I do not have the physics or math background, but simplicity and elegance (expressed as symmetry) have always appealed to me. In an online paper titled, “An Exceptionally Simple Theory of Everything,” ( arXiv:0711.0770v1 [hep-th], Nov. 6, 2008, 31 pp, PDF), A. Garrett Lisi writes:
Lisi’s inspiration lies in an elegant and intricate mathetmatical shape called E8 — a complex structure with a rank of 8 (the maximum number of mutually commutative degrees of freedom) and 248 dimensions. It was first described in 1887, but was only fully explicated by mathematicians (with NPR audio) this year.
Lisi believes the algebra underlying this shape holds the key to the so-called Theory of Everything, the elusive equation to unite Einstein’s General Relativity with quantum mechanics. Relativity explains how the universe works on very large scales; quantum mechanics describes the world of tiny elementary particles.
BTW, there are some other beautiful shapes in this paper, lucid text and head-scratching equations! Here is also a reference to Lisi’s beautiful visualization that shows projections of various rotations of this E8 root system in eight dimensions: http://deferentialgeometry.org/anim/e8rotation.mov.