Betti, Enrico (1823-1892)

Italian mathematician. Betti was the first to provide a thorough exposition and development of the theory of equations formulated by French mathematician Evariste Galois. This greatly advanced the transition from classical to abstract algebra.

Betti was born near Pistoia, Tuscany, and studied physical and mathematical sciences at Pisa, where he was professor from 1856. Betti had fought against Austria during the first wars of Italian independence and in 1862 he became a member of the new Italian parliament. He entered the government as undersecretary of state for education in 1874 and served in the senate after 1884.

Betti's most important work was on algebra and the theory of equations. In papers published in 1852 and 1855 he gave proofs of most of Galois's major theorems. In so doing he became the first mathematician to resolve integral functions of a complex variable into their primary factors. He also developed the theory of elliptical functions.

Betti turned to mathematical physics in 1863. In 1878 he gave the law of reciprocity in elasticity theory which became known as Betti's theorem. Along the way, conducting research into ‘analysis situs’ in hyperspace in 1871, he also did valuable work on numbers characterizing the connection of a variety, these later becoming known as Betti numbers.