totally ignorant of
group theory.