Guido Fubini
Encyclopedia
Guido Fubini was an Italian
mathematician
, known for Fubini's theorem
and the Fubini–Study metric.
Born in Venice
, he was steered towards mathematics at an early age by his teachers and his father, who was himself a teacher of mathematics. In 1896 he entered the Scuola Normale Superiore di Pisa
, where he studied under the notable mathematicians Ulisse Dini and Luigi Bianchi
. He gained some early fame when his 1900 doctoral thesis, entitled Clifford's parallelism
in elliptic spaces, was discussed in a widely-read work on differential geometry published by Bianchi in 1902.
After earning his doctorate, he took up a series of professorships. In 1901 he began teaching at the University of Catania
in Sicily
; shortly afterwards he moved to the University of Genoa
; and in 1908 he moved to the Politecnico in Turin
and then the University of Turin
, where he would stay for some decades.
During this time his research focused primarily on topics in mathematical analysis
, especially differential equations, functional analysis
, and complex analysis
; but he also studied the calculus of variations
, group theory
, non-Euclidean geometry
, and projective geometry
, among other topics. With the outbreak of World War I
, he shifted his work towards more applied topics, studying the accuracy of artillery fire; after the war, he continued in an applied direction, applying results from this work to problems in electrical circuits and acoustics
.
In 1939, when Fubini at the age of 60 was nearing retirement, Benito Mussolini
's Fascists adopted the anti-Jewish policies advocated for several years by Adolf Hitler
's Nazis. As a Jew, Fubini feared for the safety of his family, and so accepted an invitation by Princeton University
to teach there; he died in New York City
four years later.
Italy
Italy , officially the Italian Republic languages]] under the European Charter for Regional or Minority Languages. In each of these, Italy's official name is as follows:;;;;;;;;), is a unitary parliamentary republic in South-Central Europe. To the north it borders France, Switzerland, Austria and...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
, known for Fubini's theorem
Fubini's theorem
In mathematical analysis Fubini's theorem, named after Guido Fubini, is a result which gives conditions under which it is possible to compute a double integral using iterated integrals. As a consequence it allows the order of integration to be changed in iterated integrals.-Theorem...
and the Fubini–Study metric.
Born in Venice
Venice
Venice is a city in northern Italy which is renowned for the beauty of its setting, its architecture and its artworks. It is the capital of the Veneto region...
, he was steered towards mathematics at an early age by his teachers and his father, who was himself a teacher of mathematics. In 1896 he entered the Scuola Normale Superiore di Pisa
Scuola Normale Superiore di Pisa
The Scuola Normale Superiore di Pisa, also known in Italian as Scuola Normale , is a public higher learning institution in Italy. It was founded in 1810, by Napoleonic decree, as a branch of the École Normale Supérieure of Paris...
, where he studied under the notable mathematicians Ulisse Dini and Luigi Bianchi
Luigi Bianchi
- External links :* offers translations of some of Bianchi's papers, plus a biography of Bianchi.* PDF copy at * * * *...
. He gained some early fame when his 1900 doctoral thesis, entitled Clifford's parallelism
Clifford parallel
A Clifford parallel is a line which lies at a constant distance from some "base" line but, unlike an ordinary parallel line, does not lie in the same plane...
in elliptic spaces, was discussed in a widely-read work on differential geometry published by Bianchi in 1902.
After earning his doctorate, he took up a series of professorships. In 1901 he began teaching at the University of Catania
University of Catania
The University of Catania is a university located in Catania, Italy, and founded in 1434. It is the oldest university in Sicily, the 13th oldest in Italy and the 29th oldest university in the world...
in Sicily
Sicily
Sicily is a region of Italy, and is the largest island in the Mediterranean Sea. Along with the surrounding minor islands, it constitutes an autonomous region of Italy, the Regione Autonoma Siciliana Sicily has a rich and unique culture, especially with regard to the arts, music, literature,...
; shortly afterwards he moved to the University of Genoa
University of Genoa
The University of Genoa is one of the largest universities in Italy.Located in Liguria on the Italian Riviera, the university was founded in 1471. It currently has about 40,000 students, 1,800 teaching and research staff and about 1,580 administrative staff.- Campus :The University of Genoa is...
; and in 1908 he moved to the Politecnico in Turin
Turin
Turin is a city and major business and cultural centre in northern Italy, capital of the Piedmont region, located mainly on the left bank of the Po River and surrounded by the Alpine arch. The population of the city proper is 909,193 while the population of the urban area is estimated by Eurostat...
and then the University of Turin
University of Turin
The University of Turin is a university in the city of Turin in the Piedmont region of north-western Italy...
, where he would stay for some decades.
During this time his research focused primarily on topics in mathematical analysis
Mathematical analysis
Mathematical analysis, which mathematicians refer to simply as analysis, has its beginnings in the rigorous formulation of infinitesimal calculus. It is a branch of pure mathematics that includes the theories of differentiation, integration and measure, limits, infinite series, and analytic functions...
, especially differential equations, functional analysis
Functional analysis
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure and the linear operators acting upon these spaces and respecting these structures in a suitable sense...
, and complex analysis
Complex analysis
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is useful in many branches of mathematics, including number theory and applied mathematics; as well as in physics,...
; but he also studied the calculus of variations
Calculus of variations
Calculus of variations is a field of mathematics that deals with extremizing functionals, as opposed to ordinary calculus which deals with functions. A functional is usually a mapping from a set of functions to the real numbers. Functionals are often formed as definite integrals involving unknown...
, group theory
Group theory
In mathematics and abstract algebra, group theory studies the algebraic structures known as groups.The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces can all be seen as groups endowed with additional operations and...
, non-Euclidean geometry
Non-Euclidean geometry
Non-Euclidean geometry is the term used to refer to two specific geometries which are, loosely speaking, obtained by negating the Euclidean parallel postulate, namely hyperbolic and elliptic geometry. This is one term which, for historical reasons, has a meaning in mathematics which is much...
, and projective geometry
Projective geometry
In mathematics, projective geometry is the study of geometric properties that are invariant under projective transformations. This means that, compared to elementary geometry, projective geometry has a different setting, projective space, and a selective set of basic geometric concepts...
, among other topics. With the outbreak of World War I
World War I
World War I , which was predominantly called the World War or the Great War from its occurrence until 1939, and the First World War or World War I thereafter, was a major war centred in Europe that began on 28 July 1914 and lasted until 11 November 1918...
, he shifted his work towards more applied topics, studying the accuracy of artillery fire; after the war, he continued in an applied direction, applying results from this work to problems in electrical circuits and acoustics
Acoustics
Acoustics is the interdisciplinary science that deals with the study of all mechanical waves in gases, liquids, and solids including vibration, sound, ultrasound and infrasound. A scientist who works in the field of acoustics is an acoustician while someone working in the field of acoustics...
.
In 1939, when Fubini at the age of 60 was nearing retirement, Benito Mussolini
Benito Mussolini
Benito Amilcare Andrea Mussolini was an Italian politician who led the National Fascist Party and is credited with being one of the key figures in the creation of Fascism....
's Fascists adopted the anti-Jewish policies advocated for several years by Adolf Hitler
Adolf Hitler
Adolf Hitler was an Austrian-born German politician and the leader of the National Socialist German Workers Party , commonly referred to as the Nazi Party). He was Chancellor of Germany from 1933 to 1945, and head of state from 1934 to 1945...
's Nazis. As a Jew, Fubini feared for the safety of his family, and so accepted an invitation by Princeton University
Princeton University
Princeton University is a private research university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League, and is one of the nine Colonial Colleges founded before the American Revolution....
to teach there; he died in New York City
New York City
New York is the most populous city in the United States and the center of the New York Metropolitan Area, one of the most populous metropolitan areas in the world. New York exerts a significant impact upon global commerce, finance, media, art, fashion, research, technology, education, and...
four years later.
Books by G. Fubini
- Lezioni di analisi matematica (Società Tipografico-Editrice Nazionale, Torino, 1920)