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.
"It's a mathematical entity that we know exists, but we had to explore its inner structure," says Hermann Nicolai, a mathematical physicist at the Albert Einstein Institute in Potsdam, Germany, who was not involved in the work. "It's a bit like making a plan of a complicated building, or exploring an ancient pyramid to see how it was built."
Mathematicians take these descriptions to wild extremes by imagining the 3D objects in myriad dimensions. The group E8 encapsulates the symmetries of a geometric object like a sphere, cylinder or cone, but in 57 dimensions. E8 itself has 248 dimensions. Check out the visual representation E8 in a video after the break.
