Pythagorean theorem got you stumped? Try imagining a math
problem so complicated its answer would cover the island of
Manhattan.
Morgan Hill – Pythagorean theorem got you stumped?
Try imagining a math problem so complicated its answer would cover the island of Manhattan.
On Monday, an international team of scholars working at the American Institute of Mathematics (AIM) revealed the sprawling inner workings to one of the world’s most perplexing enigmas – E8. AIM was founded in Palo Alto in 1994 and plans to open a conference center in Morgan Hill in two years.
With a root system consisting of 240 vectors in an eight-dimensional space, math experts consider E8 the magnum opus of symmetrical objects. Discovered in 1887 by Norwegian mathematician Sophus Lie (pronounced “Lee”), who invented Lie groups to study symmetrical objects in higher dimensions, E8 is the most complicated multi-dimensional and symmetrical object ever conceived.
With 248 dimensions, the geometric object would be imperceptible to the naked eye, but scientists hope understanding its complexity furthers an understanding of the universe itself.
“It’s the Mt. Everest of symmetries,” said AIM Director Brian Conrey, describing the E8’s elaborate structure. “It’s the biggest and baddest Lie group there is.”
A team of 18 top mathematicians and computer scientists from across the world spent four years working on the project. U.S. partners included MIT, Cornell University, University of Michigan, University of Utah and University of Maryland. The scientists unveiled their findings Monday in a presentation at MIT.
Conrey compared E8’s magnitude with the Human Genome Project, which mapped all the information in a cell. But unlike the human genome, which is less than a gigabyte in size, the E8 calculation is 60 gigabytes big, enough to store 45 days of continuous music in MP3 format.
The E8 project could extend to unified string theory in physics, furthering humankind’s logical understanding of how the universe works. The sophisticated new mathematical techniques could also lead to more efficient computer hard drives.
“This is an exciting breakthrough,” said Peter Sarnak, professor of mathematics at Yale University and chair of AIM’s scientific board. “Understanding and classifying the representations of E8 and Lie groups has been critical to understanding phenomena in many different areas of mathematics and science, including algebra, geometry, number theory, physics and chemistry.”
“This is an impressive achievement,” added Hermann Nicolai, director of the Albert Einstein Institute in Potsdam, Germany. “While mathematicians have known for a long time about the beauty and uniqueness of E8, we physicists have come to appreciate its exceptional role only more recently.”
The 18-member team that cracked the E8 mystery began working together four years ago, meeting each summer at AIM’s Palo Alto headquarters. When the project was launched, no one knew if a conclusion was possible. Now Conrey thinks the success of the E8 calculation is notable both for its magnitude as well as for how it was achieved.
“The mapping of E8 breaks the mold of mathematicians typically known for their solitary style,” Conrey said. “Mathematics will now be viewed as a team sport.”
The E8 calculation is part of a project sponsored by AIM and the National Science Foundation called the Atlas of Lie Groups and Representations. The goal of the project is to determine the structures of all symmetrical geographic objects with more than three dimensions.
Founded in 1994 by Silicon Valley businessmen John Fry and Steve Sorenson, AIM is widely regarded as one of the leading math institutes in the world. It sponsors conferences and focussed-research projects for international scholars, operating on an annual budget of $2 million. The National Science Foundation supplies half of AIM’s budget while the other half comes from Fry’s Electronics and other private sources.
In fall 2009, AIM hopes to hold its first scholarly events at its new 167,000-square-foot convention hall in Morgan Hill, currently under construction on Foothill Boulevard.
Speaking of symmetry, architects have modeled designs for the new center after the Alhambra Palace in Spain, a centuries-old building renowned for – what else? – its mathematical symmetry.
