A 120 Year-Old Math Riddle Finally gets solved.
An international team of mathematicians has detailed a vast complex numerical "structure" which was invented more than a century ago.
Mapping the 248-dimensional structure, called E8, took four years of work and produced more data than the Human Genome Project, researchers said.
This Result could be used to test theories about the structure of the cosmos.
Scientists and Mathematicians said they had mapped 'E8', a problem that was discovered in 1887 but has had to wait until the era of supercomputers and Internet linked minds to resolve. E8 is the mother of all so-called Lie Groups-A category of problems invented by a 19th century Norwegian Mathematician , Sophus Lie (Pronounced "Lee"),to explore symmetry.
Spheres, cylinders or cones are familiar examples of simple symmetrical objects in 3D. But E8 is a piece of geometric origami that comes in 248 Dimensions.
E8 is as complicated as symmetry can get said a mathematics professor at MIT,who took part in the calculations.
Resolving E8 was a gigantic undertaking, the scientists said they compared it to the Human Genome Project, which patiently unraveled the human genetic code. The human genome is less than a gigabyte in size, but the E8 calculation is 60 GB big.
It took 4 Years to calculate the numbers, An expert said the E8 breakthrough was a very important advance in Physics for it could be used to test a key theory about the fundamental symmetries in nature. Among these mooted symmetries is the structure of the cosmos, created by the big Bang some 13 Billion years ago, and basic particles themselves.
The mapping of E8 is also unusual because it involved a large team of mathematicians, who are typically known for their solitary style. "People will look back on this project as a significant landmark and because of this breakthrough, mathematics will now be viewed as a team sport," said Brian Conrey, executive director of AIM.
The mapping of E8 may well have unforeseen implications in mathematics and physics that won't be evident for years to come.
A Picture of the E8 root system.
The E8 root system consists of 240 vectors in an eight-dimensional space.Those vectors are the vertices (corners) of an eight-dimensional object called the Gosset polytope 421. In the 1960s, Peter McMullen drew (by hand) a 2-dimensional representation of the Gosset polytope 421. The image shown below was computer-generated by John Stembridge, based on McMullen's drawing.
The lines in the picture connect adjacent vertices in the polytope, with colors chosen according to the length of the 2-dimensional projection. Since the picture is a 2-dimensional projection of an 8-dimensional object, it captures only some of the symmetries of the Gossett polytope.
The Lie algebra E8 is 248-dimensional: the 8-dimensional space depicted here, plus one dimension for each of the 240 root vectors.
-M.I.T , HT, BBC ,AIM
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