March 19, 2007 1:02 PM PDT
Math team solves the unsolvable E8
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Mathematicians call such an object E8 (pronounced "e eight"), a symmetrical structure whose mathematical calculation has long been considered an unsolvable problem. Yet an international team of math whizzes cracked E8's symmetrical code in a largescale computing project, which produced about 60 gigabytes of data. If they were to show their handiwork on paper, the written equation would cover an area the size of Manhattan.
David Vogan, a professor in MIT's Department of Mathematics and member of the international research team, presented the work Monday on MIT's campus. His talk was called "The Character Table for E8, or How We Wrote Down a 453,060 x 453,060 Matrix and Found Happiness."
"What's attractive about studying E8 is that it's as complicated as symmetry can get," Vogan said in a statement.
Project leaders said that the work is important for several reasons. First, it brought together 18 math professors who typically work alone, in a landmark project sponsored by the National Science Foundation. Second, that largescale computing factored heavily into solving the equation means that other difficult and longstanding math problems could be understood this way. And the work might lead to new discoveries in mathematics and physics.
"Understanding and classifying the representations of E8 ?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," said Peter Sarnak, a professor of mathematics at Princeton University who was not involved with the work.
E8 was discovered in 1887 and it's an example of a Lie (pronounced "Lee") group. The 19thcentury Norwegian mathematician Sophus Lie invented Lie groups as a way to study the symmetry of inherently symmetrical objects like the sphere. With its 248 dimensions, E8 is the largest of the higherdimension Lie groups. Under a project called Atlas, mathematicians are trying to determine the unitary representations (or symmetries of a quantum mechanical system) of all the Lie groups.
"There are lots of ways that E8 appears in abstract mathematics, and it's going to be fun to try to find interpretations of our work in some of those appearances," said Vogan. "The uniqueness of E8 makes me hope that it should have a role to play in theoretical physics as well. So far the work in that direction is pretty speculative, but I'll stay hopeful."
The 18 researchers included mathematicians from MIT, Cornell University, University of Michigan, and the University of Poitiers, in France.
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33 comments
Join the conversation! Add your comment
I just hope it's in some way useful... to somebody. :)
My gawd.
That in itself is already spooky. Spooky aweinspiring. The adjectivial clause is redundant though.
Thank heavens for that bit of information! I was just about to
pronounce E8 as "Hyundai Sonata".
and computer science/technology. Perhaps this will make it a
touch easier for (pure) mathematicians to accept help from CS in
proving some of the major unsolved math issues such as the
Rieman Hypothesis or Poincare Conjecture. Perhaps.
naf Los Altos
any mucking around with computers. Just google the name
Grigori Perelman to see some of the details. I can see how
computers could be applied to the proof of the 4 color map
theorem (by examining all the cases exhaustively) but I'm not
certain how such an approach helps with the Riemann
hypothesis (you can't ever find all its zeros no matter how long
you compute so there is no exhaustive strategy available).
Finally I think the title of this article would be more accurate if
they changed it to "solves the intractable" rather than "solves the
unsolvable" which is just plain wrong (after all there are perfectly
respectable unsolvable problems in math).
others pay for this to be done? Is this useful for ANYTHING
besides giving mathematicians something to do?
Because right now it seems like it's a big fat waste of time and
effort  unless they can use these findings or techniques to stop
certain imperial occupations from continuing, certain fascists
from taking over the world, or possibly enable faster than light
travel to distant earthlike planets. How about calculating the
best way to reverse global warming? Simulating a genetic fix to
the human lusts for violence and abuse?
Otherwise the only results we'll see from this kind of research is
tripe like What the Bleep or The Secret.. and we certainly don't
need any more of them.
 techniques to stop certain imperial occupations from continuing
 certain fascists from taking over the world
 or possibly enable faster than light travel to distant earthlike planets
 calculating the best way to reverse global warming
 simulating a genetic fix to the human lusts for violence and abuse
and more like that.
There is one annoying thing with all this however, and its the fact that before a mathematical problem is actually solved its impossible to know which of all real world problems it will help solve.
Since that is the case the most cost efficient way for society is to maintain a big list of unsolved mathematical problems and give resources to very intelligent people so they can solve them. And that is how its been done for more than a 100 years.
Regarding E8, it plays major role in string theory (AKA "theory of everything").
I1 (competition to solve this group is fierce),
U2 (the biggest group in history),
B4 (key to time travel, as requested),
I5 (first to solve will get I5s all around),
S6 (popular with dumb blond Londoners),
K9 (a dog of a problem).
If possible, this just might finally lead to a mathematical basis for TOE and Grand Unified Theory. In which case new physics, Applied Abstract Lie Algebra, Topology, and differential geometry (Abel, Einstein, Galois, Lie, Banneker, and math others would be proud) texts will need to be written to explore the implications. I thank God for blessing this team with the wisdom to work through a very complex Abelian Lie Group and am grateful computer science has finally allowed mathematicians to explore topics we have always been fascinated with but needed tremendous computer power to investigate. Now on to a universal formula for the nth prime and a way to demonstate that math is to be enjoyed by all persons not just the geeks of the world (I include myself although not your typical one).
Have a blessed week.
godsmathguy