TARTAGLIA, NICCOLO

A significant contributor to sixteenth-century mathematical scholarship, Nic-colo Tartaglia was born into an impoverished family, possibly surnamed Fon­tana, of Brescia in northern Italy. From his very early years, his life was a document in hardship. His father, a mail courier, died when the boy was about six, and afterward the family fell into poverty. In 1512 Niccolo barely escaped with his life when the French army sacked Brescia, putting much of the popu­lation to the sword. The wounds he sustained to his head and mouth, however, left him with a speech defect that earned him the name Tartaglia, from the Italian verb meaning "to stutter."

Despite the family's straitened circumstances, Tartaglia's mother managed to finance her son's early education until lack of funds obliged him to continue his studies on his own.Tartaglia's mathematical aptitude developed rapidly. When he was about eighteen years of age, he became a teacher of the abacus in Verona, where he eventually started a family before moving to Venice in 1534. He was employed as a professor of mathematics in and around that city for nearly the entire remainder of his life.

Given his limited formal schooling, Tartaglia's contributions to mathematical and humanistic scholarship were not inconsiderable. He acquired a favorable reputation for his work in the military sciences, particularly for his treatise on ballistics,Nova scientia(1537). Also noteworthy were his translations of the Greek works of Archimedes and of Euclid'sElements(1543), the latter being the first translation of that work ever to reach print in a modern language. One of his principal works, theGeneral trattato di numeri et misure(1556), became a widely used text in general arithmetic in his time.

Tartaglia, however, is primarily associated with the unfortunate controversy that surrounded his solution for cubic equations, which he achieved in the course of a public academic debate with a pupil of Scipione del Ferro in 1535. News of Tartaglia's accomplishment eventually reached the noted physician and math­ematician Girolamo Cardano* of Milan, to whom he confided the solution under an oath of secrecy. When Cardano learned of del Ferro's prior work on the subject, however, he published the solution in his algebraic textArs magna(1545), giving attribution both to Tartaglia and del Ferro. The ensuing dispute produced an exchange of published challenges in mathematics (the so-calledCartelli) between Tartaglia and Cardano's pupil Lodovico Ferrari, whose work also appears in theArs magna. The two met in public debate at Milan in 1548; although no official verdict survives, Tartaglia's defeat is suggested by his early departure from the proceedings. He eventually returned to Venice, where he died in 1557, never having achieved the professional justification nor the lasting financial security that he sought.

O. Ore, Cardano: The Gambling Scholar, 1953.