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+bx^{3} 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 |