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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