# Sophus Lie

**Sophus Lie** was a

Norwegian-born

mathematician (

1842 -

1899) who largely created the theory of continuous symmetry, and applied it to the study of geometric structures and differential equations. Lie's principal tool, and one of his greatest achievements was the discovery that continuous

transformation groups (now called

Lie groups) could be better understood by "linearizing" them, and studying the corresponding generating vector fields (the so-called infinitesimal generators). The generators obey a linearized version of the group law called the commutator bracket, and have the structure of what we today, in honour of Lie, call a

Lie algebra.