BELTRAMI, EUGENIO

born Nov. 16, 1835, Cremona, Lombardy, Austrian Empire [now in Italy] died Feb. 18, 1900, Rome, Italy Italian mathematician known for his concepts of non-Euclidean geometry, especially his theories of surfaces of constant curvature. Following his studies at the University of Pavia (1853-56) and later in Milan, Beltrami was invited to join the faculty at the University of Bologna in 1862 as a visiting professor of algebra and analytic geometry; four years later he was appointed professor of rational mechanics. He also held professorships at universities in Pisa, Rome, and Pavia. Influenced by N.I. Lobachevsky, C.F. Gauss, and Bernhard Riemann, Beltrami's work on the differential geometry of curves and surfaces removed any doubts about the validity of non-Euclidean geometry, and his method was soon followed by the German mathematician Felix Klein. Beltrami's four-volume work, Opere Matematiche (1902-20), published posthumously, contains his comments on a broad range of physical and mathematical subjects, including thermodynamics, elasticity, magnetism, optics, and electricity. Beltrami was a member of the Accademia dei Lincei, serving as president in 1898; he was elected senator a year before his death.