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 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 ...
, most famous for his work on
absolute differential calculus
In mathematics, Ricci calculus constitutes the rules of index notation and manipulation for tensors and tensor fields on a differentiable manifold, with or without a metric tensor or connection. It is also the modern name for what used to be ...
(
tensor calculus
In mathematics, tensor calculus, tensor analysis, or Ricci calculus is an extension of vector calculus to tensor fields (tensors that may vary over a manifold, e.g. in spacetime).
Developed by Gregorio Ricci-Curbastro and his student Tullio Levi ...
) and its applications to the
theory of relativity
The theory of relativity usually encompasses two interrelated theories by Albert Einstein: special relativity and general relativity, proposed and published in 1905 and 1915, respectively. Special relativity applies to all physical phenomena in ...
, 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
Pure may refer to:
Computing
* A pure function
* A 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 tool
* Pure-FTPd, F ...
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 s ...
,
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
In physics and classical mechanics, the three-body problem is the problem of taking the initial positions and velocities (or momenta) of three point masses and solving for their subsequent motion according to Newton's laws of motion and Newton's ...
), 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 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
![Levi-civita2](https://upload.wikimedia.org/wikipedia/commons/9/90/Levi-civita2.jpg)
Born into an Italian
Jewish family
Jews ( he, יְהוּדִים, , ) 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 the age of the Israelites""Th ...
in
Padua
Padua ( ; it, Padova ; vec, Pàdova) is a city and ''comune'' in Veneto, northern Italy. Padua is on the river Bacchiglione, west of Venice. It is the capital of the province of Padua. It is also the economic and communications hub of the ...
, 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 chamber of a bicameral legislature. The name comes from the ancient Roman Senate (Latin: ''Senatus''), so-called as an assembly of the senior (Latin: ''senex'' meaning "the el ...
. 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 B ...
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
Ernesto Padova (17 February 1845 – 9 March 1896) was an Italian mathematician born in Livorno.
Biography
He graduated at the University of Pisa in 1866 but he was also a student of the Scuola Normale of Pisa. He first taught in a high school i ...
) 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
tensor
In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects related to a vector space. Tensors may map between different objects such as vectors, scalars, and even other tenso ...
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 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
General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics ...
. In 1917 he introduced the notion of parallel transport in
Riemannian geometry
Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds, smooth manifolds with a ''Riemannian metric'', i.e. with an inner product on the tangent space at each point that varies smoothly from point to poin ...
, 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, a gravitational field is a model used to explain the influences that a massive body extends into the space around itself, producing a force on another massive body. Thus, a gravitational field is used to explain gravitational phenome ...
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
Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, ...
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 research university in Princeton, New Jersey. Founded in 1746 in Elizabeth as the College of New Jersey, Princeton is the fourth-oldest institution of higher education in the United States and one of the nine ...
, 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
Attilio Palatini (18 November 1889 – 24 August 1949) was an Italian mathematician born in Treviso.
Biography
Palatini was the seventh of the eight children of Michele (1855-1914) and Ilde Furlanetto (1856-1895). In 1900, during the celebrations ...
,
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
In physics and classical mechanics, the three-body problem is the problem of taking the initial positions and velocities (or momenta) of three point masses and solving for their subsequent motion according to Newton's laws of motion and Newton's ...
. 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 part ...
. 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 referr ...
quantities.
The
Royal Society
The Royal Society, formally The Royal Society of London for Improving Natural Knowledge, is a learned society and the United Kingdom's national academy of sciences. The society fulfils a number of roles: promoting science and its benefits, re ...
awarded him the
Sylvester Medal
The Sylvester Medal is a bronze medal awarded by the Royal Society (London) for the encouragement of mathematical research, and accompanied by a £1,000 prize. It was named in honour of James Joseph Sylvester, the Savilian Professor of Geometry a ...
in 1922 and elected him as a
foreign member in 1930. He became an honorary member of the
London Mathematical Society
The London Mathematical Society (LMS) is one of the United Kingdom's learned societies for mathematics (the others being the Royal Statistical Society (RSS), the Institute of Mathematics and its Applications (IMA), the Edinburgh Mathematical S ...
, of the
Royal Society of Edinburgh
The Royal Society of Edinburgh is Scotland's national academy of science and letters. It is a registered charity that operates on a wholly independent and non-partisan basis and provides public benefit throughout Scotland. It was established i ...
, 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 Rom ...
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 math ...
.
Works
All his mathematical works, except for the
monograph
A monograph is a specialist work of writing (in contrast to reference works) or exhibition on a single subject or an aspect of a subject, often by a single author or artist, and usually on a scholarly subject.
In library cataloging, ''monograph ...
s,
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."Treat ...
s and
textbook
A textbook is a book containing a comprehensive compilation of content in a branch of study with the intention of explaining it. Textbooks are produced to meet the needs of educators, usually at educational institutions. Schoolbooks are textboo ...
s, were posthumously gathered in the six volumes of his "''Collected works''", in a revised typographical form amending both
typographical error
A typographical error (often shortened to typo), also called a misprint, is a mistake (such as a spelling mistake) made in the typing of printed (or electronic) material. Historically, this referred to mistakes in manual type-setting (typography). ...
s 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
In Riemannian or pseudo Riemannian geometry (in particular the Lorentzian geometry of general relativity), the Levi-Civita connection is the unique affine connection on the tangent bundle of a manifold (i.e. affine connection) that preserves th ...
*
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 ...
*
Levi-Civita symbol
In mathematics, particularly in linear algebra, tensor analysis, and differential geometry, the Levi-Civita symbol or Levi-Civita epsilon represents a collection of numbers; defined from the sign of a permutation of the natural numbers , for some ...
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 a ...
.
* .
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