The graphic itself is just one 2-D representation of the enormous, incomprehensible 248-D structure.

There is nothing simple about Lie groups (and I'm no expert), but E8 is the most complex, non-regular class of a certain group of geometric symmetries in abstract algebra and topology. This class of symmetries appears often enough in theoretical (particle) physics to warrant the "Mt. Everest" moniker in terms of its importance.

The article in the Telegraph today has more details:

What makes this group of symmetries so exciting is that Nature also seems to have embedded it at the heart...

The graphic itself is just one 2-D representation of the enormous, incomprehensible 248-D structure.

There is nothing simple about Lie groups (and I'm no expert), but E8 is the most complex, non-regular class of a certain group of geometric symmetries in abstract algebra and topology. This class of symmetries appears often enough in theoretical (particle) physics to warrant the "Mt. Everest" moniker in terms of its importance.

The article in the Telegraph today has more details:

What makes this group of symmetries so exciting is that Nature also seems to have embedded it at the heart of many bits of physics. One interpretation of why we have such a quirky list of fundamental particles is because they all result from different facets of the strange symmetries of E8. I find it rather extraordinary that of all the symmetries that mathematicians have discovered, it is this exotic exceptional object that Nature has used to build the fabric of the universe. The symmetries are so intricate and complex that today’s announcement of the complete mapping of E8 is a significant moment in our exploration of symmetry."

I found the NYT article quite clarifying:

A 19th-century Norwegian mathematician, Sophus Lie (rhymes with tree), wrote down what are now known as Lie groups, sets of continuous transformations — meaning the changes could be a little or a lot — that leave an object unchanged in appearance.

For example, rotate a sphere any distance around any axis, and the sphere looks exactly the same.

Later mathematicians found five exceptions to the four classes of Lie groups that Lie knew about. The most complicated of the “exceptional simple Lie groups” is E8. It describes the symmetries of a 57-dimensional object that can in essen...

I found the NYT article quite clarifying:

A 19th-century Norwegian mathematician, Sophus Lie (rhymes with tree), wrote down what are now known as Lie groups, sets of continuous transformations — meaning the changes could be a little or a lot — that leave an object unchanged in appearance.

For example, rotate a sphere any distance around any axis, and the sphere looks exactly the same.

Later mathematicians found five exceptions to the four classes of Lie groups that Lie knew about. The most complicated of the “exceptional simple Lie groups” is E8. It describes the symmetries of a 57-dimensional object that can in essence be rotated in 248 ways without changing its appearance.