It took 18 people four years to work out a math problem.
But they’re not going to be punished for turning in a late assignment.
After all, the Palo Alto-based math institute that handed out the assignment knew that the problem had gone unsolved for more than a century – and that the answer would probably be billions of digits long.
Explaining the problem and solution to non-mathematicians could take nearly as long. So suffice it to say that the team of mathematicians and computer scientists mapped the inner workings of a complicated, 248-dimensional object known as the “Lie group E8.” Scientists had been befuddled by the object for 120 years.
“To say what precisely it is is something even many mathematicians can’t understand,” said Jeffrey Adams, the project’s leader and a math professor at the University of Maryland.
And the answer is not your average math proof or calculation. If written out in the tiniest of print, it would cover an area the size of Manhattan. It’s so big – made up of more than 205 billion entries, each of which is a polynomial – that it takes up 60 gigabytes of space in highly compressed form. The calculation, announced Monday, isn’t even on the Internet yet because it would take days for the public to download, math experts explained.
The achievement is considered significant for advancing our basic knowledge of math – and could be useful in other areas, including string theory and geometry. It also marks a successful marriage between mathematics and computer science, with the scientists using large-scale computing to solve the complicated problem. Once the experts figured out how to figure out the problem, it took a supercomputer about 77 hours to come up with the calculation.
“It’s like a Mount Everest of mathematical structures they’ve climbed now,” said Brian Conrey, director of the American Institute of Mathematics in Palo Alto, which funded much of the research. “Now they know their way up it and are able to make use of what they found.”
The scientists – located in Maryland, Utah, Michigan, Massachusetts and even France – get little more than bragging rights for their achievement.
They were brought together four years ago by the Palo Alto institute to solve important math problems. The institute was founded by John Fry – think Fry’s Electronics – to bring a team approach to mathematics.
Scientists are optimistic that the knowledge gleaned from the experience will one day spur advances in math, science or technology – somehow.
“I don’t know that it could lead to a smaller hard drive or a cell phone that works better,” Conrey said. “But I do think the technology from being able to do analysis on this will have some important ramifications a clever engineer will be able to see how to really make use of.”
For their part, the scientists were always optimistic they would solve the problem. They say that working four years off and on to complete it wasn’t all that bad.
Said Adams, “We actually got here sooner than I thought.”
IF YOU’RE INTERESTED
If your eyes didn’t glaze over reading this story and you’re interested in learning more, go to the American Institute of Mathematics Web site (www.aimath.org).
Contact Julie Sevrens Lyons at jlyons@mercurynews.com or (408) 920-5989.
