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, 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 ...

. He published high-level academic articles and books, not only on

mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

, but also on

physics Physics is the natural science that studies matter, its 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 which r ...

history History (derived ) is the systematic study and the documentation of the human activity. The time period of event before the History of writing#Inventions of writing, invention of writing systems is considered prehistory. "History" is an umbr ...

philosophy Philosophy (from , ) is the systematized study of general and fundamental questions, such as those about existence, reason, knowledge, values, mind, and language. Such questions are often posed as problems to be studied or resolved. Some ...

, 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 as ...

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

Accademia dei Lincei The Accademia dei Lincei (; literally the "Academy of the Lynx-Eyed", but 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 Rom ...

Early years

Beppo Levi was born on May 14, 1875, in

Turin Turin ( , Piedmontese language, Piedmontese: ; it, Torino ) 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 ...

, Italy, and he was an older brother of

Eugenio Elia Levi Eugenio Elia Levi (18 October 1883 – 28 October 1917) was an Italian mathematician, known for his fundamental contributions in group theory, in the theory of partial differential operators and in the theory of functions of several complex var ...

. He 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 ceremony ...

'' in mathematics in 1896 at age 21 from the

University of Turin The University of Turin (Italian: ''Università degli Studi di Torino'', UNITO) is a public research university in the city of Turin, in the Piedmont region of Italy. It is one of the oldest universities in Europe and continues to play an impo ...

under

Corrado Segre Corrado Segre (20 August 1863 – 18 May 1924) was an Italian mathematician who is remembered today as a major contributor to the early development of algebraic geometry. Early life Corrado's parents were Abramo Segre and Estella De Ben ...

. 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 ( it, Università degli Studi di Cagliari) is a 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 alon ...

in 1906, at the

University of Parma The University of Parma ( it, Università degli Studi di Parma, UNIPR) is a public university in Parma, Emilia-Romagna, Italy. It is organised in nine departments. As of 2016 the University of Parma has about 26,000 students. History During the ...

in 1910, and finally 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 continuo ...

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 founded and led the National Fascist Party. He was Prime Minister of Italy from the March on Rome in 1922 until his deposition in 194 ...

's power and of

antisemitism Antisemitism (also spelled anti-semitism or anti-Semitism) is hostility to, prejudice towards, or discrimination against Jews. A person who holds such positions is called an antisemite. Antisemitism is considered to be a form of racism. Antis ...

in Italy, and Levi, being Jewish, was soon expelled from his position at the University of Bologna. He emigrated to Argentina, as did many other European Jews at that time.

Life in Argentina

Levi chose Argentina because of an invitation by the engineer Cortés Plá,

dean Dean may refer to: People * Dean (given name) * Dean (surname), a surname of Anglo-Saxon English origin * Dean (South Korean singer), a stage name for singer Kwon Hyuk * Dean Delannoit, a Belgian singer most known by the mononym Dean Titles * ...

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 The National University of Rosario ( es, Universidad Nacional de Rosario, UNR) is a research public university located in the city of Rosario, province of Santa Fe, Argentina. Overview Rosario National University (UNR) was created in 1968 by ...

) 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 The Feltrinelli Prize (from the Italian "Premio Feltrinelli", also known as "International Feltrinelli Prize" or "Antonio Feltrinelli Prize") is an award for achievement in the arts, music, literature, history, philosophy, medicine, and physical and ...

. 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 is located northwest of Buenos Aires, on the west bank of the Paraná River. Rosario is the third-most populous ci ...

, 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 c ...

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 *Surf ...

. 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, a non-singular variety ''W'' with a proper birational map ''W''→''V''. For varieties over fields of characterist ...

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 di ...

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 Leb ...

, 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 ...

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 In algebraic geometry and number theory, the torsion conjecture or uniform boundedness conjecture for torsion points for abelian varieties states that the order of the torsion group of an abelian variety over a number field can be bounded in ter ...

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 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

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of a scientific meeting in

Bologna Bologna (, , ; egl, label= Emilian, Bulåggna ; lat, Bononia) is the capital and largest city of the Emilia-Romagna region in Northern Italy. It is the seventh most populous city in Italy with about 400,000 inhabitants and 150 different nat ...

, 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 University of Turin faculty Università Cattolica del Sacro Cuore faculty University of Cagliari faculty University of Parma faculty University of Bologna faculty National University of Rosario faculty