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, structure, space, models, and change. History On ...

. 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 (e.g. inner product, norm, topology, etc.) and the linear functions defi ...

, established the

Italian Mathematical Union The Italian Mathematical Union ( it, Unione Matematica Italiana) 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 P ...

(

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 ...

: "''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 Nevanlinna Prize (to be rena ...

. 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 of ...

is named after him. Pincherle was born into a

Jew Jews ( he, יְהוּדִים, , ) or Jewish people are an ethnoreligious group and nation originating from the Israelites Israelite origins and kingdom: "The first act in the long drama of Jewish history is the age of the Israelites""T ...

ish family in

Trieste Trieste ( , ; sl, Trst ; german: Triest ) is a city and seaport in northeastern Italy. It is the capital city, and largest city, of the autonomous region of Friuli Venezia Giulia, one of two autonomous regions which are not subdivided into pr ...

(then part of the

Austrian Littoral The Austrian Littoral (german: Österreichisches Küstenland, it, Litorale Austriaco, hr, Austrijsko primorje, sl, Avstrijsko primorje, hu, Osztrák Tengermellék) was a crown land (''Kronland'') of the Austrian Empire, established in 1849. I ...

) and spent his childhood in

Marseille Marseille ( , , ; also spelled in English as Marseilles; oc, Marselha ) is the prefecture of the French department of Bouches-du-Rhône and capital of the Provence-Alpes-Côte d'Azur region. Situated in the camargue region of southern Fra ...

France France (), officially the French Republic ( ), is a country primarily located in Western Europe. It also comprises of Overseas France, overseas regions and territories in the Americas and the Atlantic Ocean, Atlantic, Pacific Ocean, Pac ...

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

, 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, giv ...

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 contribution 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 (, , , ; la, Ticinum; Medieval Latin: ) is a town and comune of south-western Lombardy in northern Italy, south of Milan on the lower Ticino river near its confluence with the Po. It has a population of c. 73,086. The city was the ...

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

University of Berlin Humboldt-Universität zu Berlin (german: Humboldt-Universität zu Berlin, abbreviated HU Berlin) is a German public research university in the central borough of Mitte in Berlin. It was established by Frederick William III on the initiative ...

, Pincherle met

Karl Weierstrass Karl Theodor Wilhelm Weierstrass (german: link=no, 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 ...

. 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'', 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 biology and integral equations, being one of the founders of functional analysis. Biography Born in An ...

and explored

Laplace transform In mathematics, the Laplace transform, named after its discoverer Pierre-Simon Laplace (), is an integral transform that converts a function of a real variable (usually t, in the '' time domain'') to a function of a complex variable s (in the ...

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 ( it, Alma Mater Studiorum – Università di Bologna, UNIBO) is a public research university in Bologna, Italy. Founded in 1088 by an organised guild of students (''studiorum''), it is the oldest university in contin ...

. 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 ( ; or ) is the capital city of the Canadian province of Ontario. With a recorded population of 2,794,356 in 2021, it is the most populous city in Canada and the fourth most populous city in North America. The city is the ancho ...

Canada Canada is a country in North America. Its ten provinces and three territories extend from the Atlantic Ocean to the Pacific Ocean and northward into the Arctic Ocean, covering over , making it the world's second-largest country by to ...

. 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 (28 July 1914 11 November 1918), often abbreviated as WWI, was List of wars and anthropogenic disasters by death toll, one of the deadliest global conflicts in history. Belligerents included much of Europe, the Russian Empire, ...

. 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 teac ...

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 formal and systematic written discourse on some subject, generally longer and treating it in greater depth than an essay, and more concerned with investigating or exposing the principles of the subject and its conclusions." Tre ...

s; they were published in 1954 in

Rome , established_title = Founded , established_date = 753 BC , founder = King Romulus ( legendary) , image_map = Map of comune of Rome (metropolitan city of Capital Rome, region Lazio, Italy).svg , map_caption ...

References

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External links

* {{DEFAULTSORT:Pincherle, Salvatore 1853 births 1936 deaths Scientists from Trieste 20th-century Italian Jews 19th-century Italian mathematicians 20th-century Italian mathematicians Historians of mathematics Mathematical analysts Academic staff of the University of Palermo 19th-century Italian Jews Presidents of the Italian Mathematical Union