Paolo Ruffini

Paolo Ruffini ( born September 22, 1765 in Valentano, † May 10, 1822 in Modena) was an Italian mathematician, physician and philosopher.

Life

Ruffini was the son of a doctor who grew up in Reggio in Modena and studied from 1783 at the University of Modena mathematics, medicine, philosophy and literature. He heard geometry with Luigi Fantini and Analysis with Paolo Cassini, whose lectures he still took as a student when he took over in 1787 a post with the ruling family of Este Duke of Modena. In 1787 he made ​​his degrees in philosophy, medicine, surgery, and mathematics. In 1788 he became professor of mathematics (calculus ) in Modena and 1791, he also became the successor of Fantini as a mathematics professor. In the same year he also received a license as a physician. After the conquest of Northern Italy by Napoleon, he was a delegate in the Cisalpine Republic, founded by Napoleon in 1798 took up teaching again, but he did not want to leave for religious reasons the oath to the Republic, he lost it immediately. Instead, he taught applied mathematics at the Military Academy in Modena and practiced as a doctor. In 1814 he became rector of the University of Modena after the fall of Napoleon. He also taught mathematics and medicine at the University. In 1817 he became infected during a typhus epidemic, recovered, but never fully recovered. In 1819 he gave up his professorship in medicine. He also published in 1820 a book on typhoid and practiced until shortly before his death as a doctor.

Work

Ruffini and Gauss seem to have 1799 as the first pronounced the assumption that general polynomials not solvable in radicals are of degree greater than 4 - Today the set of Abel - Ruffini. Ruffini was simultaneously also a "proof", which, however, was still incomplete: The group theoretical foundations that are required for a complete proof, were not worked out in his time. Ruffini itself, however, contributed significantly to the development of these fundamentals, so that later was able to build Augustin Louis Cauchy because it in turn Niels Henrik Abel and Galois Évariste that the problem (and more) were finally able to solve.

During his lifetime, Ruffini had trouble at all to find resonance for his work. Joseph -Louis Lagrange, where he was sent by his book of 1799 twice, did not answer him. He then published new versions of his proof in 1803 (which after all, a response of Gianfrancesco Malfatti received, but misunderstood the evidence ), 1808 and 1813 (this version directly influenced based on the Abel and Ruffini proof of Pierre Wantzel ). Ruffini then turned directly to the Paris Academy, where the proof of Lagrange, Adrien -Marie Legendre and Sylvestre Lacroix was judged - but especially Lagrange found nothing remarkable in the evidence. The response of the Royal Society brought, although positive, no recognition. Only Cauchy, who was known to be very economical in praise other else, recognized the evidence and praised Ruffini in 1820 in a letter he wrote to him.

The now mostly Horner scheme mentioned method for simplified evaluation of polynomials Ruffini published for 15 years before William George Horner, so it is also called the " rule of Ruffini " ( it was, however, already described 500 years earlier by Zhu Shijie. )

In his philosophical works he turned against some ideas of Pierre Simon de Laplace, and he also studied with probability theory and its application in court.

Writings

  • Opere Matematiche, editor E. Bortolotti, 3 vols, Rome, 1953/1954
  • Teoria Generale delle Equazioni, in cui si dimostra impossibile la soluzione algebraica delle equazioni generalized di grado superiore al quarto, two volumes, Bologna 1799, Google Books
  • Riflessioni intorno alla rettificazione ed alla del quadratura circulo, Memorie di matematica e fisica di della Società italiana delle.scienze, Volume 9, 1802, pp. 527-557
  • Della soluzione delle equazioni algebraiche determinate particolari di grado superiore al quarto. Memorie di matematica e fisica di della Società italiana delle.scienze, Volume 9, 1802, pp. 444-526
  • Della insolubilità delle equazioni algebriche generalized di grado superiore al quarto, Memorie di matematica e fisica di della Società italiana delle scienze, Volume 10, Part 2, 1803, pp. 410-470
  • Sopra la determinazione delle Radici nelle equazioni numeriche di grado qualunque, Modena 1804
  • Della Immortalita dell'anima, Modena 1806
  • Algebra e sua appendice, 2 volumes, Modena 1807, 1808 Google Books
  • Risposta ... ai dubbi propostigli dal Gianfrancesco Malfatti socio sopra la insolubilità delle equazioni di grado superiore al quarto, Memorie di matematica e fisica di della Società italiana delle scienze, Volume 12, Part 1, 1805, pp. 213-267
  • Rillessioni ... intorno al metodo proposto dal Gianfrancesco Malfatti consocio per la soluzione di quinto grado delle equazioni, Memorie di matematica e fisica di della Società italiana delle scienze, Volume 12, Part 1, 1805, pp. 321-336
  • Della insolubilità delle equazioni algebriche generalized di grado superiore al quarto qualunque metodo si adoperi algebrico esso Siasi o trascendente, Memorie dell'Istituto nazionale italiano, Classe di fisica e di matematica, Volume 1, Part 2, 1806, pp. 433-450
  • Memoria sul tifo contagioso, 1820 ( his book on typhus )
  • Riflessioni critiche sopra il saggio Filosofico intorno all probabilità del signor conte Laplace, Modena 1821 Google Books
Abel–Ruffini theorem Group theory Adrien-Marie Legendre Sylvestre François Lacroix Horner's method Heinrich Burkhardt Digital Object Identifier Marcus du Sautoy Integrated Authority File Papal States Duchy of Modena and Reggio
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