Overview

Advances in the theory of Lie algebra (also called Lie groups), developed by Norwegian mathematician Sophus Lie (1842-1899), have long enriched mathematics, particularly in the area of group theory. In 1952 Lie algebra was used to help solve one of the most famous problems in mathematics: Hilbert's fifth problem, posed in the year 1900 by David Hilbert (1862-1943). In addition to its use in solving this problem, Lie algebra has been used to gain a better understanding of the properties of many-dimensional surfaces in general, helping to advance the mathematical discipline of topology as well.

Background

One of the keynote speakers at the 1900 International Congress of Mathematicians, David Hilbert spoke about the future of mathematics. In his address, the renowned mathematician posed 23 major unsolved problems in mathematics...