The story of the discovery of the solutions to the cubic and quartic is interesting. Here is the upshot: del Ferro found the solution of type I cubic and so an important class, Tartaglia could solve first the general cubic, Cardano assisted by Ferrari is the first who could solve the quartic.

So, the answer to the question who was the first to solve the cubic is: Scipione del Ferro and Nicolo Tartaglia. It appears clear now that these works were independent. The answer to the question who was the first to solve the quartic is Girolamo Cardano and Lodovico Ferrari. While Ferrari must have made the breakthrough to solve the quartic, it was of course heavily based on methods of Cardano and the cubic. Since by nature they collaborated heavily, it is only fair to credit both for the solution of the quartic.

Scipione del Ferro, solved n=ax+bx3 Type I	Anonio Fiore, inherited secret from del Ferro	Nicolo Tartaglia, 1535 battle with Fiore,	Girolamo Cardano, 1501-1576, got solution from Tartaglia, solved quartic	Lodovico Ferrari, 1558 battle with Tartaglia, secretary of Cardano

Please send questions and comments to knill@math.harvard.edu

Math E320| Oliver Knill | Spring 2012 | Extension School | Harvard University