That high school math problem with a page-long solution was a cakewalk compared to a recent mathematics answer that would ink an area the size of Manhattan if written out in small print.
A total of 18 mathematicians and computer scientists from several countries worked for four years to successfully map the inner working of E8 — one of the most complicated structures in math, a 248-dimensional object. The findings were reported today by the American Institute of Mathematics.
"E8 was discovered over a century ago, in 1887, and until now, no one thought the structure could ever be understood," said project leader Jeffrey Adams, a mathematician at the University of Maryland. "This groundbreaking achievement is significant both as an advance in basic knowledge, as well as a major advance in the use of large-scale computing to solve complicated mathematical problems."
The mapping of E8, according to researchers, may very well have implications in mathematics and physics which won’t be evident for years to come.
Underlying symmetrical objects such as spheres and cylinders is something called a Lie group — a mathematical group invented by the 19th century Norwegian mathematician Sophus Lie to study symmetry. E8 is an example of a Lie group.
"This is an exciting breakthrough," said Peter Sarnak, a researcher at Princeton University. "Understanding and classifying the representations of E8 and Lie groups has been critical to understanding phenomena in many different areas of mathematics and science, including algebra, geometry, number theory, physics and chemistry. This project will be invaluable for future mathematicians and scientists."
The result of E8 and all its representations is 60 gigabytes in size, enough to store 45 continuous days of music in MP3 format. In comparison, the Human Genome Project holding the entire genetic code of a cell is less than a gigabyte in size.
A unique aspect of this very large output answer is that unlike many large-scale calculations, the size of the input is small compared to the enormous and very dense answer.