An Italian mathematician (1835-1900), famous principally for his 1868 discovery that non-euclidean geometry, until then a controversial and hypothetical system, could have its axioms interpreted so as to describe a real physical situation in euclidean space.

He was studying geodesics, the shortest curves on surfaces, and found that they could be represented as straight lines on a plane just in case the surface was of constant curvature. This led him to construct an object in euclidean space called the pseudosphere, the geodesics on which behaved exactly like lines on a plane, obeying all the euclidean axioms except the parallel postulate. This was the first time that one axiom system had explicitly been used as a model for something else it wasn't intended for.

Born 16 November 1835 in Cremona, in Austrian Lombardy, he was appointed as a professor at Bologna in 1862, Pisa in 1864, Bologna in 1866, Rome in 1873, Pavia in 1876, and Rome in 1891, where he died on 18 February 1900. He was appointed senator in 1899.

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