Paolo Ruffini
| Paolo Ruffini | |
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 Paolo Ruffini
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| Born | September 22, 1765 Valentano |
| Died | May 9, 1822 Modena |
| Nationality | Italian |
| Fields | mathematics |
Paolo Ruffini (September 22, 1765 – May 10, 1822) was an Italian mathematician and philosopher.
By 1788 he had earned university degrees in philosophy, medicine/surgery, and mathematics. Among his work was an incomplete proof (Abel–Ruffini theorem[1]) that quintic (and higher-order) equations cannot be solved by radicals (1799[2]), and Ruffini's rule[3] which is a quick method for polynomial division. Ruffini also made contributions to group theory[4] in addition to probability and quadrature of the circle.
He practiced as both a professor of mathematics (University of Modena) and a doctor[5] including scientific work[6] on typhus.
[edit] Group Theory
Ruffini’s 1799 work marked a major development for group theory. Ruffini developed Joseph Louis Lagrange's work on permutation theory, following 29 years after Lagrange’s "Réflexions sur la théorie algébrique des equations" (1770–1771) which was largely ignored until Ruffini who established strong connections between permutations and the solvability of algebraic equations. Ruffini was the first to controversially assert the unsolvability by radicals of algebraic equations higher than quartics. This angered many members of the community such as Malfatti (1731–1807). Work in this area was later carried on by those such as Gauss and Galois who succeeded in such a proof.[7]
[edit] Publications
1799: "Teoria Generale delle Equazioni, in cui si dimostra impossibile la soluzione algebraica delle equazioni generali di grado superiore al quarto"
1802: "Riflessioni intorno alla rettificazione ed alla quadratura del circulo"
1802: "Della soluzione delle equazioni algebraiche determinate particolari di grado superiore al quarto"
1804: "Sopra la determinazione delle radici nelle equazioni numeriche di qualunque grado"
1806: "Della immortalità dell’anima"
1807: "Algebra elementare"
1820: "Memoria sul tifo contagioso"
1821: "Riflessioni critiche sopra il saggio filosofico intorno alle probabilità del signor conte Laplace"
[edit] References
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Wikimedia Commons has media related to: Paolo Ruffini |
- ^ http://www.britannica.com/EBchecked/topic/512337/Paolo-Ruffini
- ^ Teoria Generale delle Equazioni, in cui si dimostra impossibile la soluzione algebraica delle equazioni generali di grado superiore al quarto.
- ^ O'Connor, John J.; Robertson, Edmund F., "Paolo Ruffini", MacTutor History of Mathematics archive, University of St Andrews, http://www-history.mcs.st-andrews.ac.uk/Biographies/Ruffini.html.
- ^ http://www.stetson.edu/~efriedma/periodictable/html/Rf.html
- ^ Paolo Ruffini --- Catholic Encyclopedia article.
- ^ Memoria sul tifo contagioso.
- ^ The Genesis of the Abstract Group Concept, Hans Wussiong
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