Beppo Levi (14 May 1875 – 28 August 1961) was an

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 ...

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 published high-level academic articles and books on

mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

as well as on

physics Physics is the scientific study of matter, its Elementary particle, fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge whi ...

history History is the systematic study of the past, focusing primarily on the Human history, human past. As an academic discipline, it analyses and interprets evidence to construct narratives about what happened and explain why it happened. Some t ...

philosophy Philosophy ('love of wisdom' in Ancient Greek) is a systematic study of general and fundamental questions concerning topics like existence, reason, knowledge, Value (ethics and social sciences), value, mind, and language. It is a rational an ...

, and

pedagogy Pedagogy (), most commonly understood as the approach to teaching, is the theory and practice of learning, and how this process influences, and is influenced by, the social, political, and psychological development of learners. Pedagogy, taken ...

. Levi was a member of the Bologna Academy of Sciences and of the

Accademia dei Lincei The (; literally the "Academy of the Lynx-Eyed"), anglicised as the Lincean Academy, is one of the oldest and most prestigious European scientific institutions, located at the Palazzo Corsini on the Via della Lungara in Rome, Italy. Founded in ...

Early years

Beppo Levi was born on May 14, 1875, in

Turin Turin ( , ; ; , then ) is a city and an important business and cultural centre in northern Italy. It is the capital city of Piedmont and of the Metropolitan City of Turin, and was the first Italian capital from 1861 to 1865. The city is main ...

, Italy to 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. He was an older brother of Eugenio Elia Levi. Levi obtained his ''

laurea In Italy, the ''laurea'' is the main post-secondary academic degree. The name originally referred literally to the laurel wreath, since ancient times a sign of honor and now worn by Italian students right after their official graduation ceremo ...

'' in mathematics in 1896 at age 21 from the

University of Turin The University of Turin (Italian language, Italian: ''Università degli Studi di Torino'', UNITO) is a public university, public research university in the city of Turin, in the Piedmont (Italy), Piedmont region of Italy. It is one of the List ...

under Corrado Segre. He was appointed an assistant professor at the University of Turin three months later and shortly thereafter became a full-time Scholar. Levi was appointed Professor at the University of Piacenza in 1901, at the

University of Cagliari The University of Cagliari () is a public research university in Cagliari, Sardinia, Italy. It was founded in 1606 and is organized in 11 faculties. History The ''Studium Generalis Kalaritanum'' was founded in 1606 along the lines of the old ...

in 1906, at the

University of Parma The University of Parma () is a public university located in Parma, Emilia-Romagna, Italy. Organized into nine departments, it is one of the oldest universities in the world. As of 2016, it had approximately 26,000 students. History During the ...

in 1910, and finally 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 1928. The years that followed his last appointment saw the rise of

Benito Mussolini Benito Amilcare Andrea Mussolini (29 July 188328 April 1945) was an Italian politician and journalist who, upon assuming office as Prime Minister of Italy, Prime Minister, became the dictator of Fascist Italy from the March on Rome in 1922 un ...

's power and of

antisemitism Antisemitism or Jew-hatred is hostility to, prejudice towards, or discrimination against Jews. A person who harbours it is called an antisemite. Whether antisemitism is considered a form of racism depends on the school of thought. Antisemi ...

in Italy, and Levi, being Jewish, was soon expelled from his position at the University of Bologna. He emigrated to

Argentina Argentina, officially the Argentine Republic, is a country in the southern half of South America. It covers an area of , making it the List of South American countries by area, second-largest country in South America after Brazil, the fourt ...

, as did many other European Jews at that time.

Life in Argentina

Levi chose Argentina as a destination because of an invitation by the engineer Cortés Plá, dean of the ''Facultad de Ciencias Matemáticas, Físico-Químicas y Naturales Aplicadas a la Industria'' at the Universidad Nacional del Litoral (currently ''Facultad de Ciencias Exactas, Ingeniería y Agrimensura'' at the Universidad Nacional de Rosario) in the city of Rosario. Cortés Plá invited Levi to come to Rosario to head the recently created Instituto de Matemática. It was there that Levi did most of his work from 1939 until his death in 1961. While living in Rosario, Levi joined a group of mathematicians that included

Luis Santaló Luís Antoni Santaló Sors (October 9, 1911 – November 22, 2001) was a Spanish mathematician. He graduated from the University of Madrid and he studied at the University of Hamburg, where he received his Ph.D. in 1936. His advisor was Wilhe ...

, Simón Rubinstein, Juan Olguín, Enrique Ferrari, Fernando and Enrique Gaspar, Mario Castagnino and Edmundo Rofman. In 1940 Levi founded ''Mathematicae Notae'', the first mathematical journal in Argentina. In 1956 he was awarded the Feltrinelli Prize. He died on August 28, 1961, in

Rosario Rosario () is the largest city in the central provinces of Argentina, Argentine province of Santa Fe Province, Santa Fe. The city, located northwest of Buenos Aires on the west bank of the Paraná River, is the third-most populous city in the ...

, Argentina, and was buried in the Jewish cemetery there.

Mathematical contributions

His early work studied singularities on

algebraic curves In mathematics, an affine algebraic plane curve is the zero set of a polynomial in two variables. A projective algebraic plane curve is the zero set in a projective plane of a homogeneous polynomial in three variables. An affine algebraic plane cu ...

and

surfaces A surface, as the term is most generally used, is the outermost or uppermost layer of a physical object or space. Surface or surfaces may also refer to: Mathematics *Surface (mathematics), a generalization of a plane which needs not be flat * Sur ...

. In particular, he supplied a proof (questioned by some) that a procedure for

resolution of singularities In algebraic geometry, the problem of resolution of singularities asks whether every algebraic variety ''V'' has a resolution, which is a non-singular variety ''W'' with a Proper morphism, proper birational map ''W''→''V''. For varieties ov ...

algebraic surfaces In mathematics, an algebraic surface is an algebraic variety of dimension two. In the case of geometry over the field of complex numbers, an algebraic surface has complex dimension two (as a complex manifold, when it is non-singular) and so of dim ...

terminates in finitely many steps. Later he proved some foundational results concerning

Lebesgue integration In mathematics, the integral of a non-negative function of a single variable can be regarded, in the simplest case, as the area between the graph of that function and the axis. The Lebesgue integral, named after French mathematician Henri L ...

, including what is commonly known as Beppo Levi's lemma. He also studied the arithmetic of

elliptic curve In mathematics, an elliptic curve is a smooth, projective, algebraic curve of genus one, on which there is a specified point . An elliptic curve is defined over a field and describes points in , the Cartesian product of with itself. If the ...

s. He classified them up to isomorphism, not only over C, but also over Q. Next he studied what in modern terminology would be the subgroup of rational torsion points on an elliptic curve over Q: he proved that certain groups were realizable and that others were not. He essentially formulated the torsion conjecture for elliptic curves over the rational numbers, providing a complete list of possibilities should be, which was formulated independently by Andrew Ogg about 60 years later and finally proved by

Barry Mazur Barry Charles Mazur (; born December 19, 1937) is an American mathematician and the Gerhard Gade University Professor at Harvard University. His contributions to mathematics include his contributions to Wiles's proof of Fermat's Last Theorem in ...

in 1973.

References

Biographic and general references

* . An ample biographical paper of nearly 40 pages, an earlier version of which was published as . *

References describing his scientific contributions

* * . * For a freely downloadable offprint from the web site of one of the two authors, se
here

External links

* . The

web site A website (also written as a web site) is any web page whose content is identified by a common domain name and is published on at least one web server. Websites are typically dedicated to a particular topic or purpose, such as news, education, ...

of a scientific meeting in

Bologna Bologna ( , , ; ; ) is the capital and largest city of the Emilia-Romagna region in northern Italy. It is the List of cities in Italy, seventh most populous city in Italy, with about 400,000 inhabitants and 150 different nationalities. Its M ...

, honouring the memory of Beppo Levi. * (in

). Available from th
Edizione Nazionale Mathematica Italiana
{{DEFAULTSORT:Levi, Beppo 1875 births 1961 deaths Scientists from Turin People from Rosario, Santa Fe Argentine Sephardi Jews Argentine mathematicians 19th-century Italian mathematicians 20th-century Italian mathematicians 20th-century Italian Jews Italian emigrants to Argentina Jewish scientists Italian Sephardi Jews University of Turin alumni Academic staff of the University of Turin Academic staff of the Università Cattolica del Sacro Cuore Academic staff of the University of Cagliari Academic staff of the University of Parma Academic staff of the University of Bologna Academic staff of the National University of Rosario