Scipione del Ferro
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Scipione del Ferro (Bologna, February 6, 1465 – Bologna, November 5, 1526) was an Italian mathemtatician who first discovered a method to solve cubic equations.
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[edit] Life
Scipione del Ferro was born in Bologna, in the central North of Italy, 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 1450s and which probably allowed Scipione to access various works during early stages of his life.
He studied and later taught at the University of Bologna, teaching Arithmetic and Geometry from 1496 until the end of his life. During his last years, he also undertook commercial work.
[edit] Diffusion of his work
There are no surviving scripts from del Ferro. This is in large part due to his resistance to communicating his works. Instead of publishing his ideas, he would only show them to a small, select group of friends and students.
Despite this, he had a notebook where he recorded all his important discoveries. After his death in 1526, this notebook was inherited by his son-in-law Hannival Nave, who was married to del Ferro's daughter, Filippa. Nave was also a mathematician, who replaced del Ferro at the University of Bologna after his death.
In 1543, Gerolamo Cardano and Ludovico Ferrari (one of Cardano's students) travelled to Bologna to meet Nave and learn about his late father-in-law's notebook, where the solution to the general cubic equation appeared.
[edit] The Solution of the Cubic Equation
Mathematicians from del Ferro's time knew that the general cubic equation could be simplified to one of three cases:
The term in x2 can always be removed by appropriate substitution. It is assumed that the coefficients m and n are positive, since negative numbers were not in general use at the time. If negative numbers are allowed, there is only one case, namely:
There are conjectures about whether del Ferro worked on this topic as a consequence of a trip Luca Pacioli made to Bologna. Pacioli taught at the University of Bologna between 1501 and 1502, and discussed various mathematical topics with del Ferro. It is not known whether they discussed cubic equations, but Pacioli had included them in his famous treatise, Summa de arithmetica, geometrica, proportioni et proportionalita, which was published seven years earlier.
Some time after Pacioli's visit, del Ferro solved at least one, but possibly all three cases. In 1925, 16th century manuscripts were discovered which contain del Ferro's solutions.
Cardano, in his book Ars Magns (published in 1545) states that it was del Ferro who was the first to solve the cubic equation, and that the solution he gives is del Ferro's method.
[edit] Other contributions
Del Ferro also made other important contributions to the rationalization of fractions; he extended the methods known for denominators with square roots to denominators with sums of three cube roots.
[edit] References
- Alejandro García Venturini, Matemáticos Que Hicieron Historia.
- Ian Stewart, Galois Theory, Third Edition, (Chapman & Hall/CRC Mathematics, 2004)
