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Paolo Ruffini (
Valentano
250px, View of Valentano.
Valentano is a town and ''comune'' of the province of Viterbo, in the Lazio region of central Italy. It is from the provincial capital, Viterbo.
left, 220px, Rocca Farnese in Valentano.
The placename is of uncertain ori ...
, 22 September 1765 – Modena
Modena (, , ; egl, label= Modenese, Mòdna ; ett, Mutna; la, Mutina) is a city and '' comune'' (municipality) on the south side of the Po Valley, in the Province of Modena in the Emilia-Romagna region of northern Italy.
A town, and seat o ...
, 10 May 1822) was an Italian
Italian(s) may refer to:
* Anything of, from, or related to the people of Italy over the centuries
** Italians, an ethnic group or simply a citizen of the Italian Republic or Italian Kingdom
** Italian language, a Romance language
*** Regional Ita ...
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 philosopher.
Education and Career
By 1788 he had earned university degrees in philosophy, medicine/surgery and mathematics. His works include developments inalgebra
Algebra () is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics.
Elementary ...
:
* an incomplete proof (Abel–Ruffini theorem
In mathematics, the Abel–Ruffini theorem (also known as Abel's impossibility theorem) states that there is no solution in radicals to general polynomial equations of degree five or higher with arbitrary coefficients. Here, ''general'' means th ...
) that quintic (and higher-order) equations cannot be solved by radicals (1799),
* Ruffini's rule
In mathematics, Ruffini's rule is a method for computation of the Euclidean division of a polynomial by a Binomial (polynomial), binomial of the form ''x – r''. It was described by Paolo Ruffini (mathematician), Paolo Ruffini in 1804. The rule i ...
which is a quick method for polynomial division
In algebra, polynomial long division is an algorithm for dividing a polynomial by another polynomial of the same or lower degree, a generalized version of the familiar arithmetic technique called long division. It can be done easily by hand, beca ...
,
* contributions to group theory
In abstract algebra, group theory studies the algebraic structures known as group (mathematics), groups.
The concept of a group is central to abstract algebra: other well-known algebraic structures, such as ring (mathematics), rings, field ...
.
He also wrote on probability
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speakin ...
and the quadrature of the circle.
He was a professor of mathematics at the University of Modena
The University of Modena and Reggio Emilia ( it, Università degli Studi di Modena e Reggio Emilia), located in Modena and Reggio Emilia, Emilia-Romagna, Italy, is one of the oldest universities in Italy, founded in 1175, with a population of 2 ...
and a medical doctor including scientific work on typhus
Typhus, also known as typhus fever, is a group of infectious diseases that include epidemic typhus, scrub typhus, and murine typhus. Common symptoms include fever, headache, and a rash. Typically these begin one to two weeks after exposure. ...
.
Group theory
In 1799 Ruffini marked a major improvement forgroup theory
In abstract algebra, group theory studies the algebraic structures known as group (mathematics), groups.
The concept of a group is central to abstract algebra: other well-known algebraic structures, such as ring (mathematics), rings, field ...
, developing Joseph Louis Lagrange
Joseph-Louis Lagrange (born Giuseppe Luigi Lagrangiaquartics, which angered many members of the community such as Gian Francesco Malfatti (1731–1807). Work in that area was later carried on by those such as
* ''1799: "Teoria Generale delle Equazioni, in cui si dimostra impossibile la soluzione algebraica delle equazioni generali di grado superiore al quarto" (General Theory of equations, in which the algebraic solution of general equations of degree higher than four is proven impossible).''
* ''1802: "Riflessioni intorno alla rettificazione ed alla quadratura del circulo" (Reflections on the rectification and the squaring of the circle)''
* ''1802: "Della soluzione delle equazioni algebraiche determinate particolari di grado superiore al quarto" (On the solution of certain determined algebraic equations of degree higher than four)''
* ''1804: "Sopra la determinazione delle radici nelle equazioni numeriche di qualunque grado" (About the determination of the roots in the numerical equations of any degree)''
* ''1806: "Della immortalità dell’anima" (On the immortality of the soul)''
* ''1807: "Algebra elementare" (Elementary algebra)''
* ''1813: "Riflessioni intorno alla soluzione delle equazioni algebraiche generali" (Reflections on the algebraic solutions of equations)''
* ''1820: "Memoria sul tifo contagioso" (Essay on contagious typhoid)''
* ''1821: "Riflessioni critiche sopra il saggio filosofico intorno alle probabilità del signor conte Laplace" (Critical reflections on the philosophical essay about probability by Count Laplace)''
Abel
Abel ''Hábel''; ar, هابيل, Hābīl is a Biblical figure in the Book of Genesis within Abrahamic religions. He was the younger brother of Cain, and the younger son of Adam and Eve, the first couple in Biblical history. He was a shepherd ...
and Galois, who succeeded in such a proof.
Publications
* ''1799: "Teoria Generale delle Equazioni, in cui si dimostra impossibile la soluzione algebraica delle equazioni generali di grado superiore al quarto" (General Theory of equations, in which the algebraic solution of general equations of degree higher than four is proven impossible).''
* ''1802: "Riflessioni intorno alla rettificazione ed alla quadratura del circulo" (Reflections on the rectification and the squaring of the circle)''
* ''1802: "Della soluzione delle equazioni algebraiche determinate particolari di grado superiore al quarto" (On the solution of certain determined algebraic equations of degree higher than four)''
* ''1804: "Sopra la determinazione delle radici nelle equazioni numeriche di qualunque grado" (About the determination of the roots in the numerical equations of any degree)''
* ''1806: "Della immortalità dell’anima" (On the immortality of the soul)''
* ''1807: "Algebra elementare" (Elementary algebra)''
* ''1813: "Riflessioni intorno alla soluzione delle equazioni algebraiche generali" (Reflections on the algebraic solutions of equations)''
* ''1820: "Memoria sul tifo contagioso" (Essay on contagious typhoid)''
* ''1821: "Riflessioni critiche sopra il saggio filosofico intorno alle probabilità del signor conte Laplace" (Critical reflections on the philosophical essay about probability by Count Laplace)''
See also
* 8524 Paoloruffini, asteroid named after himReferences
{{DEFAULTSORT:Ruffini, Paolo 1765 births 1822 deaths People from the Province of Viterbo 18th-century Italian mathematicians 19th-century Italian mathematicians Algebraists