Beppo Levi
Encyclopedia
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....
. He published high-level academic articles and books not only in mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, but also in physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
, history
History
History is the discovery, collection, organization, and presentation of information about past events. History can also mean the period of time after writing was invented. Scholars who write about history are called historians...
, philosophy
Philosophy
Philosophy is the study of general and fundamental problems, such as those connected with existence, knowledge, values, reason, mind, and language. Philosophy is distinguished from other ways of addressing such problems by its critical, generally systematic approach and its reliance on rational...
, and pedagogy
Pedagogy
Pedagogy is the study of being a teacher or the process of teaching. The term generally refers to strategies of instruction, or a style of instruction....
. Levi was a member of the Bologna Academy of Sciences and of the Accademia dei Lincei
Accademia dei Lincei
The Accademia dei Lincei, , is an Italian science academy, located at the Palazzo Corsini on the Via della Lungara in Rome, Italy....
.
Early years
Beppo Levi was born on May 14, 1875 in TurinTurin
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...
, Italy. He studied at 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...
, and obtained his Ph.D. in mathematics at age 21. Three months later, Levi was appointed Assistant Professor, also at the University Of Turin, where he shortly thereafter became a full time Scholar. Levi was appointed Professor at the University of Piacenza in 1901, at the University of Cagliari
University of Cagliari
The University of Cagliari is a university located in Cagliari, Italy. It was founded in 1620 and is organized in 11 Faculties.-History:The Studium Generalis Kalaritanum was founded in 1606 along the lines of the old Spanish Universities of Salamanca, Valladolid and Lérida...
in 1906, at the University of Parma
University of Parma
The University of Parma is one of the oldest universities in the world, founded in the 11th century. It is organised in twelve faculties. The University of Parma has currently about 30,000 students.-History:...
in 1910, and finally at the University of Bologna
University of Bologna
The Alma Mater Studiorum - University of Bologna is the oldest continually operating university in the world, the word 'universitas' being first used by this institution at its foundation. The true date of its founding is uncertain, but believed by most accounts to have been 1088...
in 1928. The following years bore the signature of 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 power and rising antisemitism in Italy. As a Jew, Levi was soon expelled from his position at the University of Bologna. He emigrated to Argentina, as did many other European Jews at the time.
Life in Argentina
The choice of Argentina was in response to an invitation by engineer Cortés Plá, deanDean (education)
In academic administration, a dean is a person with significant authority over a specific academic unit, or over a specific area of concern, or both...
at 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 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....
s like Luis Santaló
Luis Santaló
Luís Antoni Santaló Sors 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 Wilhelm Blaschke...
, 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
Academic journal
An academic journal is a peer-reviewed periodical in which scholarship relating to a particular academic discipline is published. Academic journals serve as forums for the introduction and presentation for scrutiny of new research, and the critique of existing research...
in Argentina
Argentina
Argentina , officially the Argentine Republic , is the second largest country in South America by land area, after Brazil. It is constituted as a federation of 23 provinces and an autonomous city, Buenos Aires...
. In 1956 he was awarded the Italian Premio Feltrinelli.
He died on August 28, 1961 in Rosario
Rosario
Rosario is the largest city in the province of Santa Fe, Argentina. It is located northwest of Buenos Aires, on the western shore of the Paraná River and has 1,159,004 residents as of the ....
, Argentina, and was buried in the Jewish cemetery there.
Mathematical contributions
His early work studied singularitiesMathematical singularity
In mathematics, a singularity is in general a point at which a given mathematical object is not defined, or a point of an exceptional set where it fails to be well-behaved in some particular way, such as differentiability...
on algebraic curves and surfaces. In particular, he supplied a proof (questioned by some) that a procedure for resolution of singularities
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...
on algebraic surfaces terminates in finitely many steps. Later he proved some foundational results concerning Lebesgue integration
Lebesgue integration
In mathematics, Lebesgue integration, named after French mathematician Henri Lebesgue , refers to both the general theory of integration of a function with respect to a general measure, and to the specific case of integration of a function defined on a subset of the real line or a higher...
, including a statement that even today appears in many measure theory textbooks as "Beppo Levi's lemma".
He also studied the arithmetic of elliptic curves. 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 a conjecture
Mazur's torsion theorem
In algebraic geometry Mazur's torsion theorem, due to Barry Mazur, classifies the possible torsion subgroups of the group of rational points on an elliptic curve defined over the rational numbers....
as to what the complete list of possibilities should be, a conjecture that was to be made independently by Andrew Ogg
Andrew Ogg
Andrew Pollard Ogg is an American mathematician, a professor emeritus of mathematics at the University of California, Berkeley....
about 60 years later, and finally proved by Barry Mazur
Barry Mazur
-Life:Born in New York City, Mazur attended the Bronx High School of Science and MIT, although he did not graduate from the latter on account of failing a then-present ROTC requirement. Regardless, he was accepted for graduate school and received his Ph.D. from Princeton University in 1959,...
.
External links
.. The web site of a scientific meeting in BolognaBologna
Bologna is the capital city of Emilia-Romagna, in the Po Valley of Northern Italy. The city lies between the Po River and the Apennine Mountains, more specifically, between the Reno River and the Savena River. Bologna is a lively and cosmopolitan Italian college city, with spectacular history,...
, honouring the memory of Beppo Levi. (in Italian
Italian language
Italian is a Romance language spoken mainly in Europe: Italy, Switzerland, San Marino, Vatican City, by minorities in Malta, Monaco, Croatia, Slovenia, France, Libya, Eritrea, and Somalia, and by immigrant communities in the Americas and Australia...
). Available from the Edizione Nazionale Mathematica Italiana.