A Calculation the Size of Manhattan
Mathematicians solve E8 structure which will lead to potential new
discoveries in mathematics, physics and other fields
For Immediate Release
PALO ALTO, Calif., March 19, 2007
The American Institute of Mathematics (AIM), one of the leading
math institutes in the U.S., announced today that after four years
of intensive collaboration, 18 top mathematicians and computer
scientists from the U.S. and Europe have successfully mapped E8,
one of the largest and most complicated structures in mathematics.
Partners on this project included MIT, Cornell University, University
of Michigan, University of Utah and University of Maryland.
The findings will be unveiled today, Monday, March 19 at 2 p.m.
Eastern, at a presentation by David Vogan, Professor of Mathematics
at MIT and member of the team that mapped E8. The presentation is
open to the public and is taking place at MIT, Building 1, Room
190.
E8, (pronounced "E eight") is an example of a Lie (pronounced "Lee")
group. Lie groups were invented by the 19th century Norwegian
mathematician Sophus Lie to study symmetry. Underlying any symmetrical
object, such as a sphere, is a Lie group. Balls, cylinders or cones
are familiar examples of symmetric three-dimensional objects.
Mathematicians study symmetries in higher dimensions. In fact, E8
is the symmetries of a geometric object like a sphere, cylinder or
cone, but this object is 57-dimensional. E8 is itself is 248-dimensional.
For details on E8 visit http://aimath.org/E8/.
"E8 was discovered over a century ago, in 1887, and until now, no
one thought the structure could ever be understood," said Jeffrey
Adams, Project Leader and Mathematics Professor 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 may well have unforeseen implications
in mathematics and physics which wont be evident for years to come.
"This is an exciting breakthrough," said Peter Sarnak, Eugene Higgins
Professor of Mathematics at Princeton University and Chair of AIM's
Scientific Board. "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 magnitude and nature of the E8 calculation invite comparison
with the Human Genome Project. The human genome, which contains all
the genetic information of a cell, is less than a gigabyte in size.
The result of the E8 calculation, which contains all the information
about E8 and its representations, is 60 gigabytes in size. This is
enough to store 45 days of continuous music in MP3-format. If written
out on paper, the answer would cover an area the size of Manhattan.
The computation required sophisticated new mathematical techniques
and computing power not available even a few years ago. While many
scientific projects involve processing large amounts of data, the
E8 calculation is very different, as the size of the input is
comparatively small, but the answer itself is enormous, and very
dense.
"This is an impressive achievement", said Hermann Nicolai, Director
of the Albert Einstein Institute in Potsdam, Germany. "While
mathematicians have known for a long time about the beauty and the
uniqueness of E8, we physicists have come to appreciate its exceptional
role only more recently. Understanding the inner workings of E8 is
not only a great advance for pure mathematics, but may also help
physicists in their quest for a unified theory."
According to Brian Conrey, Executive Director of the American
Institute of Mathematics, "The E8 calculation is notable for both
its magnitude as well as the way it was achieved. The mapping of
E8 breaks the mold of mathematicians typically known for their
solitary style. People will look back on this project as a significant
landmark and because of this breakthrough, mathematics is now a
team sport."
The Atlas of Lie Groups Project
The E8 calculation is part of an ambitious project sponsored by AIM
and the National Science Foundation, known as the Atlas of Lie
Groups and Representations. The goal of the Atlas project is to
determine the unitary representations of all the Lie groups (E8 is
the largest of the exceptional Lie groups). This is one of the most
important unsolved problems of mathematics. The E8 calculation is
a major step, and suggest that the Atlas team is well on the way
to solving this problem.
The Atlas team consists of 18 researchers from around the globe.
The core group consists of Jeffrey Adams (University of Maryland),
Dan Barbasch (Cornell), John Stembridge (University of Michigan),
Peter Trapa (University of Utah) , Marc van Leeuwen (Poitiers),
David Vogan (MIT), and (until his death in 2006) Fokko du Cloux
(Lyon).
The Atlas project is funded by the National Science Foundation
through the American Institute of Mathematics.
About American Institute of Mathematics
The American Institute of Mathematics, a nonprofit organization,
was founded in 1994 by Silicon Valley businessmen John Fry and Steve
Sorenson, longtime supporters of mathematical research. AIM is one
of 7 mathematics institutes supported by the National Science
Foundation. The goals of AIM are to expand the frontiers of
mathematical knowledge through focused research projects, by
sponsoring conferences, and helping to develop the leaders of
tomorrow. In addition, AIM is interested in helping preserve the
history of mathematics through the acquisition and preservation of
rare mathematical books and documents and in making these materials
available to scholars of mathematical history. AIM currently resides
in temporary facilities in Palo Alto, California, the former Fry's
Electronics headquarters. A new facility is being constructed in
Morgan Hill, California. For more information, visit www.aimath.org.
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PR Contacts:
Shari Boxer Baker
408.888.5449, sboxerbaker@jdsgrouppr.com
Birgit Johnston
408.399.8088, birgitjohnston@msn.com
Spokespeople:
* Brian Conrey, AIM Director, 650.845.2071, conrey@aimath.org
* Jeffrey Adams, Project Leader and Mathematics Professor at
University of Maryland, 410.371.3272, jda@math.umd.edu
* Josh Chamot, Public Affairs Specialist and Spokesperson for the
National Science Foundation, 703.292.7730, jchamot@nsf.gov
Outside Experts:
* Peter Sarnak, Eugene Higgins Professor of Mathematics at Princeton
University and Chair of AIMs Scientific Board, 609.258.4200/
609.258.4229, sarnak@Math.Princeton.EDU
* Hermann Nicolai, Director of the Albert Einstein Institute in
Potsdam, Germany,
+49 331 567 7216 Hermann.Nicolai@aei.mpg.de
* Gregg Zuckerman, Professor of Mathematics at Yale University,
203.432.4198, gregg@math.yale.edu