Tartaglia was born Niccoló Fontana but as a boy he suffered a saber wound to his face during the French sack of Brescia (1512), his native city; this left him with a speech defect and he adopted the nickname Tartaglia (Stammerer) as a result. Tartaglia began his studies as a promising mathematician, but his interests soon became very wide-ranging. He held various posts, including school teacher, before he eventually became a professor of mathematics in Venice where he stayed.

Tartaglia is remembered chiefly for his work on solving the general cubic equation. He discovered a method in 1535 but did not publish it. Incautiously he revealed his new method to his friend the mathematician Girolamo Cardano, who published it in Ars magna (1545; The Great Skill). This, not surprisingly, was the end of their friendship and led to a violent controversy. Tartaglia eventually lost the quarrel and with it his post as lecturer at Brescia in 1548.

Tartaglia's other chief mathematical interests were in arithmetic and geometry. The pattern now known as ‘Pascal's triangle’ appeared in a work of Tartaglia's. His geometrical work centered on problems connected with the tetrahedron and he helped further the diffusion of classical mathematics by making the first translation of Euclid's Elements into a modern European language. His chief published work was the three-volume Trattato di numeri et misure (1556–60; Treatise on Numbers and Measures), an encyclopedic work on elementary mathematics. Apart from these mathematical activities Tartaglia made notable innovations in topography and the military uses of science, such as ballistics.