ancient mathematicians wanted the solutions of univariate equations (that is, equations with one variable) in the form of radical expressions, like formula_6 for the positive solution of formula_7. the ancient egyptians knew how to solve equations of degree 2 (that is equations in which the highest power of the variable is 2) in this manner. during the renaissance, gerolamo cardano solved the equation of degree 3 and lodovico ferrari solved the equation of degree 4. finally niels henrik abel proved in 1824 that the equation of degree 5 and the equations of higher degree cannot always be solved by using radicals. galois theory, named after évariste galois, were introduced to give criteria deciding if an equation is solvable using radicals.