Patrick Foster
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For four years they have locked themselves away in their laboratories, poring over some of the most abstract calculations known to mankind.
But today 18 leading mathematicians will emerge, blinking, into the public glare, to tell the American Institute of Mathematics that they have mapped E8, one of the most complicated mathematical structures.
Although it has no immediate uses, and you may need a PhD in maths to understand what it means, the group has solved a 120-year-old problem previously thought impossible.
If the calculations were written on paper it would cover an area the size of Manhattan.
E8 is an example of a Lie (pronounced “lee”) group. The brainchild of Sophus Lie, a 19th-century Norwegian mathematician, Lie groups explain the manner in which symmetrical objects could be rotated while still looking the same.
It is relatively simple to imagine a three-dimensional sphere rotating around its axes, while looking identical from every angle. E8, however, explains the symmetry of a 57-dimensional object. And for a reason known only to advanced mathematicians, E8 itself has 248 dimensions.
Jeffrey Adams, a professor of mathematics at the University of Maryland and the project’s leader, said: “It’s like the human genome project. DNA has all the information coded in it, which was mapped for the genome project.
“What we’ve done is to map the structure of E8, showing all its different manifestations. If people say we’re mad, in some sense they’re right. But it’s mathematics of the highest character. It’s the most interesting thing I can imagine thinking about.”
The human genome project needs one gigabyte of disk space to be stored. E8 needs 60, the equivalent of 45 days of continuous MP3s.
There are few clues as to E8’s use. Professor Adams believes it may help to explain some problems facing physicists.
“Amazingly, E8 comes up in physics — in string theory. Some physicists believe that plays a fundamental role in explaining the theory of matter. It may be that some day this calculation can help physicists to understand the universe.”
One of the main problems was the volume of data that the group’s calculations would produce. It took two years to programme the formula into a computer, then a further year to find a computer powerful enough to do the calculations.
In the end a supercomputer, Sage, at the University of Washington, took 77 hours to compute the answer.
“It was an enormous effort but an enormous amount of fun,” said David Vogan, a professor of mathematics at Massachusetts Institute of Technology.
“Once you get halfway up the mountain you want to get to the top. It was such a delight to be working for it.”
In the matrix
— The result of the E8 calculation is a matrix, or grid, with 453,060 rows and columns
— While many scientific projects involve processing large amounts of data, the E8 calculation is different: the size of the input is small, but the answer itself is enormous, and very dense
— The E8 root system consists of 240 vectors in an eight-dimensional space, illustrated above
Source: American Institute of Mathematics

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Hmm,
Most of the comments seem to be coming from people who think more along the lines of "how many pints of stella before the stella goggles become truly effective"
Everything that happens in this world has a mathematical explanation.
English may be the most commonly spoken, but in terms of explaining how everything works, maths is universal - it is the language of life itself.
Those here who mock are entitled to, i can see the funny side too, but these people devote large parts of their life to unlocking the mysteries of life and should be applauded, not ridiculed.
Without these people, we wouldnt have sent probes to the edge of the universe, or put men on the moon.
Mark, Warrington, UK
The interesting thing about math is that theories discovered and thought "useless" much later come to use as science evolves.
- Boolean algebra in the 1800's - used for computers a hundred years later
- Imaginary numbers - used for AC (Alternating Current) calculations
- Fractals - very hot for digital sound/radio/TV
- E8 - who knows a hundred years from now
Ake, Stockholm, Sweden
Even though I am totally confused about what is being said in the article above, I think people that write in with ignorant views are pathetic. The people that come up with theories like this are more intelligent than you could begin to imagine and should not be made fun of. My dad is a mathmetician and although none of the maths genes were passed on to me, I have the upmost respect for him and others like him, as they are the ones that could run rings around the arrogants on here.
Tricia, Boston, Lincolnshire
Should have asked me for the answer,yours The Doctor.(presently off Earth in the TARDIS)
John Winston Price, Oldham, England
About Time!
Only a 2-D matrix.. how démodé!
Simple tesselation is SO-O-O-O-O last Age!
Sum.. Err!.. Ergo Sum, London,
21 over 32 is the answer.
cw, bromley, uk
The good thing is that by mapping 248 dimensions we are likely to be able to triangulate superstring geometry across a unform trime-base. This, of course, can only be a good thing.
Thicasa Planck, London,
At the end of the day ...the mind 'boggles' !!!! Well mine does anyway ...what happened to the fat lady ?
COLIN STANSBIE, PORTLAND, DORSET
The big question is just how many football fields would the calcualtion cover were it to be written out, surely?
Richard, Plymouth, Devon
Other than in the headline, I can't see a zero anywhere, great, big or otherwise. This is an triumph of the human spirit, ranking with all sorts of arty farty crap like the Taj Mahal, the Sistine Chapel, the revived Take That and String Theory. It's fun for those who can understand it and are bothered to give it a go, and it can nourish us all in the apocalyptic wasteland that we currently inhabit.
robert, Birmingham, UK
Great, manifolds as a parabolic expression. We may now fully appreciate the significance of the amino-acids. In applying basi- cranial indices as further data we may finally identify an Arabic character both with Greek logic and, critically, identify this as developing further African nomadic dialogue.
Christopher Rea, Oxford, U.K.
The quality of the spelling in these replies doesn't say very much for the school system. Get a grip!
dave, Reading,
Yes they do get paid for it - just because you can have little understanding or insight into someone else's work does not mean it is irrelevant nor unuseful.
I'm sure Einsteins theory of relativety was greeted in a similar manner by equivalents of yourself of the time, think before you speak!
Ryan O'Neill, Southampton, Hampshire
Surprised to see some astonishingly ignorant views expressed here. Pure mathematical and scientific research like this is often viewed with scepticism and seen as irrelevant to everyday life; however it is precisely this sort of discovery which has lead to inventions such as the silicon chip, and gives us the tools to understand more about ourselves and the universe around us.
John from Peterhead, shame on you!
Former Chemist, London,
Awesome! I can't even contemplate a 5 dimensional object, let alone a 57 dimension one. I sit here in awe of what mathematics (mathematicians) have accomplished and wonder at what they will discover next.
P/NP anyone?
c. frost, mildenhall, suffolk, England
They may even get paid for it, John.
James Minchew, Gloucester, England
To Barry Holroyd:
Three-quarters of seven eighths is twenty-one thirty-seconds.
David, Alyth, Perthshire
We have the computer power.
Now we have a way of using it -- to achieve -- not sure what.
Have fun
DavidN, Melbourne,
but can they tell me what three-quarters of seven-eights is?
Barry Holroyd, Leeds, England
and thy get payed for this
john, peterhead, uk
Thank God we have that! I've no idea what we'd have done with out it. What worries me though is how much they have got paid to work out something that helps them and those like them but not the common man.
Rob, Brynamman, South Wales, UK.