## News from the world of maths: The eventful life of Lodovico Ferrari

### The eventful life of Lodovico Ferrari

Lodovico Ferrari was an Italian mathematician famed for solving the quartic equation. Ferrari was born in 1522 in Bologna and at the age of 14 became the servant of Gerolamo Cardan, a celebrated Italian Renaissance mathematician, physician, astrologer and gambler.

Ferrari showed mathematical promise at a young age, and at the age of 20 became a public lecturer in geometry. He was also a player in a great mathematical controversy of the time - who should get credit for the development of solutions for the cubic and quartic equations.

The controversy includes another notable mathematician of his day, Nicolo Fontana Tartaglia. Tartaglia was an Italian mathematician who was the first to apply mathematics to the investigation of the paths of cannonballs. He had developed his own solutions to the cubic equations, and when Cardan heard of this achievement, nagged a reluctant Tartaglia to show him his work. He succeeded only when he challenged him to a debate and implied that through his influence he could arrange a potentially lucrative contact with the governor of Milan. Tartaglia agreed to tell Cardan his method if Cardan would swear never to reveal it and to only ever write it down in code so that even if he died, nobody would ever discover it. Cardan agreed to this, and Tartaglia enigmatically handed over his formula in the form of a poem.

Several years later however, Cardan and Ferrari saw unpublished work by Scipione del Ferro who had independently devised the same solution as Tartaglia. This work was dated before the work of Tartaglia, and so they decided to break their promise and the include Tartaglia's solution in their published work. Based on Tartaglia's formula, Cardan and Ferrari found proofs for all cases of the cubic and, more impressively, solved the quartic equation - this was reportedly largely due to the work of Ferrari.

Tartaglia then started a campaign of public abuse directed at Cardan and Ferrari, and whilst most of the insults washed off Cardan - who was now established as the world's leading mathematician - Ferrari wrote to Tartaglia challenging him to a public debate. Tartaglia however did not consider Ferrari as worthy of debate - it was Cardan he wanted. Ferrari and Tartaglia traded insults for over a year until 1548 when Tartaglia received an offer of a lectureship in Brescia. To establish his credentials for the post, he was asked to take part in the debate with Ferrari.

Tartaglia was an experienced debater and expected to win. However, by the end of the first day, it was clear that things were not going his way and that Ferrari understood the cubic and quartic equations more thoroughly. Tartaglia decided to flee that night, with victory left to Ferrari. Ferrari's fame soared and he was inundated with offers of employment, including a request from the emperor.

Ferrari was appointed tax assessor to the governor of Milan, and after transferring to the service of the church, retired as a young (aged 42) and rich man. He moved back to his home town of Bologna and in with his widowed sister Maddalena. He died in 1565 of white arsenic poisoning, most likely administered by Maddalena. Maddalena did not grieve at his funeral and having inherited his fortune, remarried two weeks later. Her new husband promptly left her with all her fortune and she died in poverty.

For more information on cubic equations, see Plus articles Mathematical Mysteries: Trisecting the Angle, and Woman joins Adams Family. And for more on Ferrari, see MacTutor

*posted by Plus @ 4:22 PM*