Lie groups were first found by studying matrix subgroups formula_2 contained in formula_3 or formula_4, the groups of formula_5 invertible matrices over formula_6 or formula_7. These are now called the classical groups, as the concept has been extended far beyond these origins. Lie groups are named after Norwegian mathematician Sophus Lie (1842–1899), who laid the foundations of the theory of continuous transformation groups. Lie's original motivation for introducing Lie groups was to model the continuous symmetries of differential equations, in much the same way that finite groups are used in Galois theory to model the discrete symmetries of algebraic equations.