Most beautiful math structure appears in lab for first time New Scientist Physics & Math, Jan. 7, 2010
The structure is also the basis for another proposed theory of everything advanced in 2007 by surfer-physicist Garrett Lisi, who refers to E8 as “perhaps the most beautiful structure in mathematics“.
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From the New Scientist link:
Radu Coldea of the University of Oxford and his colleagues chilled a crystal made of cobalt and niobium to 0.04 °C above absolute zero. Atoms in the crystal are arranged in long, parallel chains. Because of a quantum property called spin, electrons attached to the atom chains act like tiny bar magnets, each of which can only point up or down.
Strange things occurred when the experimenters applied a powerful 5.5-Tesla magnetic field perpendicular to the direction of these electron “magnets”. Patterns appeared spontaneously in the electron spins in the chains – in a simplified example with three electrons, the spins could read up-up-down or down-up-down, among other possibilities. Each distinct pattern has a different energy associated with it.
The ratio of these different energy levels showed that the electron spins were ordering themselves according to mathematical relationships in E8 symmetry.