Mathematicians solve century-old puzzle
An international team of mathematicians and computer scientists announced on Monday they have mapped out a 248-dimension mathematical structure that had confounded the world's top number-crunchers for 120 years.
The calculation of the structure, known as E8, takes about 60 gigabytes of space on a computer, or enough space to hold about 15,000 songs in MP3 format. It took 18 researchers from the United States and Europe four years to produce the E8 calculation and 77 hours for a U.S. supercomputer called Sage 77 to provide the solution.
Solving E8 is seen as a major step in the study of symmetry, a mathematical field important to our understanding of the origins of the universe.
E8 is an example of a Lie group. Lie groups were invented by the 19th-century Norwegian mathematician Sophus Lie to define objects that have the underlying characteristics of symmetry. Spheres, cylinders and cones are familiar examples of symmetrical shapes that belong to Lie groups.
E8 is the most complex Lie group known, a 453,060 by 453,060 matrix that exists only in abstract mathematics. Because of its large size, solving its structure was not possible until computing power could improve, according to Jeffrey Adams, the project leader and a mathematics professor at the University of Maryland.
"E8 was discovered over a century ago, in 1887, and until now, no one thought the structure could ever be understood," said Adams in a statement. "This groundbreaking achievement is significant both as an advance in basic knowledge, as well as a major advance in the use of large-scale computing to solve complicated mathematical problems."
Many of the recent developments in theoretical physics have made use of the math behind symmetry and Lie groups to discover previously unknown symmetries in nature, from the discovery 30 years ago of quarks and other particles in quantum physics to work today in superstring theory.
MIT Prof. David Vogan said the solution could possibly have implications in our understanding of the universe.
"The uniqueness of E8 makes me hope that it should have a role to play in theoretical physics as well. So far the work in that direction is pretty speculative, but I'll stay hopeful," he said.