Lodovico arrived at Cardan's house on 30 November, a fourteen year old boy ready to take over his cousin Luke's position and become a servant. Cardan, upon the discovery that the lad could read and write, exempted him from menial tasks and appointed the youngster as his secretary. It was soon clear to Cardan that his secretary was an exceptionally gifted young man and he decided to teach him mathematics. Ferrari repaid his master by helping him with his manuscripts and, when he was eighteen years old, he began to teach. When Cardan generously resigned his post at the Piatti Foundation in Milan to make way for him in 1541, Ferrari easily defeated Zuanne da Coi, his only rival for the post, in a debate and, at the age of twenty, became a public lecturer in geometry.
Cardan and Ferrari made remarkable progress on the foundations that Tartaglia had unwillingly given them. They worked on problems set by Zuanne da Coi and eventually were able to extend solutions discovered in these special cases. Ferrari discovered the solution of the quartic equation in 1540 with a quite beautiful argument but it relied on the solution of cubic equations so could not be published before the solution of the cubic had been published. However, there was no way to make this public without the breaking the sacred oath made by Cardan. Despairing of ever publishing their ground breaking work, Cardan and Ferrari travelled to Bologna to call upon their mathematical colleague, Annibale della Nave, who had been appointed there on the death of Scipione del Ferro. Cardan and Ferrari satisfied della Nave that they could solve the ubiquitous cosa and cube problem, and della Nave showed them in return the papers of the late del Ferro, proving that Tartaglia was not the first to discover the solution of the cubic.
Cardan published both the solution to the cubic and Ferrari's solution to the quartic in Ars Magna (1545) convinced that he could break his oath since Tartaglia was not the first to solve the cubic. Tartaglia was furious and Ferrari wrote to Tartaglia, berating him mercilessly and challenging him to a public debate. Tartaglia was extremely reluctant to dispute with Ferrari, still a relatively unknown youngster, against whom even a victory would do little material good.
Tartaglia wrote back to Ferrari, trying to bring Cardan into the debate. Ferrari and Tartaglia wrote fruitlessly to each other for about a year, trading the most offensive personal insults but achieving little in the way of resolving the dispute. Things seemed to fizzle out when suddenly, in 1548, Tartaglia received an impressive offer of a lecturing position in his home town, Brescia. To establish he was the man for the job, Tartaglia was asked to journey to Milan and conclude the contest with Ferrari.
On 10 August 1548, the contest which all Italy wanted to see, for the correspondence between the two antagonists had taken the form of open letters, took place in the Church in the Garden of the Frati Zoccolanti in Milan. A huge crowd had gathered, and the Milanese celebrities came out in force, with Don Ferrante di Gonzaga, governor of Milan, the supreme arbiter. Ferrari was confident of success, despite his inexperience in such matters, and brought a large crowd of friends and supporters. Alone but for his brother, Tartaglia was a vastly experienced disputant and also fancied his chances.
By the end of the first day, it was clear that things were not going Tartaglia's way. He was unwilling to give Ferrari time to respond to his criticisms and when he did, it was Ferrari who got in the more telling blows. Ferrari clearly understood the cubic and quartic equations more thoroughly than his opponent who decided that he would leave Milan that very night and thus leave the contest unresolved, so victory went to Ferrari. On the strength of this challenge, Ferrari's fame soared and he was inundated with offers of employment, including a request from the emperor himself, who wanted a tutor for his son.
Ferrari fancied a more financially rewarding position though, and took up an appointment as tax assessor to the governor of Milan, Ferrando Gonzaga. After transferring to the service of the church, he retired as a young and very rich man. He moved back to his home town of Bologna where he lived with his widowed sister Maddalena, and was called to a professorship of mathematics at the University of Bologna in 1565 but, sadly, Ferrari died later that year. It is claimed that he died of white arsenic poisoning, administered by his own sister. Certainly, according to Cardan, Maddalena refused to grieve at her brother's funeral and, having inherited Ferrari's fortune, she remarried two weeks later. Having transferred all her possessions to her new husband, he promptly left her and she died in poverty.
Article by: J J O'Connor and E F Robertson