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Betti is noted for his contributions to algebra and topology.Betti studied at the University of Pisa, later was to become a professor (1857) and rector there and director of its teacher's college. Under his leadership the Scuola Normale Superiore in Pisa became the leading Italian centre for mathematical research and mathematical education.
Betti is noted for his contributions to algebra and topology. His early work is in the area of equations and algebra. Betti extended and gave proofs relating to the algebraic concepts of Evariste Galois. These had been previously given without proofs. Betti thus made an important contribution to the transition from classical to modern algebra. He published this in several works starting in 1851. He was the first to give a proof that the Galois group is closed under multiplication.
In 1854 Betti showed that the quintic equation could be solved in terms of integrals resulting in elliptic functions.
In 1858 Betti, along with Brioschi and Casorati, visited the mathematical centres of Europe. They visited Göttingen, Berlin and Paris making many important mathematical contacts.
Bernhard Riemann arrived in Pisa in 1863. Influenced by his friend Bernhard Riemann, Betti did important work in theoretical physics, in particular in potential theory and elasticity. He also published papers on the theory of functions, concentrating on elliptic functions.
Riemann inspired Betti's memoir on topology which Betti had neglected for 40 years.
Betti also served in several political positions.
References (7 books/articles)
References elsewhere in this archive:
Tell me about Betti's part in the development of group theory
Tell me about Betti's work on topology