Niccolo Fontana Tartaglia

There is a story that Tartaglia learned only half the alphabet from a private tutor before funds ran out, and he had to learn the rest for himself. Be that as it may, he was essentially self-taught. He and his contermporaries, working outside the academies, were responsible for the spread of classic works in modern languages among the educated middle class.

His work on Euclid in 1543 was especially significant. For two centuries Euclid had been taught from two Latin translations taken from an Arabic source; these contained errors in Book V, the Eudoxian theory of proportion, which rendered it unusable. Tartaglia's edition was based on Zamberti's Latin translation of an uncorrupted Greek text, and rendered Book V correctly. He also wrote the first modern and useful commentary on the theory. Later, the theory was an essential tool for Galileo, just as it had been for Archimedes.

Tartaglia is perhaps best known today for his conflicts with Gerolamo Cardano. Cardano nagged Tartaglia into revealing his solution to the cubic equations, by promising not to publish them. Several years later, Cardano happened to see unpublished work by another mathematician who independently came up with the same solution as Tartaglia. As the unpublished work was dated before Tartaglia's, Cardano decided his promise could be broken, and included Tartaglia's solution in his next publication. In spite of the fact that Cardano credited his discovery, Tartaglia was extremely upset. He responded by publicly insulting Cardano personally as well as professionally.

Tartaglia is also known for giving an expression (Tartaglia's formula) for the volume of a tetrahedron (incl. any irregular tetrahedra) in terms of the distance values measured pairwise between its four corners:

This is in generalization of Heron's formula for the area of a triangle.

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