Sophus Lie was a Norwegian mathematician born on December 17, 1842, and he is best known for founding the field of Lie groups and Lie algebras. His work focused on continuous transformation groups, which are essential in various areas of mathematics and theoretical physics. Lie's contributions helped to unify different mathematical concepts and provided tools for solving differential equations. Lie's ideas have had a lasting impact on modern mathematics, influencing areas such as geometry, differential equations, and symmetry. His legacy continues through the application of his theories in fields like quantum mechanics and general relativity, where understanding symmetries is crucial for describing physical phenomena.