Salvatore Pincherle (March 11, 1853 – July 10, 1936) was an Italian

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, mathematical structure, structure, space, Mathematica ...

. He contributed significantly to (and arguably helped to found) the field of

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 (for example, Inner product space#Definition, inner product, Norm (mathematics ...

, established the

Italian Mathematical Union The Italian Mathematical Union () is a mathematical society based in Italy. It was founded on December 7, 1922, by Luigi Bianchi, Vito Volterra, and most notably, Salvatore Pincherle, who became the Union's first President. History Salvator ...

(

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

: "''Unione Matematica Italiana''"), and was president of the Third

International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the IMU Abacus Medal (known before ...

. The

Pincherle derivative In mathematics, the Pincherle derivative T' of a linear operator T: \mathbb \to \mathbb /math> on the vector space of polynomials in the variable ''x'' over a field \mathbb is the commutator of T with the multiplication by ''x'' in the algebra o ...

is named after him.

Life and Works

Pincherle was born into a

Jew Jews (, , ), or the Jewish people, are an ethnoreligious group and nation, originating from the Israelites of ancient Israel and Judah. They also traditionally adhere to Judaism. Jewish ethnicity, religion, and community are highly inte ...

ish family in

Trieste Trieste ( , ; ) is a city and seaport in northeastern Italy. It is the capital and largest city of the Regions of Italy#Autonomous regions with special statute, autonomous region of Friuli-Venezia Giulia, as well as of the Province of Trieste, ...

(then part of the

Austrian Littoral The Austrian Littoral (, , , , ) was a crown land (''Kronland'') of the Austrian Empire, established in 1849. It consisted of three regions: the Margraviate of Istria in the south, Gorizia and Gradisca in the north, and the Imperial Free City ...

) and spent his childhood in

Marseille Marseille (; ; see #Name, below) is a city in southern France, the Prefectures in France, prefecture of the Departments of France, department of Bouches-du-Rhône and of the Provence-Alpes-Côte d'Azur Regions of France, region. Situated in the ...

France France, officially the French Republic, is a country located primarily in Western Europe. Overseas France, Its overseas regions and territories include French Guiana in South America, Saint Pierre and Miquelon in the Atlantic Ocean#North Atlan ...

. After completing his basic schooling in Marseille, he left in 1869 to study mathematics at the

University of Pisa The University of Pisa (, UniPi) is a public university, public research university in Pisa, Italy. Founded in 1343, it is one of the oldest universities in Europe. Together with Scuola Normale Superiore di Pisa and Sant'Anna School of Advanced S ...

, where he was a student under both

Enrico Betti Enrico Betti Glaoui (21 October 1823 – 11 August 1892) was an Italian mathematician, now remembered mostly for his 1871 paper on topology that led to the later naming after him of the Betti numbers. He worked also on the theory of equations ...

and

Ulisse Dini Ulisse Dini (14 November 1845 – 28 October 1918) was an Italian mathematician and politician, born in Pisa. He is known for his contributions to real analysis, partly collected in his book "''Fondamenti per la teorica delle funzioni di variabil ...

. After he graduated in 1874, he taught at a school in

Pavia Pavia ( , ; ; ; ; ) is a town and comune of south-western Lombardy, in Northern Italy, south of Milan on the lower Ticino (river), Ticino near its confluence with the Po (river), Po. It has a population of c. 73,086. The city was a major polit ...

until he received a scholarship in 1877. After winning the scholarship and studying abroad at the

University of Berlin The Humboldt University of Berlin (, abbreviated HU Berlin) is a public research university in the central borough of Mitte in Berlin, Germany. The university was established by Frederick William III on the initiative of Wilhelm von Humbol ...

, Pincherle met

Karl Weierstrass Karl Theodor Wilhelm Weierstrass (; ; 31 October 1815 – 19 February 1897) was a German mathematician often cited as the " father of modern analysis". Despite leaving university without a degree, he studied mathematics and trained as a school t ...

. Pincherle contributed to Weierstrass' theory of

analytic function In mathematics, an analytic function is a function that is locally given by a convergent power series. There exist both real analytic functions and complex analytic functions. Functions of each type are infinitely differentiable, but complex ...

s, and in 1880, influenced by Weierstrass, he wrote an expository paper in the ''

Giornale di Matematiche (), known from its founding in 1974 until 1983 as (), is an Italian-language daily newspaper published in Milan with an average circulation of 28,933 in May 2023. In 2006, it was considered one of Italy's main national newspapers. History an ...

'', which proved to be a significant paper in the field of analysis. Throughout his life, Pincherle's work greatly reflected the influence that Weierstrass had on him. He later collaborated with

Vito Volterra Vito Volterra (, ; 3 May 1860 – 11 October 1940) was an Italian mathematician and physicist, known for his contributions to Mathematical and theoretical biology, mathematical biology and Integral equation, integral equations, being one of the ...

and explored

Laplace transform In mathematics, the Laplace transform, named after Pierre-Simon Laplace (), is an integral transform that converts a Function (mathematics), function of a Real number, real Variable (mathematics), variable (usually t, in the ''time domain'') to a f ...

s and other parts of functional analysis. From 1880 until 1928, Pincherle was a Professor of Mathematics at the

University of Bologna The University of Bologna (, abbreviated Unibo) is a Public university, public research university in Bologna, Italy. Teaching began around 1088, with the university becoming organised as guilds of students () by the late 12th century. It is the ...

. In 1901, collaborating with Ugo Amaldi, he published his main scientific book, ''Le Operazioni Distributive e loro Applicazioni all'Analisi''. In Bologna in 1922, he established the Italian Mathematical Union and became its first President and held the position until 1936. In 1924, he attended the Second International Congress of Mathematicians in

Toronto, Ontario Toronto ( , locally pronounced or ) is the List of the largest municipalities in Canada by population, most populous city in Canada. It is the capital city of the Provinces and territories of Canada, Canadian province of Ontario. With a p ...

Canada Canada is a country in North America. Its Provinces and territories of Canada, ten provinces and three territories extend from the Atlantic Ocean to the Pacific Ocean and northward into the Arctic Ocean, making it the world's List of coun ...

. Four years later, he became President of the Third International Congress and played a significant role in re-admitting German mathematicians after a ban imposed because of

World War I World War I or the First World War (28 July 1914 – 11 November 1918), also known as the Great War, was a World war, global conflict between two coalitions: the Allies of World War I, Allies (or Entente) and the Central Powers. Fighting to ...

. At this Congress,

Jacques Hadamard Jacques Salomon Hadamard (; 8 December 1865 – 17 October 1963) was a French mathematician who made major contributions in number theory, complex analysis, differential geometry, and partial differential equations. Biography The son of a tea ...

declared in his review lecture that Pincherle was one of the most prominent founders of functional analysis. Following the Third Congress, Pincherle retired from university. In honor of the centenary of his birth, the Italian Mathematical Union edited a selection of 62 of his notes and

treatise A treatise is a Formality, formal and systematic written discourse on some subject concerned with investigating or exposing the main principles of the subject and its conclusions."mwod:treatise, Treatise." Merriam-Webster Online Dictionary. Acc ...

s; they were published in 1954 in

Rome Rome (Italian language, Italian and , ) is the capital city and most populated (municipality) of Italy. It is also the administrative centre of the Lazio Regions of Italy, region and of the Metropolitan City of Rome. A special named with 2, ...

References

* *

External links

* {{DEFAULTSORT:Pincherle, Salvatore 1853 births 1936 deaths Scientists from Trieste Emigrants from the Austrian Empire Immigrants to France Immigrants to Italy 20th-century Italian Jews 19th-century Italian mathematicians 20th-century Italian mathematicians Italian historians of mathematics Italian mathematical analysts Academic staff of the University of Palermo 19th-century Italian Jews Presidents of the Italian Mathematical Union