Rafael Bombelli – Italian mathematician

Rafael Bombelli was born on January 20, 1526, in Bologna, Italy and died on 1572, in Rome, Italy. The original family name was Mazzoli. The Mazzolis, who seem to have been small landowners, adopted the name Bombelli early in the sixteenth century. Rafael Bombelli was the eldest son, and he was one of a family of six children. Rafael received no university education.

He was trained by an engineer- architect Pier Francesco Clementi and worked as an engineer-architect until died on 1573 without much recognition until hundred years later by the math society as a great Italian mathematician.

Bombelli followed Clementi into the profession and acquired a patron, Alessandro Rufini. The major engineering project on which Bombelli was employed was the reclamation of the marshes of the Val du Chiana. It was at a time when the reclamation work had been suspended that he wrote his treatise on algebra in the peaceful atmosphere of his patron’s villa in Rome.

Rafael Bombelli was the first to propose the idea of complex numbers. Bombelli wrote about imaginary numbers in his very influential book Algebra which was published in 1572. In his book, Bombelli solved equations, using the method of del Ferro/Tartaglia, he introduced +i and -i and described how they both worked in Algebra.
Rafael Bombelli – Italian mathematician

Scipione del Ferro (1465-1526)

Scipione del Ferro was an Italian mathematician who is believed to have found a solution to the cubic equation. In mid 16th century Italy, there was much interest and debate over the solution of the cubic, or third degree, polynomial.

Before the publication in about 1545 of Girolamo Cardano’s controversial book Artis magnae sive de regulis algebraicis liber unus, del Ferro had already discovered the general solution of certain cubic equations some decades earlier.

Del Ferro was born on February 6, 1465, in Bologna, Italy. His father was Floriana Ferro, a papermaker, and his mother was named Filippa.

Del Ferro attended the University of Bologna and he became a lecturer in arithmetic and geometry at the university, where he remained from 1496 to 1526. He retained his post for the rest of his life although during the last few years he also did some commercial work.

Although none of his work survives he is known to have influenced the study of fractions with irrational denominators. He kept a notebook where he recorded all his important discoveries.

After his death in 1526, this notebook was inherited by his son in-law Hannival Nave. Del Ferro died on November 5, 1526 in Bologna.
Scipione del Ferro (1465-1526)

Lodovico Ferrari (2 February 1522 – 5 October 1565)

Lodovico Ferrari was an Italian mathematician, was the first to find an algebraic solution to the biquadratic or quartic equation.  Honorably named and little more, of he died young and left no written works behind him.

Born in Bologna, Italy, Lodovico's grandfather, Bartholomew Ferrari, was forced out of Milan to Bologna. Lodovico settled in Bologna, Italy.

He came to Gerolamo Cardano as a youth in November 30, 1536 and Cardano has described that day with a lot of enthusiasm in his writing.  Ferrari was fourteen when he started working in the household of Cardano.

He was extremely bright. He was a boy of very extraordinary natural ability, so Cardano treated him first like a disciple and then as collaborator.

By attending Cardano’s lectures, Ferrari learned Latin, Greek and mathematics.  At the age of eighteen Ferrari was able to obtain a prestigious teaching post after Cardano resigned from it and recommended him.

Ferrari aided Cardano on his solutions for quadratic equations and cubic equations, and was mainly responsible for the solution of quartic equations that Cardano published in Ars magna (1545; Great Art).

The publication of Ars magna brought Ferrari into a celebrated controversy with the noted Italian mathematician Niccolo Tartaglia over the solution of the cubic equation.

He was twenty years old when he contested publicly with Zuanne da Coi and Tartaglia: Tartaglia declares in his own book that he, Tartaglia, was left the victor: Cardano states that Ferrari overcame them both and appeals confidently, in support of his assertion, to the public records then extant and the common understanding in the town.

Two years afterwards the brilliant young scholar was held in so much esteem, that the possession of his services was contended for by the great men around him.

Ferrari eventually retired young (only 42) and quite rich.  He then moved back to his home town of Bologna where he lived with his widowed sister Maddalena to take up a professorship in mathematics at the University of Bologna in 1565, where he died shortly thereafter due to white arsenic poisoning.

Ferrari death was a pro-found loss to Cardano. Cardano wrote an account of Ferrari’s life and achievements and acknowledge that he had no more loyal friend and co-worker.
Lodovico Ferrari (2 February 1522 – 5 October 1565)