It Took 100 Years, But Key Maths Conundrum is Finally Cracked

A mathematical problem that remained unsolved for more than a century has finally been cracked by an international team of 18 scientists.

The puzzle, which is so complex that its handwritten proof would cover an area the size of Manhattan, took researchers four years to unravel and takes up as much computer space as 45 days of continuous music in MP3 format.

The solution maps the inner workings of E8, an esoteric 248-dimensional structure that is an example of a Lie (pronounced "Lee") group. Lie groups were invented by the 19th-century Norwegian mathematician Sophus Lie to help understand symmetry.

The groups underlie the symmetry in objects such as balls, cylinders and cones that remain symmetrical under any degree of rotation.

Although the solution itself does not have any direct applications, it will influence a range of other fields such as algebra, geometry, number theory, physics and chemistry.

"What's attractive about studying E8 is that it's as complicated as symmetry can get," said David Vogan, professor of mathematics at the Massachusetts Institute of Technology. "Mathematics can almost always offer another example that's harder than the one you're looking at now, but for Lie groups E8 is the hardest one."

Prof Vogan said the full significance of the discovery may take time to become apparent. "There are lots of ways that E8 appears in abstract mathematics, and it's going to be fun to try to find interpretations of our work in some of those appearances," he said.

"The uniqueness of E8 makes me hope that it should have a role to play in theoretical physics as well. So far the work in that direction is pretty speculative, but I'll stay hopeful."

More information on the calculation and its applications at aimath.org/E8/