Math team solves the unsolvable E8

If you thought writing calculations to describe three-dimensional objects in math class was hard, consider doing the same for one with 248 dimensions.

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 large-scale 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 large-scale computing factored heavily into solving the equation means that other difficult and long-standing 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 19th-century 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 higher-dimension 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.

[cameronjpu]

What?

Huh?

[ss_Whiplash]

What?

I was just thinking the same thing. This is so far over my head it's not even funny.

I just hope it's in some way useful... to somebody. :-)

[be_free]

What?

If you want to get really confused, check the Wikipedia entry: http://en.wikipedia.org/wiki/E8_(mathematics)

My gawd.

[GGGlen]

Big deal

Call me when they understand women.

[The_Nirvana]

And we all know....

that there are more than 248 dimensions to a woman ;-).

[CarpalDiem]

Re: Big Deal

It's speculated that a woman's states are described by E12. So get cracking; you have a lot of work to do.

[mahurshi]

it is too complicated to solve

that would be so much harder than E8. it is more along the lines of E∞ (prounounced, E Infinity).

the reason? : you think you've reached a solution and the next thing you know.. it doesn't work when you plug it back into the equation. it just doesn't make any logical sense.

there is no need to get disappointed though. theoretically, there exists is a solution. but you need to solve the infinite equations of E∞ to obtain it.

BTW.. let me know what the answer is if you get around to actually solving it. :-)

Mahurshi Akilla

[pjianwei]

Enough grapes here to make a fine wine.

Waiting for the cnet branded wine, shall be a vintage.

[windridr]

What about the CS

What about the Computer Science behind this? I am curious what machine(s) language(s) etc were used.

[GGGlen]

To start a flame war;

We all know that they were using Macs running OS X ;-)

[tundraboy]

You don't say

"... it brought together 18 math professors who typically work alone"

That in itself is already spooky. Spooky awe-inspiring. The adjectivial clause is redundant though.

[GGGlen]

Informative article

"E8 (pronounced "e eight")".
Thank heavens for that bit of information! I was just about to
pronounce E8 as "Hyundai Sonata".

[J_Satch]

LMAO!

Thanks!

[kwarley]

maths team solves the unsolvable E8

this is wonderful,and this tells us that there is nothing on this world that can not be solved.thanks to those mathematicians.can we see the equation or the solution to the problem?

[nick fortis]

E8

To me a big plus here is the blending, if you will, of mathematics
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

[Steve Bryan]

?

First, the Poincare conjecture has already been solved without
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).

[arluthier]

Now-a-days Mathmatics≈CS

Most of the mathematicians I know (and I work with several) indicate that universities now-a-days combine many of the CS disiplines into mathematics programs. I think you will see more of these types of "solvings" in the future as more new mathematicians get experience and build their own calculation systems.

[the1kingarthur]

RE: You don't say

My compliments to you for such a wise and factual observation. AND THIS IS NO JOKE.

[Hobyx]

uhh why? and who paid for this?

Why on earth did this need solving? Did the NSF pay for this? Did
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 earth-like 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.

[flowerboy2001]

The big issues

As you speculated, this kind of mathematical research is never a waste of time and money. The point is you solve them once and then they can be used to solve real world problems. Problems like:
- techniques to stop certain imperial occupations from continuing
- certain fascists from taking over the world
- or possibly enable faster than light travel to distant earth-like 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.

[swamijie]

because you don't understand it, it shouldn't be investigated?

So let's list all of the things that would never have been investigated and all of the problems that would never have been solve because most of us don't understand them and don't see any use for, therefore don't think are worth investigating or trying to solve... any takers?

[Seaspray0]

Good question

You have a valid reason for bringing up that question, especially after seeing how the government spends money on research that makes no sense. I suspect it was funded because there are examples in physics that can be related to the E8 equation, probably on some subatomic level. But, I can give you an example where research has more than paid for itself, the technology advances derived from the space program are worth more than the cost of the program. Not always is it like this, but it does happen. Feel free to ask that question, it is a worthy one to ask, however it might be better to ask it before the money is spent.

[alegr]

We'll see

When Evariste Galois invented his theory (as abstract as it gets) circa 1830, nobody knew that it would lead to development of Reed-Solomon error-correcting codes, widely used in hard disk drives these days.

Regarding E8, it plays major role in string theory (AKA "theory of everything").

[Thomas, David]

B1 (Pronounced B "one")

eom

[dmm]

Next up

Mathematicians are now turning to the study of these groups:
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).

[godsmathguy]

OUTSTANDING!

I am quite proud of this accomplishment and give much love to my fellow engineers and mathematicians for the tremendous amount of research and brainpower that went into making this happen. Although I am a military officer (former engineer and applied mathematician)I still can appreciate the potential this work has.
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 n-th 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