Scipione del Ferro
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Scipione del Ferro (February 6, 1465 – November 5, 1526) was an Italian mathemtatician who first discovered a means to solve cubic equations.
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[edit] Life
Scipione del Ferro was born on in Bologna, in the central North of Italy, where he also died on November 5, 1526, to Floriano and Filippa Ferro. His father, Floriano, worked in the paper industry, which owed its existence to the invention of the press in the decade of the 1450s, which probably allowed Scipione to access various works during early stages of his life.
del Ferro studied at the University of Bologna, where he would teach Arithmetic and Geometry from 1496 till the end of his life. During his last times he also dedicated to commercial transactions.
[edit] Diffusion of his work
There are no surviving scripts from del Ferro. That is due to his resistance to divulgate his works. He would rather communicate and show them to a reduced number of students and friends.
Despite this, he had a notebook where he recorded all his important discoveries. At del Ferro's death in 1526, this notebook was inherited by Hannival Nave. Nave was also a mathematician, who replaced del Ferro at the University of Bologna after his death. He was also married to del Ferro's daughter, Filippa.
In 1543, Gerolamo Cardano and Ludovico Ferrari (one of Cardano's students) travelled to Bologna to meet Nave and learn about his difunt father-in-law's notebook, where the solution to cubic equations appeared.
[edit] The Cubic Equation Problem
Mathematicians from del Ferro's times knew that the problem of the cubic equation resultion could be simplified to x3 + mx = n and x3 = mx + n, where m > 0 and n > 0 (the term in x2 could always be removed using adequate substitution). Of course, if negative coefficients would have been used (which were not by then), there would have only been one case.
There are conjectures on whether del Ferro worked on this topic as a consequence of a trip Luca Pacioli made to Bologna. Pacioli taught in the University of Bologna between 1501 and 1502, and discussed various mathematical topics with del Ferro. It is not known whether they discussed about cubical equations, but Pacioli included it in his famous treaty, Summa de arithmetica, geometrica, proportioni et proportionalita, which had been published seven years before. Some time after Pacioli's visit, del Ferro had solved one of the two cases (or maybe both). Anyhow, in 1925, examining 16th century manuscripts, the method to solve cubic equations is found:
3x3 + 18x = 60
For Cardano, it would have been del Ferro and the first to solve a cubic equation, and that is why it is published in his Ars Magna. Cardano maintains that what is published is del Ferro's method.
[edit] Other contributions
Del Ferro also did other important contributions to the rationalisation of fractions, extended the methods known for denominators with square roots to denominators with sumes of three cube roots.
[edit] References
- Alejandro García Venturini, Matématicos Que Hicieron Historia.
