# Tullio Levi-Civita

**Levi-CivitaTullio Levi CivitaLevi-Civita, TullioT. Levi-Civita**

Tullio Levi-Civita, (, ; 29 March 1873 – 29 December 1941) was an Italian 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.wikipedia

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### Ricci calculus

**tensor index notationabsolute differential calculusantisymmetrization of indices**

Tullio Levi-Civita, (, ; 29 March 1873 – 29 December 1941) was an Italian 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.

It is also the modern name for what used to be called the absolute differential calculus (the foundation of tensor calculus), developed by Gregorio Ricci-Curbastro in 1887–1896, and subsequently popularized in a paper written with his pupil Tullio Levi-Civita in 1900.

### Gregorio Ricci-Curbastro

**RicciGregorio Ricci CurbastroRicci-Curbastro**

He was a pupil of Gregorio Ricci-Curbastro, the inventor of tensor calculus. In 1900 he and Ricci-Curbastro published the theory of tensors in Méthodes de calcul différentiel absolu et leurs applications, which Albert Einstein used as a resource to master the tensor calculus, a critical tool in the development of the theory of general relativity.

With his former student Tullio Levi-Civita, he wrote his most famous single publication, a pioneering work on the calculus of tensors, signing it as Gregorio Ricci.

### Tensor calculus

**tensor notation**

Tullio Levi-Civita, (, ; 29 March 1873 – 29 December 1941) was an Italian 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.

Developed by Gregorio Ricci-Curbastro and his student Tullio Levi-Civita, it was used by Albert Einstein to develop his theory of general relativity.

### Italians

**ItalianItalian peopleItalian descent**

Tullio Levi-Civita, (, ; 29 March 1873 – 29 December 1941) was an Italian 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.

Gregorio Ricci-Curbastro invented tensor calculus and absolute differential calculus, which were popularized in a work he co-wrote with Tullio Levi-Civita, and used in the development of the theory of relativity; Ricci-Curbastro also wrote meaningful works on algebra, infinitesimal analysis, and papers on the theory of real numbers.

### University of Padua

**PaduaUniversity of PadovaPadua University**

He graduated in 1892 from the University of Padua Faculty of Mathematics.

The university became one the universities of the Kingdom of Italy in 1873, and ever since has been one of the most prestigious in the country for its contributions to scientific and scholarly research: in the field of mathematics alone, its professors have included such figures as Gregorio Ricci Curbastro, Giuseppe Veronese, Francesco Severi and Tullio Levi Civita.

### Tensor

**tensorsorderclassical treatment of tensors**

In 1900 he and Ricci-Curbastro published the theory of tensors in Méthodes de calcul différentiel absolu et leurs applications, which Albert Einstein used as a resource to master the tensor calculus, a critical tool in the development of the theory of general relativity.

Tensors were conceived in 1900 by Tullio Levi-Civita and Gregorio Ricci-Curbastro, who continued the earlier work of Bernhard Riemann and Elwin Bruno Christoffel and others, as part of the absolute differential calculus.

### Levi-Civita field

He developed the Levi-Civita field, a system of numbers that includes infinitesimal quantities.

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.

### Libera Trevisani Levi-Civita

**Levi-Civita, Libera TrevisaniLibera Trevisani**

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.

In 1912, she graduated at the University of Padova, under the scientific guide of the mathematician Tullio Levi-Civita, with a thesis titled "About the average motion within the three body problem".

### Attilio Palatini

**PalatiniPalatini, Attilio**

Among his PhD students were Octav Onicescu, Attilio Palatini and Gheorghe Vrânceanu.

He graduated in mathematics in 1913 at the University of Padua, where he was a student of Ricci-Curbastro and of Levi-Civita.

### Ernesto Padova

**Padova, Ernesto**

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.

In this field, among his students was Tullio Levi-Civita.

### Gheorghe Vrănceanu

**Gheorghe VrânceanuGheorghe VranceanuVrănceanu, Gheorghe**

Among his PhD students were Octav Onicescu, Attilio Palatini and Gheorghe Vrânceanu.

Thereafter, he went to the University of Rome, where he studied under Tullio Levi-Civita, obtaining his doctorate on November 5, 1924.

### Octav Onicescu

**Onicescu, Octav**

Among his PhD students were Octav Onicescu, Attilio Palatini and Gheorghe Vrânceanu.

In 1919, Onicescu went to study geometry at the University of Rome, under the guidance of Tullio Levi-Civita.

### Padua

**PadovaPadua, ItalyPatavium**

Born into an Italian Jewish family in Padua, Levi-Civita was the son of Giacomo Levi-Civita, a lawyer and former senator.

### Sylvester Medal

The Royal Society awarded him the Sylvester Medal in 1922 and elected him as a foreign member in 1930.

### Infinitesimal

**infinitesimalsinfinitely closeinfinitesimally**

He developed the Levi-Civita field, a system of numbers that includes infinitesimal quantities.

The mathematical study of systems containing infinitesimals continued through the work of Levi-Civita, Giuseppe Veronese, Paul du Bois-Reymond, and others, throughout the late nineteenth and the twentieth centuries, as documented by Philip Ehrlich (2006).

### Levi-Civita symbol

**Levi-Civita tensorpermutation symbolLevi-Civita**

, for some positive integer n. It is named after the Italian mathematician and physicist Tullio Levi-Civita.

### Levi-Civita connection

**Christoffel symbolconnectionsLevi-Civita**

The Levi-Civita connection is named after Tullio Levi-Civita, although originally "discovered" by Elwin Bruno Christoffel.

### Levi-Civita parallelogramoid

**resulting segments**

It is named for its discoverer, Tullio Levi-Civita.

### Levi-Civita (crater)

**Levi-CivitaLevi-Civita crater**

It was named after Italian mathematician Tullio Levi-Civita.

### Antonio Signorini

**Signorini, Antonio**

He was awarded the gold medal of the Accademia Nazionale delle Scienze detta dei XL in 1920, while he was working at the University of Palermo: the members of the judging commission were Luigi Bianchi, Guido Castelnuovo and Tullio Levi-Civita.

### Albert Joseph McConnell

**Albert McConnellMcConnell, Albert Joseph**

He carried out his postgraduate studies in the Sapienza University of Rome under the direction of Tullio Levi-Civita and was awarded his doctorate there in 1928.

### Evan Tom Davies

**Davies, Evan Tom**

Davies would move to Rome in August 1926 to study with the leading expert on absolute differential calculus, Tullio Levi-Civita.

### Mathematician

**mathematiciansapplied mathematicianMathematics**

### Theory of relativity

**relativityrelativisticrelativity theory**

### Pure mathematics

**pureabstract mathematicspure mathematician**

His work included foundational papers in both pure and applied mathematics, celestial mechanics (notably on the three-body problem), analytic mechanics (the Levi-Civita separability conditions in the Hamilton–Jacobi equation) and hydrodynamics.