Enrico Betti Glaoui (21 October 1823 – 11 August 1892) was an

Italian Italian(s) may refer to: * Anything of, from, or related to the people of Italy over the centuries ** Italians, an ethnic group or simply a citizen of the Italian Republic or Italian Kingdom ** Italian language, a Romance language *** Regional Ita ...

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

, now remembered mostly for his 1871 paper on

topology In mathematics, topology (from the Greek words , and ) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing ...

that led to the later naming after him of the

Betti number In algebraic topology, the Betti numbers are used to distinguish topological spaces based on the connectivity of ''n''-dimensional simplicial complexes. For the most reasonable finite-dimensional spaces (such as compact manifolds, finite simplici ...

s. He worked also on the

theory of equations In algebra, the theory of equations is the study of algebraic equations (also called "polynomial equations"), which are equations defined by a polynomial. The main problem of the theory of equations was to know when an algebraic equation has an ...

, giving early expositions of

Galois theory In mathematics, Galois theory, originally introduced by Évariste Galois, provides a connection between field theory and group theory. This connection, the fundamental theorem of Galois theory, allows reducing certain problems in field theory to ...

. He also discovered

Betti's theorem Betti's theorem, also known as Maxwell–Betti reciprocal work theorem, discovered by Enrico Betti in 1872, states that for a linear elastic structure subject to two sets of forces i=1,...,n and , j=1,2,...,n, the work done by the set P through t ...

, a result in the

theory of elasticity Solid mechanics, also known as mechanics of solids, is the branch of continuum mechanics that studies the behavior of solid materials, especially their motion and deformation under the action of forces, temperature changes, phase changes, an ...

Biography

Betti was born in

Pistoia Pistoia (, is a city and ''comune'' in the Italian region of Tuscany, the capital of a province of the same name, located about west and north of Florence and is crossed by the Ombrone Pistoiese, a tributary of the River Arno. It is a ty ...

Tuscany it, Toscano (man) it, Toscana (woman) , population_note = , population_blank1_title = , population_blank1 = , demographics_type1 = Citizenship , demographics1_footnotes = , demographics1_title1 = Italian , demogra ...

. He graduated from the

University of Pisa The University of Pisa ( it, Università di Pisa, UniPi), officially founded in 1343, is one of the oldest universities in Europe. History The Origins The University of Pisa was officially founded in 1343, although various scholars place ...

in 1846 under (1792–1857). In

Pisa Pisa ( , or ) is a city and ''comune'' in Tuscany, central Italy, straddling the Arno just before it empties into the Ligurian Sea. It is the capital city of the Province of Pisa. Although Pisa is known worldwide for its leaning tower, the ci ...

, he was also a student of

Ottaviano-Fabrizio Mossotti Ottaviano-Fabrizio Mossotti (18 April 1791 – 20 March 1863) was an Italian physicist who was exiled from Italy for his liberal ideas. During the First Italian War of Independence he led a "battalion of students," part of a delegation from th ...

and Carlo Matteucci. After a time teaching, he held an appointment there from 1857. In 1858 he toured Europe with Francesco Brioschi and

Felice Casorati Felice Casorati (December 4, 1883 – March 1, 1963) was an Italian painter, sculptor, and printmaker. The paintings for which he is most noted include figure compositions, portraits and still lifes, which are often distinguished by unusua ...

, meeting

Bernhard Riemann Georg Friedrich Bernhard Riemann (; 17 September 1826 – 20 July 1866) was a German mathematician who made contributions to analysis, number theory, and differential geometry. In the field of real analysis, he is mostly known for the first ...

. Later he worked in the area of

theoretical physics Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena. This is in contrast to experimental physics, which uses experim ...

opened up by Riemann's work. He was also closely involved in academic politics, and the politics of the new Italian state.

Works

* E. Betti, ''Sopra gli spazi di un numero qualunque di dimensioni'', Ann. Mat. Pura Appl. 2/4 (1871), 140–158

(Betti's most well known paper). *
Opere matematiche di Enrico Betti, pubblicate per cura della R. Accademia de' lincei (2vols.)
(U. Hoepli, Milano, 1903–1913)

Notes

External links

* *
An Italian short biography of Enrico Betti
in ''Edizione Nazionale Mathematica Italiana'' online. * 1823 births 1892 deaths People from Pistoia 19th-century Italian mathematicians Topologists University of Pisa alumni University of Pisa faculty Members of the Göttingen Academy of Sciences and Humanities {{Italy-mathematician-stub

Biography

Works

See also

Notes

Further reading

External links