Paolo Ruffini (mathematician)

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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, grew up in Reggio near Modena and studied mathematics, medicine, philosophy and literature at the University of Modena from 1783. He heard geometry from Luigi Fantini and analysis from Paolo Cassini, whose lectures he took over as a student when he took up an office in the ducal family of the Este ruling in Modena in 1787. In 1787 he made his degrees in philosophy, medicine, surgery and mathematics. In 1788 he became professor of mathematics (analysis) in Modena and in 1791 he also succeeded Fantini as mathematics professor. In the same year he was also licensed as a doctor. After Napoleon's conquest of northern Italy, he became a delegate in the Cisalpine Republic founded by Napoleon, resumed teaching in 1798, but since he did not want to take the oath to the republic for religious reasons, he lost it immediately. Instead, he taught applied mathematics at the military school in Modena and practiced as a doctor. In 1814, after the fall of Napoleon, he became rector of the University of Modena. He also taught mathematics and medicine at the university. In 1817 he became infected during a typhoid epidemic, recovered but never fully recovered. In 1819 he gave up his professorship in medicine. He also published a book on typhus in 1820 and practiced as a doctor until shortly before his death.

plant

In 1799, Ruffini and Gauss seem to have been the first to suggest that general polynomials of degree greater than 4 cannot be resolved into radicals - today the Abel-Ruffini theorem . At the same time, Ruffini also gave a “proof” for this, which was, however, still incomplete: the group-theoretical foundations required for a complete proof had not yet been worked out at his time. Ruffini himself, however, contributed significantly to the elaboration of these principles, so that Augustin Louis Cauchy could build on it later , Niels Henrik Abel (whose proof Pierre Wantzel simplified) and Évariste Galois , who were finally able to solve the problem (and more).

During his lifetime, Ruffini had difficulty finding any resonance for his work. Joseph-Louis Lagrange , to whom he sent his 1799 book twice, did not reply. He then published new versions of his proof in 1803 (which at least received an answer from Gianfrancesco Malfatti , who misunderstood the proof, however), 1808 and 1813 (this version directly influenced Pierre Wantzel's proof based on Abel and Ruffini ). Ruffini then turned directly to the Paris Academy, where the evidence was assessed by Lagrange, Adrien-Marie Legendre, and Sylvestre Lacroix - Lagrange in particular, however, found nothing remarkable about the evidence. The Royal Society's response, although more positive, brought no recognition either. Only Cauchy, who was otherwise known to be very sparing in praising others, recognized the evidence and praised Ruffini in a letter he wrote to him in 1820. In Italy, however, he received support from Pietro Paoli .

Ruffini published the procedure for the simplified evaluation of polynomials, mostly known today as Horner's scheme , 15 years before William George Horner , so that it is also known as the "Ruffini rule" (although it was described by Zhu Shijie 500 years earlier .)

In his philosophical works he opposed some ideas of Pierre Simon de Laplace and he also dealt with probability theory and its application in court.

Fonts

Teoria generale delle equazioni , 1799
  • Opere Matematiche , editor E. Bortolotti, 3 volumes, Rome, 1953/1954
  • Teoria Generale delle Equazioni, in cui si dimostra impossibile la soluzione algebraica delle equazioni generali di grado superiore al quarto , 2 volumes, Bologna 1799, Google Books , doi: 10.3931 / e-rara-15207
  • Riflessioni intorno alla rettificazione ed alla quadratura del circulo , Memorie di matematica e di fisica 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 di fisica della Società italiana delle.scienze, Volume 9, 1802, pp. 444-526
  • Della insolubilità delle equazioni algebriche generali di grado superiore al quarto , Memorie di matematica e di fisica della Società italiana delle scienze, Volume 10, Part 2, 1803, pp. 410-470, doi: 10.3931 / e-rara-12170
  • Sopra la determinazione delle radici nelle equazioni numeriche di qualunque grado , Modena 1804, doi: 10.3931 / e-rara-12171
  • Della immortalità dell'anima , Modena 1806
  • Algebra e sua appendice , 2 volumes, Modena 1807, 1808, Google Books
  • Risposta ... ai dubbi propostigli dal socio Gianfrancesco Malfatti sopra la insolubilità delle equazioni di grado superiore al quarto , Memorie di matematica e di fisica della Società italiana delle scienze, Volume 12, Part 1, 1805, pp. 213-267
  • Rillessioni ... intorno al metodo proposto dal consocio Gianfrancesco Malfatti per la soluzione delle equazioni di quinto grado , Memorie di matematica e di fisica della Società italiana delle scienze, Volume 12, Part 1, 1805, pp. 321-336
  • Della insolubilità delle equazioni algebriche generali 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 alle probabilità del signor conte Laplace , Modena 1821, Google Books

literature

  • Ettore Carruccio: Ruffini, Paolo . In: Charles Coulston Gillispie (Ed.): Dictionary of Scientific Biography . tape 11 : A. Pitcairn - B. Rush . Charles Scribner's Sons, New York 1975, p. 598-600 .
  • Ettore Carruccio: Paolo Ruffini matematico e pensatore , Memorie della R. Accademia di scienze, lettere ed arti in Modena, series 6, volume 8, 1966, liii-lxix.
  • Heinrich Burkhardt : The beginnings of group theory with Paolo Ruffini , magazine for mathematics and physics, volume 37, 1892, supplement, pp. 119-159, online
  • Raymond G. Ayoub: Paolo Ruffini's Contributions to the Quintic , Archive for the History of Exact Science, Volume 23, 1980, pp. 253-277, doi : 10.1007 / BF00357046
  • Gustavo Barbensi: Paolo Ruffini nel suo tempo , Modena 1955
  • Ettore Bortolotti : Influenza dell'opera matematica di Paolo Ruffini sullo svolgimento delle teorie algebriche , Annuario della R. Università di Modena (1902-1903), pp. 21-77
  • Marcus du Sautoy : The moonlight seekers. Mathematicians decipher the secret of symmetry , CH Beck 2008
  • Jörg Bewersdorff : Algebra für Einsteiger , Vieweg, 3rd edition 2007, doi : 10.1007 / 978-3-8348-9204-1 (p. 54ff on Ruffini's argument in the work from 1813)
  • Florian Cajori : Horner's method of approximation anticipated by Ruffini , Bulletin AMS, Volume 17, 1911, pp. 409-411, online
  • Florian Cajori : Pierre Laurent Wantzel , Bull. Amer. Math. Soc., Vol. 24, 1918, pp. 339-347, (with a discussion of the evidence by Ruffini, Abel, and Wantzel), Online .

Web links

Individual evidence

  1. ↑ Paolo Ruffini: Della insolubilità delle equazioni algebraiche generali di grado superiore al quarto. In: Memorie della Società Italiana delle Scienze 10 (1803), pp. 410-470. See F. Cajori: Horner's Method of Approximation Anticipated by Ruffini. In: Bulletin of American Mathematical Society 17 (1911), pp. 409-414, doi : 10.1090 / S0002-9904-1911-02072-9
personal data
SURNAME Ruffini, Paolo
BRIEF DESCRIPTION Italian mathematician and philosopher
DATE OF BIRTH September 22, 1765
PLACE OF BIRTH Valentano , Papal States , today Italy
DATE OF DEATH May 10, 1822
Place of death Modena , Duchy of Modena , now Italy