47. 248-Dimensional Math Problem Solved

By Jessica Marshall|Friday, January 04, 2008

One hundred twenty years after it was first discovered, mathematicians have successfully mapped out a 248-dimensional object called E8. The complete description of E8—one of the most complicated structures in all of mathematics—is a table with more than 200 billion entries. Printed out on paper, it would cover all of Manhattan.

Scientists hope to use the map to sim­plify calculations and help them understand the universe. David Vogan, the MIT mathematician who announced the project’s completion in March, calls it a map of possibilities, “a little bit like the periodic table is for chemistry.”

Objects similar to E8 keep showing up in the real world. One of them describes the motions of the solar system and the positions of electrons surrounding atoms; another defines how a single wave travels down a canal or traffic flows on a highway.

What E8 will do for us is not yet clear. It was correctly predicted in 1887 to be the most complex of the Lie (pronounced LEE) groups, which are collections of symmetries. One of the simplest sets of symmetries is the group that comprises the symmetries of a sphere: Rotate a sphere as much as you like around any axis or flip it inside out, and it looks exactly the same. E8 is the group that comprises the symmetries of a 57-dimensional object. Superstring theorists have already employed this group in potential theories of everything. Whether or not those string theories turn out to be true, Vogan says, E8 probably reflects the real world somehow: “Everything interesting does.”

Go to the next story: 48. Robotic Ankle Takes First Step

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