Mathematicians have mapped the inner workings of one of the most complicated structures ever studied: the object known as the exceptional Lie group E8. This achievement is significant both as an advance in basic knowledge and because of the many connections between E8 and other areas, including string theory and geometry. The magnitude of the calculation is staggering: the answer, if written out in tiny print, would cover an area the size of Manhattan. Mathematicians are known for their solitary work style, but the assault on E8 is part of a large project bringing together 18 mathematicians from the U.S. and Europe for an intensive four-year collaboration.
The magnitude of the E8 calculation invites comparison with the Human Genome Project. 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.
The team that produced the E8 calculation began work four years ago. They meet together at the American Institute of Mathematics every summer, and in smaller groups throughout the year. Their work requires a mix of theoretical mathematics and intricate computer programming. According to team member David Vogan from MIT, “The literature on this subject is very dense and very difficult to understand. Even after we understood the underlying mathematics it still took more than two years to implement it on a computer.” And then there came the problem of finding a computer large enough to do the calculation.