New knowledge: 60 GB math object advances engineering

By Control Engineering Staff March 27, 2007

Palo Alto, CA —The recent scaling of a long-standing Mount Everest of mathematics is expected to lead to new discoveries in algebra, geometry, number theory, physics, and chemistry, as well as related fields such as engineering and software development. A long 110 years after discovery of a multi-dimensional mathematical object called E8, its mapping is complete. The task created 60 times as much information as the map of the Human Genome. On paper, the E8 calculation would be the size of Manhattan.

The March 19 unveiling followed four years of intensive collaboration from 18 top mathematicians and computer scientists from the U.S. and Europe. E8 is considered one of the largest and most complicated structures in mathematics, according to The American Institute of Mathematics (AIM). Partners on this project included MIT, Cornell University, University of Michigan, University of Utah, and University of Maryland.

E8, is an example of a Lie (pronounced “Lee”) group. Lie groups were invented by the 19th century Norwegian mathematician Sophus Lie to study symmetry. Underlying any symmetrical object, such as a sphere, is a Lie group. Balls, cylinders, or cones are familiar examples of symmetric three-dimensional objects. E8 is 248-dimensional. AIM provides a rich two-dimensional image of E8 root system , actually 240 vectors in eight-dimensional space.

” E8 was discovered over a century ago, in 1887, and until now, no one thought the structure could ever be understood,” said Jeffrey Adams, project leader and mathematics professor at the University of Maryland, as quoted in the AIM announcement. “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.” The E8 mapping may have implications in mathematics, physics, and other areas, which won’t be evident for years to come, he suggested.

The magnitude and nature of the E8 calculation invite comparison with the Human Genome Project, AIM says. The human genome, which contains all the genetic information of a cell, is less than a gigabyte in size. The result of the E8 calculation, which contains all the information about E8 and its representations, is 60 gigabytes in size, enough to store 45 days of continuous music in MP3-format. The AIM site provides more details, and explains how E8 fits into a larger project sponsored by AIM and the National Science Foundation .

Upcoming AIM workshops include Fourier analytic methods or computational wave propagation and scattering .

Mark T. Hoske , editor in chief,
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