By combining the language of groups with that of geometry and linear algebra, Marius Sophus Lie created one of math’s most ...

Group gradings provide a powerful framework for decomposing algebraic structures into subspaces that are systematically indexed by a group. In the context of Lie algebras, which play a central role in ...

Modern physics began with a sweeping unification: in 1687 Isaac Newton showed that the disparate theories describing everything from planetary motion to tides to pendulums were all aspects of a ...

This monthly journal, published since 1900, is devoted entirely to research in pure and applied mathematics, and, in general, includes longer papers than those in the Proceedings of the American ...

A bit over two years ago, news sources and science blogs lit up when a pre-print paper from Dr. A. Garrett Lisi came to light that proposed a novel theory of everything—one theory that accurately ...