Tartaglia (Nicolò Fontana) | Biography

Tartagliawas a self-taught mathematician whose work in algebra led to the first generalized solution of cubic equations. He was neither prominent nor well connected and spent most of his life earning a meager salary as a school teacher. In addition to his work in algebra, Tartaglia also made contributions to the fields of fundamental arithmetic, ballistics, military engineering, cartography, and the development of certain instruments used in surveying. His Italian translations of some of the works of Euclid and Archimedes represented the first time this information had been available in a modern language.

Tartaglia's given name was Nicolò (or Niccolò) Fontana. He was born in Brescia, Italy, in 1499 or possibly 1500. His father, Michele, was a postal courier who worked for the government of Brescia. When his father died in about 1506, the family was left in poverty. In 1512, the French army attacked Brescia. During the attack a French soldier set upon young Nicolò with a saber and left him with five head wounds. Although Nicolò eventually recovered, his mouth was so disfigured that he could no longer speak clearly. As a result of this speech impediment, he was given the nickname Tartaglia, from the Italian word tartagliare, which means "to stammer." Rather than being offended, Nicolò kept the nickname as a surname and used it for the rest of his life.

When he was about 14 years old, Tartaglia went to a tutor to learn the alphabet. By the time he reached the letter "k," he was no longer able to pay for lessons and subsequently taught himself from books. Tartaglia learned quickly and acquired enough skill at mathematics that he was able to obtain a position as a teacher of practical mathematics in Verona sometime between 1516 and 1518. He stayed in Verona until 1534 and rose to the position of headmaster of a school there. Some evidence indicates that Tartaglia had a family in Verona, although his income was barely enough to support them. In 1534, he moved to Venice to become a professor of mathematics. Except for a period of 18 months in 1548-1549, Tartaglia remained in Venice until his death.

Discovers a Solution to Cubic Equations

Tartaglia's most notable contribution to mathematics came shortly after he moved to Venice. As was the custom of the times, persons in academic positions were often subject to challenges of their knowledge and skills. In 1535, Tartaglia was challenged to a contest by Antonio Fior. Fior had been an aspiring but below average student of the mathematician Scipione dal Ferro, before dal Ferro's death in 1526. Just before his death, dal Ferro had given Fior a method for solving the so-called "depressed cubic" equation, in which there was no second power term. In turn, Fior had kept this method secret until he decided to use it to boost his floundering career by challenging Tartaglia. For his part, Tartaglia already knew how to solve cubic equations that lacked the first power term, and so he readily accepted Fior's challenge. Each person was to submit 30 problems for the other to solve. Rather than give Tartaglia problems covering a wide range of mathematical topics, Fior gambled and gave Tartaglia nothing but depressed cubics. After many days, with the deadline drawing near, Tartaglia discovered the solution and quickly solved all 30 problems. Fior, on the other hand, solved only a few of the problems posed by Tartaglia and suffered a humiliating defeat.

Tartaglia now knew the solutions to two types of cubic equations, and this knowledge put him in an enviable position among his fellow mathematicians. One in particular, Girolamo Cardano, repeatedly beseeched Tartaglia to share his secrets. Finally, in 1539, Tartaglia gave Cardano the solutions on the condition that Cardano not reveal them until Tartaglia had published them himself. Armed with this new knowledge, Cardano set about to discover the solution to a generalized cubic equation, in which all of the terms were present. Working with his new student, Ludovico Ferrari, Cardano discovered a method for reducing any generalized cubic equation to a depressed cubic. Then, using Tartaglia's methods, they could solve the equation. Unfortunately, Cardano was still bound by his promise not to reveal Tartaglia's methods. Then, in 1543, Cardano discovered that it was dal Ferro who had originally solved the depressed cubic equation, not Tartaglia. With this information Cardano went ahead and published his solution to a generalized cubic equation in 1545, giving full credit to dal Ferro and Tartaglia for their work. Tartaglia was outraged at this perceived breech of trust and wrote hotly and offensively about Cardano. Ferrari rose to Cardano's defense and began a long series of acrimonious correspondence with Tartaglia, ending in a public debate in Ferrari's home town of Milan in 1548. Backed by a sympathetic and unruly audience, Ferrari easily defeated Tartaglia, who was forced to withdraw in fear of his life.

Makes Contributions in Other Fields

In addition to his work in mathematics, Tartaglia's work drew interest in other areas. His work in ballisticsincluded the determination that the maximum theoretical range of a projectile is obtained when the firing angle is 45 degrees. He also proposed the concept of firing tables in which range is correlated to firing angle, powder charge, and other factors. In surveying, he showed how to apply the compass and proposed the design of two instruments for determining the heights and distances to inaccessible points.

Tartaglia published his Italian translation of Euclid's Elementsin 1543, and produced his translation of a Latin version of some of Archimedes' works the same year. He made additional translations of Archimedes' works in 1551, adding his own commentary. Tartaglia's translations contributed to the dissemination of knowledge by making these ancient works available in a modern language.

Tartaglia died impoverished in his home in Venice on December 13, 1557.