Editing Nicolo Tartaglia (section)

==Solution to cubic equations==
Tartaglia is perhaps best known today for his conflicts with [[Gerolamo Cardano]]. In 1539, Cardano cajoled Tartaglia into revealing his solution to the [[cubic equation]]s by promising not to publish them. Tartaglia divulged the secrets of the solutions of three different forms of the cubic equation in verse.<ref>{{harvnb|Katz|1998|loc=p. 359}}</ref> Several years later, Cardano happened to see unpublished work by [[Scipione del Ferro]] who independently came up with the same solution as Tartaglia.  (Tartaglia had previously been challenged by del Ferro's student Fiore, which made Tartaglia aware that a solution existed.)<ref>{{Cite journal|last=Feldmann|first=Richard W.|date=1961|title=The Cardano-Tartaglia dispute|url=https://www.jstor.org/stable/27956338|journal=The Mathematics Teacher|volume=54|issue=3|pages=160–163|jstor=27956338 |issn=0025-5769|quote=His student, Antonio Maria Fiore, knew the solution and attempted to gain a reputation by exploiting his master's discovery. He challenged Tartaglia with thirty questions, all of which reduced to the solution of x<sup>3</sup> + ax = b.}}</ref>

As the unpublished work was dated before Tartaglia's, Cardano decided his promise could be broken and included Tartaglia's solution in his next publication. Even though Cardano credited his discovery, Tartaglia was extremely upset and a famous public challenge match resulted between himself and Cardano's student, [[Ludovico Ferrari]]. Widespread stories that Tartaglia devoted the rest of his life to ruining Cardano, however, appear to be completely fabricated.<ref>[[Tony Rothman]], [https://arxiv.org/ftp/arxiv/papers/1308/1308.2181.pdf Cardano v Tartaglia: The Great Feud Goes Supernatural.]</ref> Mathematical historians now credit both Cardano and Tartaglia with the formula to solve cubic equations, referring to it as the "[[Cardano–Tartaglia formula]]".