Lodovico Ferrari of Bologna (1522-1565) was the first to discover an alegebraic solution to the quartic or biquadratic equation.
Taken in and trained by Gerolamo Cardano, he learned from his patron's lectures and eventually succeeded him as a lecturer in mathematics in Milan. Ferrari publicly challenged fellow mathematician Nicolo Tartaglia over how to solve a cubic equation, and won a math contest against him in 1548. This success brought him a chance at the job of tax assessor in Mantua, where he gained considerable wealth. Later he quarreled with the Cardinal and had to leave this post.