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Paolo Ruffini ( Valentano, 22 September 1765 – Modena, 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 It ...
mathematician 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 a ...
:
* 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 t ...
) that quintic (and higher-order) equations cannot be solved by radicals
Radical may refer to:
Politics and ideology Politics
*Radical politics, the political intent of fundamental societal change
*Radicalism (historical), the Radical Movement that began in late 18th century Britain and spread to continental Europe and ...
(1799),
* Ruffini's rule which is a quick method for polynomial division,
* contributions to group theory
In abstract algebra, group theory studies the algebraic structures known as groups.
The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces, can all be seen as ...
.
He also wrote on probability and the quadrature of the circle
Squaring the circle is a problem in geometry first proposed in Greek mathematics. It is the challenge of constructing a square with the area of a circle by using only a finite number of steps with a compass and straightedge. The difficulty ...
.
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 20, ...
and a medical doctor including scientific work on typhus.
Group theory
In 1799 Ruffini marked a major improvement forgroup theory
In abstract algebra, group theory studies the algebraic structures known as groups.
The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces, can all be seen as ...
, 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 w ...
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
85 may refer to:
* 85 (number)
* one of the years 85 BC, AD 85, 1885, 1985, 2085
See also
*
* M85 (disambiguation), including "Model 85"
* 1985 (disambiguation) 1985 was a year.
1985 may also refer to:
Literature
* ''1985'' (Burgess novel) ...
, asteroid named after him
References
{{DEFAULTSORT:Ruffini, Paolo 1765 births 1822 deaths People from the Province of Viterbo 18th-century Italian mathematicians 19th-century Italian mathematicians Algebraists