Paolo Ruffini (22 September 1765 – 10 May 1822) 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, mathematical structure, structure, space, Mathematica ...
and
philosopher
Philosophy ('love of wisdom' in Ancient Greek) is a systematic study of general and fundamental questions concerning topics like existence, reason, knowledge, Value (ethics and social sciences), value, mind, and language. It is a rational an ...
.
Education and career
By 1788 he had earned university degrees in philosophy, medicine/surgery and mathematics. His works include developments in
algebra
Algebra is a branch of mathematics that deals with abstract systems, known as algebraic structures, and the manipulation of expressions within those systems. It is a generalization of arithmetic that introduces variables and algebraic ope ...
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 ...
radicals
Radical (from Latin: ', root) may refer to:
Politics and ideology Politics
*Classical radicalism, the Radical Movement that began in late 18th century Britain and spread to continental Europe and Latin America in the 19th century
*Radical politics ...
(1799).
Abel
Abel ( ''Hébel'', in pausa ''Hā́ḇel''; ''Hábel''; , ''Hābēl'') is a biblical figure in the Book of Genesis within the Abrahamic religions. Born as the second son of Adam and Eve, the first two humans created by God in Judaism, God, he ...
would complete the proof in 1824.
*
Ruffini's rule
In mathematics, Ruffini's rule is a method for computation of the Euclidean division of a polynomial by a binomial of the form ''x – r''. It was described by Paolo Ruffini in 1809. The rule is a special case of synthetic division in which the ...
, 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 a branch of mathematics and statistics concerning events and numerical descriptions of how likely they are to occur. The probability of an event is a number between 0 and 1; the larger the probability, the more likely an e ...
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 (geometry), square with the area of a circle, area of a given circle by using only a finite number of steps with a ...
.
He was a professor of mathematics at the
University of Modena
The University of Modena and Reggio Emilia (), located in Modena and Reggio Emilia, Emilia-Romagna, Italy, is one of the oldest universities in Europe, founded in 1175, with a population of 20,000 students.
The medieval university disappeared b ...
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 exposu ...
.
Group theory
In 1799 Ruffini marked a major improvement for
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 ( ...
, 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
Abel
Abel ( ''Hébel'', in pausa ''Hā́ḇel''; ''Hábel''; , ''Hābēl'') is a biblical figure in the Book of Genesis within the Abrahamic religions. Born as the second son of Adam and Eve, the first two humans created by God in Judaism, God, he ...
* 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")