Born into an ItalianJewish family inPadova, Levi-Civita was the son of Giacomo Levi-Civita, a lawyer and formersenator. He graduated in 1892 from theUniversity of Padova 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 Padova Chair of Rational Mechanics (left uncovered by death ofErnesto Padova) where he met and, in 1914, marriedLibera Trevisani, one of his students.[5] He remained in his position at Padova until 1918, when he was appointed to the Chair of Higher Analysis at theUniversity of Rome; in another two years he was appointed to the Chair of Mechanics there.
In 1900 he andRicci-Curbastro published the theory oftensors inMéthodes de calcul différentiel absolu et leurs applications,[6] whichAlbert Einstein used as a resource to master tensor calculus, a critical tool in the development of the theory ofgeneral relativity. In 1917 he introduced the notion of parallel transport[7][8] inRiemannian geometry, motivated by the will to simplify the computation of the curvature of aRiemannian manifold.[9] Levi-Civita's series of papers on the problem of a staticgravitational 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".[10] In 1933 Levi-Civita contributed toPaul Dirac's equations inquantum mechanics as well.[11]
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 toPrinceton, United States and lived there with him for a year. But when the risk of war in Europe again rose, he returned to Italy. The1938 race laws enacted by the Italian Fascist government deprived Levi-Civita of his professorship and of his membership of all scientific societies.[12] Isolated from the scientific world, he died in his apartment in Rome on 29 December, 1941.[12]
Analytical dynamics was another aspect of Levi-Civita's studies: many of his articles examine thethree-body problem. He wrote articles on hydrodynamics and on systems of differential equations. He is credited with improvements to theCauchy–Kowalevski theorem, on which he wrote a book in 1931. In 1933, he contributed to work on theDirac equation. He developed theLevi-Civita field, a system of numbers that includesinfinitesimal quantities.
All his mathematical works, except for themonographs,treatises andtextbooks, were posthumously gathered in the six volumes of his "Collected works", in a revised typographical form amending bothtypographical errors and author's oversights.
Levi-Civita, Tullio (1956),Opere Matematiche. Memorie e Note [Collected mathematical works. Memoirs and notes](PDF) (in French and Italian), vol. secondo (1901−1907), Pubblicate a cura dell'Accademia Nazionale dei Lincei, Roma: Zanichelli Editore, pp. VI, 636.
Levi-Civita, Tullio (1957),Opere Matematiche. Memorie e Note [Collected mathematical works. Memoirs and notes](PDF) (in French and Italian), vol. terzo (1908−1916), Pubblicate a cura dell'Accademia Nazionale dei Lincei, Roma: Zanichelli Editore, pp. VI, 600.
Levi-Civita, Tullio (1960),Opere Matematiche. Memorie e Note [Collected mathematical works. Memoirs and notes](PDF) (in French and Italian), vol. quarto (1917−1928), Pubblicate a cura dell'Accademia Nazionale dei Lincei, Roma: Zanichelli Editore, pp. VI, 608.
Levi-Civita, Tullio (1970),Opere Matematiche. Memorie e Note [Collected mathematical works. Memoirs and notes] (in French and Italian), vol. quinto (1929−1937), Pubblicate a cura dell'Accademia Nazionale dei Lincei, Roma: Zanichelli Editore, pp. VI, 670.
Levi-Civita, Tullio (1970),Opere Matematiche. Memorie e Note [Collected mathematical works. Memoirs and notes] (in French and Italian), vol. sesto (1938−1941), Pubblicate a cura dell'Accademia Nazionale dei Lincei, Roma: Zanichelli Editore, pp. VI, 502.
Levi-Civita, Tullio (2007) [1895],Pamphlets, mathematics,University of Michigan, retrieved14 January 2017. A collection of some of his published papers (in their original typographical form), probably an unordered uncorrected collection of offprints.
^Goodstein, Judith R. (2018).Einstein's Italian mathematicians : Ricci, Levi-Civita, and the birth of general relativity. American Mathematical Society. pp. 115–117.ISBN978-1470428464.
^Levi-Civita, Tullio (2022). "Notion of Parallelism on a Generic Manifold and Consequent Geometrical Specification of the Riemannian Curvature".arXiv:2210.13239 [gr-qc].
^Hentschel, Ann (1998).The Collected Papers of Albert Einstein, Vol. 8 (English): The Berlin Years: Correspondence, 1914-1918. (English supplement translation.). Princeton, NJ:Princeton University Press. p. 363.ISBN9780691048413.
^C Cattani and M De Maria, Geniality and rigor: the Einstein – Levi-Civita correspondence (1915–1917),Riv. Stor. Sci. (2) 4 (1) (1996), 1–22; as cited in MacTutor archive.
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