Problem Solved: Century-Old Math Mystery Deciphered

David Hyun
URL:http://www.bloomberg.com/apps/news?pid=20601103&sid=abM.SNM8uq3c&refer=us
March 21 (Bloomberg) -- Researchers using supercomputers unraveled a 120-year-old mathematics mystery, a solution they said promises advances in their field much like the mapping of the humane genome is aiding developments in medicine.
The solution of the math structure E8, unveiled this week at the Massachusetts Institute of Technology in Cambridge, would cover an area the size of Manhattan if written on paper. E8, discovered in 1887, is a mathematical problem related to equations used to explain symmetry.
``It's a big step,'' said Jeffrey Adams, 50, a mathematics professor at the University of Maryland in College Park who led the project by 18 mathematicians and computer scientists from the U.S. and Europe. ``You never know where it's going to lead.''
The project will help math researchers find solutions to problems related to symmetry, string theory and geometry, Adams said. Understanding how E8 works also might help physicists develop a unified theory that takes in gravity and other fundamental forces, said Hermann Nicolai, a director at the Max Planck Institute for Gravitational Physics in Potsdam, Germany, in a report on the discovery.
The E8 solution might be the math field's equivalent to the basic knowledge produced by human-genome mapping in the 1990s and early 2000s, Adams said. That work spurred a wave of methods for analyzing genetic causes of disease and led to the discovery of genes that may predict a person's risk of disease or other biological clues that may help doctors in treatment decisions.
``I like to say that the human genome itself doesn't give you drugs and cures for cancer,'' Adams said.
Other Researchers
Besides researchers from MIT and Maryland, the project drew collaborators from France and from U.S. universities including Cornell, Harvard, Stanford, Michigan and Utah.
E8, discovered in 1887, is a mathematical problem from the Lie groups, which were developed by Norwegian Sophus Lie during his study of symmetry. Mathematicians explore symmetries in theoretical dimensions greater than the familiar three- dimensional objects such as balls and cylinders. E8 has 248 dimensions. The E8 calculation is part of a larger project on all the Lie groups.
It took researchers two years of ``pencil and paper'' work and one more for software writing before the solution could be tackled by computer, Adams said in a telephone interview. The single calculation required computer power and memory that wasn't available until recently, said the National Science Foundation, which provided funding along with the American Institute of Mathematics.
Underlying Math
``The literature on this subject is very dense and very difficult to understand,'' said team member David Vogan from MIT in the report on the project. ``Even after we understood the underlying mathematics, it still took more than two years to implement it on a computer.''
Researchers broke the puzzle into smaller parts, producing partial answers that were later assembled to find the eventual solution. The final calculation took about 77 hours on the Sage supercomputer, built by San Diego-based Western Scientific.
The calculation created a file 60 gigabytes in size, enough to store music that could play for 45 days in the MP3 format. Data on the human genome, which contains all of the genetic information of a cell, can be stored on less than a gigabyte.