BELTRAMI, EUGENIO Italian mathema tician, was born at Cremona. He came of a well-known and cul tured family; was educated at Cremona and later at Pavia, where he studied mathematics under Brioschi. Beltrami held an appoint ment in the administration of the Italian railways until 1862 when he began his academic career as professor extraordinarius in algebra, and geometry at Bologna. The following year he was appointed professor of geodesy at Pisa, but he returned to Bologna in 1866 as professor of rational mechanics. In 1873 Beltrami be came professor at Rome and was elected a member of the Reale Accademia dei Lincei. Between 1876 and 1891 he lectured on mathematical physics and higher mechanics at Pavia, then re turned to Rome where he remained until his death, after an unsuccessful operation, on Feb. 18, 'goo.
Beltrami's work on non-Euclidean geometry follows on that of Riemann and Lobatchewsky; his most important contributions, dealing with the theory of hyperbolic space, were published in the Giornale Matematico di Napoli (1868) . He was also the author of papers on differential parameters in which he used the theory of invariants (186g), on flexures of ruled surfaces and on the general theory of surfaces. While at Pavia and Rome Beltrami wrote a number of papers on various branches of mathematical physics such as hydrodynamics, elasticity, physical optics, theory of potential, electricity, magnetism, conduction of heat and ther modynamics. A good deal of this work aims at clearing up some of the obscurities present in Maxwell's work. After his death Beltrami's papers were collected and published under the title Opere Matematiche by the University of Rome (3 vols., 1902-10).