The Theory of Everything in 248 Easy Steps

Mar 22, 02:09 PM

Current Headlines: By Steve Connor

Four years of work by a team of 18 mathematicians have borne fruit in the shape of a proof that may help scientists to find the elusive theory of everything - a single unifying force of nature.

The structure has 248 dimensions and is known as E8. It refers to a mathematical concept called "the exceptional Lie group". The task was so daunting that the researchers struggled to find a computer large enough to handle the complex series of equations, which represents some 60 gigabytes of data - about 60 times bigger than the digital information of the human genome.

Lie groups were invented in the 19th century by the Norwegian Sophus Lie to study the rules of symmetry. Lie groups are at the heart of all 3D symmetrical structures, from spheres and cylinders to cones and squares.

"What's attractive about studying E8 is that it's as complicated as symmetry can get. Mathematicians can always offer another example that's harder than the one you're looking at now, but for Lie groups E8 is the hardest one," said Professor David Vogel of the Massachusetts Institute of Technology.

"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 Professor Vogel. "The uniqueness of E8 makes me hope that it should have a role to play in theorectical physics as well."

Professor Vogel presented the description of E8 at a lecture earlier this week entitled "The Character Table for E8, or how we wrote down a 453,060 x 453,060 matrix and found happiness".

Professor Peter Sarnak of Princeton University, who was not part of the work, said E8 was an exciting breakthrough because its solution may underline so many other fields of science.

"Understanding and classifying the representations of E8 and Lie groups has been critical to understanding phenomena in many areas, including algebra, geometry, number theory, physics and chemistry. This project will be invaluable for future mathematicians and scientists," Professor Sarnak said.

Hermann Nicolai, director of the Max Planck Institute in Potsdam, Germany, said the achievement was impressive given the scale of the problem faced by the team. "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," Dr Nicolai said. "Yet, in our attempts to unify gravity with the other fundamental forces into a consistent theory of quantum gravity, we now encounter it at almost every corner," he said.

"Thus, 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."

Mathematics is usually a solitary activity and it was unusual for such as large group to work together so closely, said Brian Conrey, of the American Institute of Mathematics."People will look back on this project as a significant landmark and because of this breakthrough, mathematics will now be viewed as a team sport."

Still unsolved...

Birch and Swinnerton-Dyer Conjecture Deals with the difficulties of finding solutions to equations with whole numbers

Yang-Mills Theory A description of elementary particles using structures that occur in geometry

Riemann Hypothesis This describes the distribution of prime numbers among other natural numbers

Navier-Stokes Equations Explains why waves follow a boat crossing a lake

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