Eugenio Beltrami

Eugenio Beltrami was an Italian mathematician, born on 16 November 1835 in Cremona, then part of the Austrian Empire and now in Italy, who died in Rome on 18 February 1900. He studied at Pavia under Francesco Brioschi, and held chairs at Bologna, Pisa, Rome and Pavia before returning to Rome in 1891. His work on the geometry of curves and surfaces showed that the surfaces whose geodesics can be drawn as straight lines in the plane are exactly those of constant curvature. In his 1868 essay on an interpretation of non-Euclidean geometry he gave a concrete realisation of the geometry of Lobachevsky and Bolyai on the pseudosphere and connected it with Riemann's geometry. He also worked on optics, thermodynamics, elasticity, electricity and magnetism, and in 1889 he brought Saccheri's 1733 study of the parallel postulate to the attention of mathematicians.