Lodovico Ferrari

Ludovico Ferrari (also known as Lodovico Ferrari; Bologna, Italy, February 2, 1522 - ibid, October 5, 1565) was an Italian mathematician. Like Rafael Bombelli, he was a student of mathematics and together with his patron and collaborator Gerolamo Cardano, he became one of the greatest representatives of the Bologna school, which was mainly dedicated to the study of algebra. He discovered the general procedure for the algebraic resolution of quadratic equations, and collaborated with Cardano in proving the formula for solving quadratic equations. It is said that he died poisoned with white arsenic by his sister Maddalena.

Biography

Lodovico Ferrari's grandfather, Bartholomeo Ferrari, moved to Bologna from Milan because of the war. In northern Italy at that time the cities were in the hands of great families or depended on the Papal States. But also the French and Spanish fought for these possessions. In this turbulent time, Ludovico, son of Alexandro Ferrari, was born. Initially he was educated at home, then when his father died, Lodovico went to live with his uncle Vincenzo de el. A son of this and cousin of Lodovico went to Milan and began working at Cardano's house, although he returned to his house shortly after. When Cardano contacted Vincenzo to try to get him to return, Vincenzo took the opportunity to send his nephew Ludovico in his place.

This is how Ludovico came to Cardano's house at the age of 14 and became his servant. Cardano soon discovered that Lodovico knew how to read and write and took him on as secretary to write his own books. He soon realized that Ludovico was also a fast learner and began to teach him mathematics. Ferrari wrote all of Cardano's manuscripts and when he turned 18 he began teaching others. When Cardano resigned his position at the Piatti foundation in Milan in 1541, Ferrari easily won this position in opposition to a rival and at the age of 20 he began teaching geometry.

Cardano and Ferrari studied the solution of the cubics that Tartaglia had told them. They solved the problems that Zuanne da Coi had proposed and wrote the cases in which a cubic could occur with positive coefficients. In this process, Ferrari also discovered the general solution of the quartic in 1540, which with a beautiful argument reduced the problem to solving a cubic by Tartaglia's method. As Cardano had sworn to Tartaglia that he would not publish the solution of the cubics, he could not publish the quartics that depended on the solution of those either.

Then they both traveled to Bologna, where it was said that Professor Scipione del Ferro, dead for some years, had managed to solve a particular case of the cubic. There they visited Cardano's son-in-law, Annibale de la Nave, who now held his position as professor of mathematics at the University of Bologna. It seems that he showed them some supposed del Ferro manuscripts, where there was a way to solve a case of the cubic. They decided that Tartaglia was not the first to discover the solution of the cubic and that Cardano was released from his promise to Tartaglia. Interestingly these supposed manuscripts were never published.

Afterwards, Cardano, although he was not the discoverer of any of them, published the solution of the cubics and quartics in his famous book Ars Magna (1545). This book marked an important milestone in the history of Italian mathematics, since it influenced and was studied by almost all subsequent mathematicians for several centuries. However, this book, an example of plagiarism, marked with misfortune its two protagonists, Cardano and Ferrari, who died tragically and violently.

Tartaglia was enraged and wrote to Cardano on several occasions, without being answered by him. Instead, Ferrari wrote to Tartaglia, challenging him to a public duel or mathematical debate, a popular occurrence during the Renaissance. These debates were made with a notary and proposals of problems by both contenders. Tartaglia did not want to compete in the challenge with Ferrari, since he considered him a secondary actor.

Tartaglia was wrong about this and, after a year of exchanging letters and insults with Ferrari without receiving an answer from Cardano himself, he had to accept Ferrari's challenge. Indeed, Tartaglia, whose economic situation was never good, received an attractive job offer from his own city of Brescia. But they made it a condition that he accept the challenge with Ferrari, which had already become famous.

On August 10, 1548, the long-awaited debate took place in the church and gardens of Frati Zoccolanti in Milan. A large crowd gathered and all the notables of the city were awaiting his resolution, including the governor of Milan (dependent on the Spanish crown), Don Fernando de Gonzaga, who was the ultimate judge. Although Tartaglia had experience and had won other debates, Ferrari had a better knowledge of the practical problems of cubics and especially quartics that he himself had solved for his Cardano pattern book.

Tartaglia, with less character and older, soon realized that the public celebrated every action of his opponent and that he himself did not know how to solve some of the problems that involved quartics. He decided to leave Milan overnight without waiting to conclude the debate, in which Ferrari was finally declared the winner. As a consequence of this fact, Ferrari gained fame and had many job offers, including one from the emperor himself, who wanted a tutor for his son. Ferrari would never work on mathematics again.

Ferrando Gonzaga landed a position as tax adviser to the governor of Milan to Ferrari, who retired young and rich to his hometown of Bologna, where he lived with his widowed sister Maddalena. In 1565, he was offered a professorship at the University of Bologna, but unfortunately, Ferrari died that same year, said to have been poisoned with arsenic by his own sister. According to Cardano, his sister did not weep at his funeral, and having inherited his fortune, she remarried within a few weeks.