Tullio Levi-Civita
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Tullio Levi-Civita, (, ; 29 March 1873 – 29 December 1941) was an
Italian Italian may refer to: * Anything of, from, or related to the people of Italy Italy ( it, Italia ), officially the Italian Republic ( it, Repubblica Italiana, links=no ), is a country consisting of a peninsula delimited by the Alps ...
mathematician A mathematician is someone who uses an extensive knowledge of mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces ...

mathematician
, most famous for his work on
absolute differential calculus In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities and t ...
(
tensor calculus In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities and ...
) and its applications to the
theory of relativity The theory of relativity usually encompasses two interrelated theories by Albert Einstein Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born , widely acknowledged to be one of the greatest physicists of all time ...
, 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 inventor of tensor calculus, but also published important works in other fields. With his former student Tullio Levi-Civita, he wrote his most f ...
, the inventor of tensor calculus. His work included foundational papers in both
pure Pure may refer to: Computing * A pure function * A virtual function, pure virtual function * PureSystems, a family of computer systems introduced by IBM in 2012 * Pure Software, a company founded in 1991 by Reed Hastings to support the Purify too ...
and
applied mathematics Applied mathematics is the application of mathematical methods by different fields such as physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and be ...
,
celestial mechanics Celestial mechanics is the branch of astronomy that deals with the motion (physics), motions of celestial object, objects in outer space. Historically, celestial mechanics applies principles of physics (classical mechanics) to astronomical obje ...
(notably on the
three-body problem In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force. ...
), analytic mechanics (the Levi-Civita separability conditions in the
Hamilton–Jacobi equation In physics, the Hamilton–Jacobi equation, named after William Rowan Hamilton and Carl Gustav Jacob Jacobi, is an alternative formulation of classical mechanics, equivalent to other formulations such as Newton's laws of motion, Lagrangian mechan ...
) and
hydrodynamics In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force. ...
.


Biography

Born into an Italian
Jewish family Jews ( he, יְהוּדִים ISO 259-2 , Israeli pronunciation ) 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 ...
in
Padua Padua ( ; it, Padova ; vec, Pàdova) is a city and ''comune The (; plural: ) is a Administrative division, local administrative division of Italy, roughly equivalent to a township or municipality. Importance and function The pro ...
, Levi-Civita was the son of Giacomo Levi-Civita, a lawyer and former
senator A senate is a deliberative assembly, often the upper house or Debating chamber, chamber of a bicameral legislature. The name comes from the Ancient Rome, ancient Roman Senate (Latin: ''Senatus''), so-called as an assembly of the senior (Lat ...
. 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 it, Veneto (man) it, Veneta (woman) , population_note = , population_blank1_title = , p ...
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, 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
tensor In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities a ...

tensor
s 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 physicists of all time. Einstein is known for developing the theory of relativity The theo ...

Albert Einstein
used as a resource to master the tensor calculus, a critical tool in the development of the theory of
general relativity General relativity, also known as the general theory of relativity, is the geometric Geometry (from the grc, γεωμετρία; '' geo-'' "earth", '' -metron'' "measurement") is, with arithmetic, one of the oldest branches of mathema ...
. In 1917 he introduced the notion of parallel transport in
Riemannian geometry #REDIRECT Riemannian geometry#REDIRECT Riemannian geometry Riemannian geometry is the branch of differential geometry Differential geometry is a Mathematics, mathematical discipline that uses the techniques of differential calculus, integral ...
, 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 In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force. "P ...

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. Dirac made fundamental contributions to the early develop ...

Paul Dirac
's equations in
quantum mechanics Quantum mechanics is a fundamental theory A theory is a reason, rational type of abstraction, abstract thinking about a phenomenon, or the results of such thinking. The process of contemplative and rational thinking is often associated with ...
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 Princeton University is a private Private or privates may refer to: Music * "In Private "In Private" was the third single in a row to be a charting success for United Kingdom, British singer Dusty Springfield, after an absence of nearly tw ...

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 A Doctor of Philosophy (PhD, Ph.D., or DPhil; Latin Latin (, or , ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally spoken in the area around Rome, known a ...
students were
Octav Onicescu
Octav Onicescu
, Attilio Palatini, Giovanni Lampariello and
Gheorghe VrânceanuGheorghe is a Romanian given name and surname. It is a variant of George, also a name in Romanian but with soft g's. It may refer to: Given name * Gheorghe Adamescu * Gheorghe Albu * Gheorghe Alexandrescu * Gheorghe Andriev * Gheorghe Apostol ...
. 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 In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force. ...
. 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. He developed the Levi-Civita field, a system of numbers that includes infinitesimal quantities. The Royal Society awarded him the Sylvester Medal in 1922 and elected him as a Fellow_of_the_Royal_Society#Foreign_Member_of_the_Royal_Society_(ForMemRS), 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, following his participation in their colloquium in 1930 at the University of St Andrews. He was also a member of the Accademia dei Lincei and the Pontifical Academy of Sciences. Like Vito Volterra, being Jewish and anti-fascist, Levi-Civita was expelled from the Academy in his country as a consequence of the Italian Racial Laws.


Works

All his mathematical works, except for the monographs, the treatises and the textbooks are published in the six volumes of his "''Collected works''", in a revised typographical form, both amending typographical errors and author's oversights.


Articles

* . * . * .


Books

* Tullio Levi-Civita and Ugo Amaldi ''Lezioni di meccanica razionale'' (Bologna: N. Zanichelli, 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 crater * Levi-Civita field * Levi-Civita parallelogramoid * 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. * .


Publications dedicated to his memory

* .


External links

* *
Scienceworld biography



An 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