Gregorio Ricci-Curbastro (; 12January 1925) was an Italian

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 ...

. He is most famous as the inventor of 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 ...

, but also published important works in other fields.
With his former student Tullio Levi-Civita
Tullio Levi-Civita, (, ; 29 March 1873 – 29 December 1941) was an Italians, 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 ...

, he wrote his most famous single publication, a pioneering work on the calculus 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 ...

s, signing it as Gregorio Ricci. This appears to be the only time that Ricci-Curbastro used the shortened form of his name in a publication, and continues to cause confusion.
Ricci-Curbastro also published important works in other fields, including a book on higher algebra
Algebra (from ar, الجبر, lit=reunion of broken parts, bonesetting, translit=al-jabr) is one of the areas of mathematics, broad areas of mathematics, together with number theory, geometry and mathematical analysis, analysis. In its most ge ...

and infinitesimal analysis, and papers on the theory of real number
In mathematics
Mathematics (from Greek: ) includes the study of such topics as numbers ( and ), formulas and related structures (), shapes and spaces in which they are contained (), and quantities and their changes ( and ). There is no g ...

s, an area in which he extended the research begun by Richard Dedekind
Julius Wilhelm Richard Dedekind (6 October 1831 – 12 February 1916) was a German
German(s) may refer to:
Common uses
* of or related to Germany
* Germans, Germanic ethnic group, citizens of Germany or people of German ancestry
* For citiz ...

.Early life and education

Completing privately his high school studies at only 16 years of age, he enrolled on the course of philosophy-mathematics at Rome University (1869). The following year thePapal State
The Papal States ( ; it, Stato Pontificio), officially the State of the Church ( it, Stato della Chiesa, ; la, Status Ecclesiasticus; also '), were a series of territories in the Italian Peninsula
The Italian Peninsula (Italian
Ital ...

fell and so Gregorio was called by his father to the city of his birth, Lugo di Romagna. Subsequently he attended courses at Bologna, but after only one year he enrolled at the Scuola Normale Superiore di Pisa
The Scuola Normale Superiore (commonly known in Italy as "la Normale") is a university institution of higher education based in Pisa and Florence, Tuscany, Italy, currently attended by about 600 undergraduate and postgraduate (PhD) students.
It ...

.
In 1875 he graduated in Pisa
Pisa ( , or ) 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 provides essential public ser ...

in physical sciences and mathematics with a thesis on differential equations, entitled "On Fuches's Research Concerning Linear Differential Equations". During his various travels he was a student
of mathematicians of the calibre of Enrico Betti
Enrico Betti Glaoui (21 October 1823 – 11 August 1892) was an Italians, Italian mathematician, now remembered mostly for his 1871 paper on topology that led to the later naming after him of the Betti numbers. He worked also on the theory of equa ...

, Eugenio Beltrami
Eugenio Beltrami (16 November 1835 – 18 February 1900) was an Italy, Italian mathematician notable for his work concerning differential geometry and mathematical physics. His work was noted especially for clarity of exposition. He was the f ...

, Ulisse Dini
Ulisse Dini (14 November 1845 – 28 October 1918) was an Italia
Italy ( it, Italia ), officially the Italian Republic ( it, Repubblica Italiana, links=no ), is a country consisting of Italian Peninsula, a peninsula delimited by the Alps ...

and Felix Klein
Christian Felix Klein (; 25 April 1849 – 22 June 1925) was a German mathematician and mathematics educator, known for his work with group theory
In mathematics
Mathematics (from Greek: ) includes the study of such topics as ...

.
Studies on absolute differential calculus

In 1877 Ricci-Curbastro obtained a scholarship at theTechnical University of Munich
The Technical University of Munich (TUM or TU Munich) (german: Technische Universität München) is a public research university
A research university is a university
A university ( la, universitas, 'a whole') is an educational institution ...

, Bavaria, and he later worked as an assistant of
Ulisse Dini, his teacher.
In 1880 he became a lecturer of mathematics at the University of Padua where he
dealt with 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 ...

and differential quadratic forms.
He formed a research group in which Tullio Levi-Civita worked, with whom he wrote
the fundamental treatise on absolute differential calculus (also known as Ricci
calculus) with coordinates or tensor calculus on Riemannian manifold, which then
became the lingua franca
A lingua franca (; ; for plurals see ), also known as a bridge language, common language, trade language, auxiliary language, vehicular language, or link language, is a language or dialect
The term dialect (from , , from the word , 'disco ...

of the subsequent theory of 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 ...

's general relativity.
In fact absolute differential calculus had a crucial role in developing the theory,
as is shown in a letter written by Albert Einstein to Ricci-Curbastro's nephew. In this context Ricci-Curbastro identified the so-called Ricci tensor In differential geometry, the Ricci curvature tensor, named after Gregorio Ricci-Curbastro, is a geometric object which is determined by a choice of Riemannian manifold, Riemannian or pseudo-Riemannian manifold, pseudo-Riemannian metric on a manifol ...

which would have a crucial role within that theory.
Influences

The advent of tensor calculus in dynamics goes back toLagrange
Joseph-Louis Lagrange (born Giuseppe Luigi Lagrangia

, who originated the general treatment of a dynamical system
In mathematics, a dynamical system is a system in which a Function (mathematics), function describes the time dependence of a Point (geometry), point in a Manifold, geometrical space. Examples include the mathematical models that describe the ...

, and to Riemann
Georg Friedrich Bernhard Riemann (; 17 September 1826 – 20 July 1866) was a German mathematician
A mathematician is someone who uses an extensive knowledge of mathematics
Mathematics (from Greek: ) includes the study of such topics ...

, who was the first to think about geometry in an arbitrary number of dimensions. He was also influenced by the works of Christoffel and of LipschitzLipschitz, Lipshitz, or Lipchitz is an Ashkenazi Jewish surname. The surname has many variants, including: Lifshitz (Lifschitz), Lifshits, Lifshuts, Lefschetz; Lipschitz, Lipshitz, Lipshits, Lopshits, Lipschutz (Lipschütz), Lipshutz, Lüpschütz; ...

on the quadratic forms. In fact, it was essentially Christoffel's idea of covariant differentiation
In mathematics, the covariant derivative is a way of specifying a derivative along tangent vectors of a manifold. Alternatively, the covariant derivative is a way of introducing and working with a connection (mathematics), connection on a manifol ...

that allowed Ricci-Curbastro to make the greatest progress.
Recognition

Ricci-Curbastro received many honours for his contributions. He is honoured by mentions in various Academies amongst which are: * The Veneto Institute of Science - Istituto veneto di scienze - letters and articles (from 1892), of which he was then president from 1916 to 1919. *The Lincei Academy - Accademia dei Lincei - of which he was a member from 1899. *The Academy of Padua - Accademia di Padova - from 1905. *The Science Academy of Turin - Accademia delle Scienze di Torino - from 1918. *The Galileian Academy of Science - Accademia Galileiana di Scienze, Lettere ed Arti - letters and articles, of which he was then president from 1920 to 1922. *The Academy of Sciences of the Institute of Bologna - Reale Accademia di Bologna - from 1922. *The Pontifical Academy of Sciences - Accademia Pontificia delle Scienze - from 1925. He participated actively in political life, both in his native town and in Padua, and contributed with his projects to the Ravenna-area land drainage and the Lugo aqueduct. An asteroid, List of minor planets: 13001–14000, 13642 Ricci, is named after him.Publications

* *See also

*Ricci calculus *Ricci curvature *Ricci decomposition *Ricci flow *Web_(differential_geometry)#Alternative_definition, Ricci's gridReferences

Other sources * *External links

* * {{DEFAULTSORT:Ricci-Curbastro, Gregorio 1853 births 1925 deaths People from Lugo, Emilia-Romagna Italian Roman Catholics Differential geometers 19th-century Italian mathematicians 20th-century Italian mathematicians