Gino Fano

Gino Fano (January 5, 1871 – November 8, 1952) was an Italian mathematician known for his foundational work in projective geometry and finite geometries.

Fano studied at the University of Turin under Corrado Segre, earning his doctorate in 1892. He then worked as an assistant to Segre and later became a professor at the University of Messina, and subsequently at the University of Turin. In 1938, due to the racial laws enacted under the Fascist regime in Italy, Fano, who was Jewish, was dismissed from his position. He emigrated to Switzerland, where he remained for the rest of his life.

Fano is best known for his work on the axioms of projective geometry, particularly his discovery of the smallest non-degenerate projective plane, now known as the Fano plane. This plane contains seven points and seven lines, with each point lying on three lines and each line containing three points. It represents a fundamental example in the study of finite geometries and demonstrates the independence of Desargues's theorem from weaker axiomatic systems.

Beyond his work on projective geometry, Fano also contributed to the study of algebraic surfaces and algebraic varieties. His research helped to lay the groundwork for subsequent developments in algebraic geometry and finite geometry.