Betti, Enrico

Betti, Enrico

▪ Italian mathematician
born October 21, 1823, Pistoia, Tuscany [Italy]
died August 11, 1892, Pisa, Kingdom of Italy

      mathematician who wrote a pioneering memoir on topology, the study of surfaces and higher-dimensional spaces, and wrote one of the first rigorous expositions of the theory of equations developed by the noted French mathematician Évariste Galois (Galois, Évariste) (1811–32).

      Betti studied mathematics and physics at the University of Pisa. After graduating with a degree in mathematics in 1846, he stayed on to work as an assistant until 1849 when he returned home to Pistoia to teach at a secondary school. From 1854 he taught at another secondary school in Florence. In 1857 he obtained a professorship in mathematics at Pisa, where he remained for the rest of his academic life. He fought in two battles for Italian independence and was elected to the new Italian parliament in 1862.

      Betti's early work was in the theory of equations and algebra. He extended and furnished proofs for Galois's work, which had previously been stated in part without demonstrations or proofs. (Before Galois could finish his work, he died in a duel at age 21.) The arrival in Pisa of the German mathematician Bernhard Riemann (Riemann, Bernhard) in 1863 decisively affected the course of Betti's research. They became close friends, and Riemann awakened Betti's interest in mathematical physics, in particular potential theory and elasticity, and inspired his memoir on topology. Betti's study of spaces of higher dimensions (greater than three) in the latter work did much to open up the subject, and it led the French mathematician Henri Poincaré (Poincaré, Henri) to give the name Betti numbers to certain numbers that characterize the connectivity of a manifold (the higher-dimensional analog of a surface).

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Universalium. 2010.

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  • Enrico Betti — (* 21. Oktober 1823 in Pistoia/Toskana; † 11. August 1892 in Soiana) war ein italienischer Mathematiker und Ingenieur. Er wurde durch seine 1871 erschienene Arbeit über Topologie bekannt, die später zu den (von …   Deutsch Wikipedia

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  • Enrico Betti — Infobox Scientist name = PAGENAME box width = image size =150px caption = PAGENAME birth date = 21 October 1823 birth place = Pistoia, Tuscany death date = 11 August 1892 death place = residence = citizenship = nationality = Italy ethnicity =… …   Wikipedia

  • Betti — ist eine Namensvariante von Elisabeth Betti ist der Familienname folgender Personen: Biagio Betti (1535–1605), italienischer Maler Carlo Giuliano Betti, italienischer regisseur und Drehbuchautor Dino Betti van der Noot (* 1936), italienischer… …   Deutsch Wikipedia

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  • Betti's theorem — Betti s theorem, which was discovered by Enrico Betti in 1872, states that for a linear elastic structure subject to two sets of forces {Pi} i=1,...,m and {Qj}, j=1,2,...,n, the work done by the set P through the displacements produced by the set …   Wikipedia

  • Betti number — In algebraic topology, the Betti number of a topological space is, in intuitive terms, a way of counting the maximum number of cuts that can be made without dividing the space into two pieces. This defines, in fact, what is called the first Betti …   Wikipedia

  • Betti —  Cette page d’homonymie répertorie des personnes partageant un même patronyme italien. Betti est un nom de famille d origine italienne notamment porté par :Biagio Betti, peintre florentin du XVIe siècle Enrico Betti, mathématicien… …   Wikipédia en Français

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