E₈ is first of all the largest exceptional root system, which is a set of vectors in an 8-dimensional real vector space satisfying certain properties. Root systems were classified by Wilhelm Killing in the 1890s. He found 4 infinite classes of Lie algebras, labelled A_n, B_n, C_n, and D_n, where n=1,2,3…. He also found 5 more exceptional ones: G₂, F₄, E₆, E₇, and E₈. it is the name of an exceptional simple Lie algebra as well as that of the associated simple Lie groups. It is also the name given to the corresponding root system, root lattice, and Wey/Coxeter group.

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.

This article appeared in MIT Tech Talk (PDF version).