E8, that most complex exceptional simple Lie group, has just been solved.
E8 is a 248-dimensional Lie algebra, and is described as 1 of the most complicated mathematical structures ever studied. A group of 18 mathematicians collaborated for 4 years used 77 hours of time on a supercomputer to arrive at the E8 calculation which is/can be represented as a matrix with 205,263,363,600 entries.
According to folks who ought to know, namely the American Institute of Mathematics, this is a big deal. A paraphrased, de-mathematized, 10-second version of the excellent AIM piece entitled Mathematicians Map E8 explanation of E8 and why it matters, might read something like the following: “At the most basic level, the E8 calculation is an investigation of symmetry. Mathematicians invented the Lie groups to capture the essence of symmetry. The elucidation of E8 as a great advance for pure mathematics and might help physicists to develop a Grand Unified Theory of how the universe works”. …some ancillary lecture notes on E6, E7, E8 are available at this link.
But in keeping with the theme of symmetry, we offer a countervailing viewpoint for the above, courtesy of Peter Woit, a mathematician over at Columbia University who is wont to defame bad science and poor math via his blog Not Even Wrong. While the acerbic E8 Media Blitz lauds the computing of E8 itself, he downplays the importance of the feat and decries it’s potential application to string theory, universes and the like. …ouch.
While we reflect on the significance, if any, of the calculation of E8, it might help to ponder one of the 5 Platonic solids, the icosahedron, and its 120 symmetries:
The Scientific Promise of Perfect Symmetry – New York Times, March 20 2007
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