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Tullio Levi-Civita (March 29, 1873 - December 29, 1941) (pronounced le-vee chee-vee-tah) was an Italian born 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, the inventor of tensor calculus. His work included foundational papers in both pure and applied mathematics, celestial mechanics (notably on the three-body problem) and hydrodynamics.

Contents 1 Biography 2 References 3 See also 4 External links

Born into a Jewish family at Padua, Levi-Civita was the son of Giacomo Levi-Civita, a lawyer and former senator. He graduated in 1892 from the University of Padua Faculty of Mathematics. In 1894 he earned a teaching diploma after which he was appointed to the Pavia Faculty of Science teacher's college. In 1898 he was appointed to the Padua Chair of Rational Mechanics 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.^[1]

In 1900 he and Ricci-Curbastro published the theory of tensors in Méthodes de calcul differential absolu et leures applications which Albert Einstein used as a resource to master the tensor calculus, a critical tool in Einstein's development of the theory of general relativity. 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 theory of relativity. Levi-Civita methodically kept all of Einstein's replies to him, and even though Einstein hadn't kept Levi-Civita's, the entire correspondence could be re-constructed from Levi-Civita's archive. It's evident from these letters that, after numerous letters, two men had grown to respect each other. In one of the letters, regrading 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's equations in quantum mechanics as well.^[1]

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 more than a century after its first publication, with several translations available.

In 1938, when racial laws were passed by Italian Fascist government, Levi-Civita lost his professorship and membership in all scientific societies. He eventually died isolated from the rest of the scientific world in his apartment in Rome in 1941.

Among his Ph.D. students were Octav Onicescu and Gheorghe Vrânceanu.

Later on, when asked what he liked best about Italy, Einstein said "spaghetti and Levi-Civita".^{[citation needed]}

1. ↑ ^a  O'Connor, John J., and Edmund F. Robertson. "Tullio Levi-Civita". MacTutor History of Mathematics archive.
2. ↑  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.
3. Amir D. Aczel, God's Equation, MJF Books, New York, 1999.

• Levi-Civita connection
• Levi-Civita symbol

• Tullio Levi-Civita at the Mathematics Genealogy Project
• Scienceworld biography
• Another short biography