E8 refers to a group of closely related mathematical structures. One of them, the E8 Gosset polytope, appears as a beautiful, intricate pattern when graphed in two dimensions.

Computer-generated image of E8 by John Stembridge based on Peter McMullen's hand drawing from the 1960s.

In 2007, E8 captured my imagination not only becaue of its artistic beauty but also because of its potential to explain some of the deepest scientific mysteries.

A Theory of Everything

Garrett Lisi, 39, proposed a new theory of the universe, one which could succeed in unifying not only matter and energy but also gravity. He based his work on E8, a mathematical pattern that has 248 dimensions. His article was published on Nov. 6, 2007 online. Though Lisi himself thinks the odds are against it, his theory may succeed where Einstein and the latest string theory proponents have not.

According to Lee Smolin, Perimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada, Lisi's work "... is one of the most compelling unification models I've seen in many, many years."  Lisi discovered a way to place the elementary atomic particles and forces on the 248 points contained in E8. Lisi has made predictions about 20 particles that may be tested when the Large Hadron Collider becomes available. Located near Geneva, Switzerland, completion of the collider is scheduled for May 2008.

Exploring E8

A fascinating way to explore the beauty of E8 is to zoom and pan inside a PDF file (http://aimath.org/E8/images/e8.pdf). When opened in Adobe Acrobat, you can zoom to 6400% to see the details of the thousands of colored lines and intersections that make up the pattern.

Understanding E8 is quite a different story. On March 19, 2007, a team of mathematicians organized through the American Institute of Mathematics announced the successful completion of four years of work devoted to mapping E8's inner workings. The calculations are more than 60 times greater than those for mapping the humane genome. Classifying and understanding structures related to E8 has been critical to understanding phenomena in the areas of algebra, chemistry, geometry, number theory and physics.

It took the team two years to do the computer programming necessary to perform the calculations and another year to streamline the program so that it could run on an existing supercomputer. In the end it ran for 77 hours on a supercomputer running open source SAGE software written in Python, a language at the foundation of our Web site. 

More About E8

Wikepedia entries: 
E8 polytype - http://en.wikipedia.org/wiki/E8_polytope
E8 (mathematics) - http://en.wikipedia.org/wiki/E8_%28mathematics%29
E8 main page - American Institute of Mathematics - http://aimath.org/E8/
An Exceptionally Simple Theory of Everything by Garrett Lisi, Nov. 6, 2007, http://arxiv.org/abs/0711.0770

E8 Diagrams:
Blue-green image available under Creative Commons license: http://en.wikipedia.org/wiki/Image:E8_graph.svg
American Institute of Mathematics images: http://aimath.org/e8/mcmullen.html

Three-dimensional modeling with Zome:
http://www.zometool.com/about-everything.html

By Wells H. Anderson