Tullio Levi-Civita, (, ; 29 March 1873 – 29 December 1941) 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 It ...
mathematician, most famous for his work on
absolute differential calculus (
tensor calculus) and its applications to the
theory of relativity, but who also made significant contributions in other areas. He was a pupil of
Gregorio Ricci-Curbastro
Gregorio Ricci-Curbastro (; 12January 1925) was an Italian mathematician. He is most famous as the discoverer of tensor calculus.
With his former student Tullio Levi-Civita, he wrote his most famous single publication, a pioneering work on the ...
, the inventor of tensor calculus. His work included foundational papers in both
pure and
applied mathematics
Applied mathematics is the application of mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and industry. Thus, applied mathematics is a combination of mathematical ...
,
celestial mechanics
Celestial mechanics is the branch of astronomy that deals with the motions of objects in outer space. Historically, celestial mechanics applies principles of physics (classical mechanics) to astronomical objects, such as stars and planets, to ...
(notably on the
three-body problem), analytic mechanics (the Levi-Civita separability conditions in the
Hamilton–Jacobi equation) and
hydrodynamics
In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids—liquids and gases. It has several subdisciplines, including ''aerodynamics'' (the study of air and other gases in motion) and ...
.
Biography
Born into an Italian
Jewish family in
Padua, Levi-Civita was the son of Giacomo Levi-Civita, a lawyer and former
senator. He graduated in 1892 from the
University of Padua
The University of Padua ( it, Università degli Studi di Padova, UNIPD) is an Italian university located in the city of Padua, region of Veneto, northern Italy. The University of Padua was founded in 1222 by a group of students and teachers from ...
Faculty of Mathematics. In 1894 he earned a teaching diploma after which he was appointed to the Faculty of Science teacher's college in Pavia. In 1898 he was appointed to the Padua Chair of Rational Mechanics (left uncovered by death of
Ernesto Padova) where he met and, in 1914, married
Libera Trevisani
Libera Trevisani Levi-Civita (17 May 1890 – 11 December 1973) was an Italian mathematician born in Verona.
Biography
Libera Trevisani earned her classical lyceum A levels in 1908 at the "Bernardino Telesio" Lyceum in Cosenza. In the 1908–19 ...
, one of his pupils. He remained in his position at Padua until 1918, when he was appointed to the Chair of Higher Analysis at the
University of Rome; in another two years he was appointed to the Chair of Mechanics there.
In 1900 he and
Ricci-Curbastro published the theory of
tensors in ''Méthodes de calcul différentiel absolu et leurs applications'', which
Albert Einstein
Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest and most influential physicists of all time. Einstein is best known for developing the theory ...
used as a resource to master the tensor calculus, a critical tool in the development of the theory of
general relativity. In 1917 he introduced the notion of parallel transport in
Riemannian geometry, motivated by the will to simplify the computation of the curvature of a Riemannian manifold. Levi-Civita's series of papers on the problem of a static
gravitational field were also discussed in his 1915–1917 correspondence with Einstein. The correspondence was initiated by Levi-Civita, as he found mathematical errors in Einstein's use of tensor calculus to explain the theory of relativity. Levi-Civita methodically kept all of Einstein's replies to him; and even though Einstein had not kept Levi-Civita's, the entire correspondence could be re-constructed from Levi-Civita's archive. It is evident from this that, after numerous letters, the two men had grown to respect each other. In one of the letters, regarding Levi-Civita's new work, Einstein wrote "I admire the elegance of your method of computation; it must be nice to ride through these fields upon the horse of true mathematics while the like of us have to make our way laboriously on foot". In 1933 Levi-Civita contributed to
Paul Dirac
Paul Adrien Maurice Dirac (; 8 August 1902 – 20 October 1984) was an English theoretical physicist who is regarded as one of the most significant physicists of the 20th century. He was the Lucasian Professor of Mathematics at the Univer ...
's equations in
quantum mechanics as well.
His textbook on tensor calculus, ''The Absolute Differential Calculus'' (originally a set of lecture notes in Italian co-authored with Ricci-Curbastro), remains one of the standard texts almost a century after its first publication, with several translations available.
In 1936, receiving an invitation from Einstein, Levi-Civita traveled to
Princeton, United States and lived there with him for a year. But when the risk of war in Europe again rose, he returned to Italy. The
1938 race laws enacted by the Italian Fascist government deprived Levi-Civita of his professorship and of his membership of all scientific societies. Isolated from the scientific world, he died in his apartment in Rome in 1941.
Among his
PhD students were
Octav Onicescu
Octav Onicescu (; August 20, 1892 – August 19, 1983) was a Romanian mathematician and a member of the Romanian Academy. Together with his student, Gheorghe Mihoc, he is considered to be the founder of the Romanian school of probability theory ...
,
Attilio Palatini,
Giovanni Lampariello and
Gheorghe Vrânceanu.
Later on, when asked what he liked best about Italy, Einstein said "spaghetti and Levi-Civita".
Other studies and honors
Analytical dynamics was another aspect of Levi-Civita's studies: many of his articles examine the
three-body problem. He wrote articles on hydrodynamics and on systems of differential equations. He is credited with improvements to the
Cauchy–Kowalevski theorem, on which he wrote a book in 1931. In 1933, he contributed to work on the
Dirac equation
In particle physics, the Dirac equation is a relativistic wave equation derived by British physicist Paul Dirac in 1928. In its free form, or including electromagnetic interactions, it describes all spin- massive particles, called "Dirac p ...
. He developed the
Levi-Civita field
In mathematics, the Levi-Civita field, named after Tullio Levi-Civita, is a non-Archimedean ordered field; i.e., a system of numbers containing infinite and infinitesimal quantities. Each member a can be constructed as a formal series of the form
...
, a system of numbers that includes
infinitesimal
In mathematics, an infinitesimal number is a quantity that is closer to zero than any standard real number, but that is not zero. The word ''infinitesimal'' comes from a 17th-century Modern Latin coinage ''infinitesimus'', which originally ref ...
quantities.
The
Royal Society awarded him the
Sylvester Medal in 1922 and elected him as a
foreign member in 1930. He became an honorary member of the
London Mathematical Society, of the
Royal Society of Edinburgh, and of the
Edinburgh Mathematical Society
The Edinburgh Mathematical Society is a mathematical society for academics in Scotland.
History
The Society was founded in 1883 by a group of Edinburgh school teachers and academics, on the initiative of Alexander Yule Fraser FRSE and Andrew Je ...
, following his participation in their colloquium in 1930 at the
University of St Andrews
(Aien aristeuein)
, motto_lang = grc
, mottoeng = Ever to ExcelorEver to be the Best
, established =
, type = Public research university
Ancient university
, endowment ...
. He was also a member 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 Ro ...
and the
Pontifical Academy of Sciences
The Pontifical Academy of Sciences ( it, Pontificia accademia delle scienze, la, Pontificia Academia Scientiarum) is a scientific academy of the Vatican City, established in 1936 by Pope Pius XI. Its aim is to promote the progress of the mat ...
.
Works
All his mathematical works, except for the
monographs,
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." Trea ...
s and
textbooks, were posthumously gathered in the six volumes of his "''Collected works''", in a revised typographical form amending both
typographical errors and author's oversights.
Articles
* .
* .
* .
Books
* Tullio Levi-Civita and Ugo Amaldi ''Lezioni di meccanica razionale'' (Bologna: N.
Zanichelli
Zanichelli editore S.p.A. is an Italian publishing company founded in Modena, Italy, in 1859.
It publishes mainly textbooks for school, university and professional books (legal texts and medicine), dictionaries, and reference books.
History
The ...
, 1923)
* Tullio Levi-Civita ''Questioni di meccanica classica e relativistica'' (Bologna, N. Zanichelli, 1924)
* Tullio Levi-Civita ''Lezioni di calcolo differenziale assoluto'' (Roma: Alberto Stock Editore 1925)
** ''The Absolute Differential Calculus'' (London & Glasgow, Blackie & Son 1927) (edited by Enrico Persico, trans. by Marjorie Long)
* Tullio Levi-Civita and Enrico Persico ''Fondamenti di meccanica relativistica'' (Bologna : N. Zanichelli, 1928)
* Tullio Levi-Civita ''Caratteristiche dei sistemi differenziali e propagazione ondosa'' (Bologna, N. Zanichelli 1931)
* Tullio Levi-Civita and Ugo Amaldi ''Nozioni di balistica esterna'' (Bologna: N. Zanichelli, 1935)
* Tullio Levi ''Problème des Corps en relativité générale'' (Gauthier-Villars, Paris, 1950, Mémorial des sciences mathématiques )
* .
* .
* .
* .
* .
* .
* . A collection of some of his published papers (in their original typographical form), probably an unordered uncorrected collection of offprints.
See also
*
Levi-Civita connection
*
Levi-Civita crater
*
Levi-Civita field
In mathematics, the Levi-Civita field, named after Tullio Levi-Civita, is a non-Archimedean ordered field; i.e., a system of numbers containing infinite and infinitesimal quantities. Each member a can be constructed as a formal series of the form
...
*
Levi-Civita parallelogramoid
In the mathematical field of differential geometry, the Levi-Civita parallelogramoid is a quadrilateral in a curved space whose construction generalizes that of a parallelogram in the Euclidean plane. It is named for its discoverer, Tullio Levi-C ...
*
Levi-Civita symbol
Notes
References
Biographical references
* "Professor T. Levi-Civita, Member of Vatican Academy," ''The Jewish Chronicle'' (UK), February 6, 1942.
General references
* . The "''Inaugural address''" (English translation of the contribution title) of Beniamino Segre, a commemoration describing briefly many aspects of the life and the work of Levi-Civita.
Scientific references
* .
* . "''Electromagnetism in the work of Levi-Civita''" (English translation of the contribution title) is a survey of some of the works of Levi-Civita on the theory of
electromagnetism
In physics, electromagnetism is an interaction that occurs between particles with electric charge. It is the second-strongest of the four fundamental interactions, after the strong force, and it is the dominant force in the interactions of ...
.
* .
Publications dedicated to his memory
* .
External links
*
*
Scienceworld biographyAn Italian short biography of Tullio Levi-Civita in Edizione Nazionale Mathematica Italiana online.
{{DEFAULTSORT:Levi-Civita, Tullio
1873 births
1941 deaths
Scientists from Padua
Differential geometers
Italian relativity theorists
Foreign Members of the Royal Society
Members of the French Academy of Sciences
Members of the Lincean Academy
Institute for Advanced Study visiting scholars
University of Padua alumni
University of Padua faculty
Sapienza University of Rome faculty
19th-century Italian mathematicians
20th-century Italian mathematicians
20th-century Italian Jews
Fluid dynamicists
Jewish physicists