Niccolò Tartaglia

Timeline

1. c. 1499–1534Brescia · LombardyHis father was a poor messenger who died early, leaving the family in hardship. When French troops sacked Brescia in 1512, the young Fontana took refuge in the cathedral and was sabred on the jaw and palate; his speech impaired afterwards, he gained the nickname 'Tartaglia' (the stammerer). He taught himself mathematics almost entirely, began tutoring in Verona around 1516, settled in Venice in 1534, and built his reputation through public polemics.
2. 1534–1539Venice · Republic of VeniceIn 1535 he agreed to a contest with Antonio Fior of the Bologna school, each posing thirty problems; on the morning of 13 February he conceived a method for cubics of the form 'cube plus unknown equals number' and solved all his opponent's problems within hours. In 1537 he published 'Nova Scientia', discussing projectile trajectories and elevation angles geometrically and proposing propositions such as maximum range at forty-five degrees, a pioneering work in mathematical ballistics.
3. 1539–1548Venice · Republic of VeniceAfter Cardano swore an oath of secrecy in 1539, Tartaglia revealed the cubic solution in verse. In 1543 Cardano saw Ferraro's earlier manuscript in Bologna and published the solution in his 1545 'Ars Magna', citing the source. Enraged, Tartaglia denounced him in 'Quesiti et inventioni diverse' in 1546. In 1543 he also issued the first Italian translation of Euclid's Elements. In 1548 he lost a public debate with Ferrari in Milan.
4. 1548–1557Rialto, Venice · Republic of VeniceAfter the Milan debate he was briefly engaged to lecture in his native Brescia, but the promised fees were never paid; after a fruitless lawsuit he returned to his old post in Venice. He continued editing Archimedes' works but failed to secure a stable position on the strength of his cubic formula. He died in poverty on 13 December 1557. Later ages often call the cubic formula the Cardano–Tartaglia formula.