# Tartaglia

# Tartaglia

**1499-1557**

**Italian Mathematician**

Tartaglia, whose given name was Nicolò Fontana, is remembered for a number of achievements in applied mathematics, as well as for his translations of Euclid (c. 325-c. 250 b.c.) and Archimedes (c. 287-212 b.c.) His most memorable achievement, however, was his work in algebra leading to a generalized solution of cubic equations. The latter placed him at the center of a heated conflict involving fellow mathematicians Girolamo Cardano (1501-1576) and Cardano's assistant Ludovico Ferrari (1522-1565).

Born in Brescia, Italy, in 1499, Nicolò Fontana was the son of a humble postal courier who died when he was seven. The family was rendered destitute by the father's death, and as if this were not enough, the French army attacked the town five years later. A French soldier disfigured young Nicolò's face, cutting his mouth so badly it was difficult for him to talk thereafter. Therefore he acquired the nickname Tartaglia, drawn from the Italian word *tartagliare,* "to stammer." Rather than be ashamed, however, Fontana took on the epithet as his name.

Tartaglia was almost entirely a self-made man, and by sheer force of will taught himself enough that by about the age of 18 he had obtained a position as a teacher of practical mathematics in Verona. He remained in Verona for more than 16 years, during which time he rose to the position of headmaster and may have married and had children. In 1534, he moved to Venice, where he would spend virtually the remainder of his life.

During the following year, Tartaglia inadvertently became involved in the cubic-equation problem. It so happened that Scipione dal Ferro (1465-1526) had developed a method for solving a cubic equation lacking a second-power term—a so-called "depressed cubic"—and before his death had shared it with his assistant, Antonio Fior. The latter was a man of no great genius; moreover, Fior quaked with fright at the prospect of a public challenge from a competing mathematician (a not-uncommon occupational hazard for mathematical scholars of the day), which would reveal his ignorance for all to see. Therefore he took what he thought was a preemptive strike, and challenged Tartaglia to a contest of wits.

Whereas Tartaglia presented his opponent with 30 problems involving a variety of mathematical topics, Fior hit Tartaglia with 30 problems that required the use of the depressed cubic for their solution. Thus Tartaglia was forced to figure out the depressed cubic ace public disgrace and probable loss of his position—so he did, soundly defeating Fior, who could only answer a few of his questions.

Later Cardano begged Tartaglia to teach him his secret, and Tartaglia agreed on condition that Cardano would not reveal it to anyone else until Tartaglia published it himself. Of course Tartaglia had no intention of publishing information that gave him an advantage over other mathematicians, and in time Cardano revealed what he knew to his assistant Ferrari. As a result, the two men developed a method for reducing any generalized cubic equation to a depressed cubic—and thus they unlocked the secret of solving cubic equations.

Later, when they discovered that dal Ferro had developed the depressed cubic first, Cardano no longer considered himself under obligation to Tartaglia, and published his findings, giving credit both to dal Ferro and Tartaglia. Tartaglia was furious, and began conducting a fierce letterwriting campaign against Cardano. Ferrari defended his mentor, and the conflict came to a head in a public debate in Milan in 1548. It so happened that Ferrari was from Milan, and thus possessing the "home-field advantage," he and his supporters forced Tartaglia to back down.

Though he is known primarily for his involvement in the fascinating cubic-equation imbroglio, Tartaglia also contributed to areas including ballistics and surveying. His translations of Euclid and Archimedes into Italian marked the first time that many works by these ancients had appeared in a modern language. Despite his many achievements, however, he lived most of his life in poverty, and died poor in Venice on December 13, 1557.

**JUDSON KNIGHT**

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