Luca Pacioli (1445-1514) wrote in his Summa de arithmetica, geometria,
proportioni et proportionalità that it was not possible to solve the cubic.
Ironically, the solution of the cubic is now attributed to Scipione del Ferro
(1465-1526) who was living at the same time as Luca Pacioli. Scipione del
Ferro never published his findings, but revealed them to a student of his,
Antonio Maria Fiore. Before long rumours started that the solution to the
cubic was known, and this pushed Niccolò Tartaglia (1500-1557) to search for
the solution, which he found independently of Scipione del Ferro. A contest
was organized between Fiore and Tartaglia, where each of them had to solve 30
problems posed by the other contestant. It is told that a few days before the
contest Tartaglia managed to find the general method of solving another kind
of cubic
, so the problems he posed to
his opponent were all of this second type that Fiore did not know how to
solve. Apparently Tartaglia managed to solve all the 30 problems given by
Fiore in a couple of hours, while Fiore did not manage to solve any of
Tartaglia's problems. Tartaglia was the winner, and when news of this contest
reached the ears of Girolamo Cardano (1501-1576) the latter invited Tartaglia
to Milan with the vague promise of introducing him to a nobleman who could
have given him a pension. Instead Cardano asked Tartaglia to reveal to him his
method for solving cubics so that he could include it in his book, the Ars
magna. Tartaglia at first told him that he himself wanted to write a treatise
of algebra, so he would have published the method in his book, but he
successively disclosed his method to Cardano under somlemn oath of keeping it
secret until he had published his treatise. Following this meeting Cardano
went to Bologna to study Scipione del Ferro's papers, and he found the
solution that Cardano had revealed to him. Cardano felt therefore that the
oath was not binding as the solution was not original, and published it in the
Ars magna.