Scipione del Ferro (6 February 1465 – 5 November 1526) was an Italian
mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems.
Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change.
History
On ...
who first discovered a method to solve the depressed
cubic equation
In algebra, a cubic equation in one variable is an equation of the form
:ax^3+bx^2+cx+d=0
in which is nonzero.
The solutions of this equation are called roots of the cubic function defined by the left-hand side of the equation. If all of the ...
.
Life
Scipione del Ferro was born in
Bologna
Bologna (, , ; egl, label= Emilian, Bulåggna ; lat, Bononia) is the capital and largest city of the Emilia-Romagna region in Northern Italy. It is the seventh most populous city in Italy with about 400,000 inhabitants and 150 different nat ...
, in northern
Italy
Italy ( it, Italia ), officially the Italian Republic, ) or the Republic of Italy, is a country in Southern Europe. It is located in the middle of the Mediterranean Sea, and its territory largely coincides with the homonymous geographical re ...
, to Floriano and Filippa Ferro. His father, Floriano, worked in the
paper
Paper is a thin sheet material produced by mechanically or chemically processing cellulose fibres derived from wood, rags, grasses or other vegetable sources in water, draining the water through fine mesh leaving the fibre evenly distributed ...
industry, which owed its existence to the invention of the
press
Press may refer to:
Media
* Print media or news media, commonly called "the press"
* Printing press, commonly called "the press"
* Press (newspaper), a list of newspapers
* Press TV, an Iranian television network
People
* Press (surname), a fam ...
in the 1450s and which probably allowed Scipione to access various works during the early stages of his life. He married and had a daughter, who was named Filippa after his mother.
He likely studied at the
University of Bologna
The University of Bologna ( it, Alma Mater Studiorum – Università di Bologna, UNIBO) is a public research university in Bologna, Italy. Founded in 1088 by an organised guild of students (''studiorum''), it is the oldest university in continuo ...
, where he was appointed a lecturer there in
Arithmetic
Arithmetic () is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers— addition, subtraction, multiplication, division, exponentiation, and extraction of roots. In the 19th ...
and
Geometry
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...
in 1496. During his last years, he also undertook commercial work.
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.
It is suspected that this is due to the practice of mathematicians at the time of publicly challenging one another. When a mathematician accepted another's challenge, each mathematician needed to solve the other's problems. The loser in a challenge often lost funding or his university position. Del Ferro was fearful of being challenged and likely kept his greatest work secret so that he could use it to defend himself in the event of a challenge.
Despite this secrecy, 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
Annibale della Nave Annibale is the Italian names, Italian masculine name, masculine given name and surname equivalent to Hannibal (given name), Hannibal.
In English, it may refer to :
Given name
* Annibale Albani (1682–1751), Italian cardinal
* Annibale I Bentivog ...
, who was married to del Ferro's daughter, Filippa. Nave was also a
mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems.
Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change.
History
On ...
and a former student of del Ferro's, and he replaced del Ferro at the
University of Bologna
The University of Bologna ( it, Alma Mater Studiorum – Università di Bologna, UNIBO) is a public research university in Bologna, Italy. Founded in 1088 by an organised guild of students (''studiorum''), it is the oldest university in continuo ...
after his death.
In 1543,
Gerolamo Cardano
Gerolamo Cardano (; also Girolamo or Geronimo; french: link=no, Jérôme Cardan; la, Hieronymus Cardanus; 24 September 1501– 21 September 1576) was an Italian polymath, whose interests and proficiencies ranged through those of mathematician, ...
and
Lodovico Ferrari
Lodovico de Ferrari (2 February 1522 – 5 October 1565) was an Italian mathematician.
Biography
Born in Bologna, Lodovico's grandfather, Bartolomeo Ferrari, was forced out of Milan to Bologna. Lodovico settled in Bologna, and he began his c ...
(one of Cardano's students) travelled to
Bologna
Bologna (, , ; egl, label= Emilian, Bulåggna ; lat, Bononia) is the capital and largest city of the Emilia-Romagna region in Northern Italy. It is the seventh most populous city in Italy with about 400,000 inhabitants and 150 different nat ...
to meet Nave and learn about his late father-in-law's notebook, where the solution to the depressed
cubic equation
In algebra, a cubic equation in one variable is an equation of the form
:ax^3+bx^2+cx+d=0
in which is nonzero.
The solutions of this equation are called roots of the cubic function defined by the left-hand side of the equation. If all of the ...
appeared.
The solution of the cubic equation
Mathematicians from del Ferro's time knew that the general cubic equation could be simplified to one of two cases called the depressed cubic equation, for positive numbers
,
,
:
:
:
The term in
can always be removed by letting
for an appropriate constant
.
While it is not known today with certainty what method del Ferro used, it is thought that he used the fact that
solves the equation
to conjecture that