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Gregorio Ricci-Curbastro (; 12January 1925) was an Italian
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 ...
. He is most famous as the discoverer of
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 ...
. With his former student
Tullio 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 significa ...
, he wrote his most famous single publication, a pioneering work on the calculus 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, 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 () is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics. Elementary a ...
and infinitesimal analysis, and papers on the theory of
real number In mathematics, a real number is a number that can be used to measure a ''continuous'' one-dimensional quantity such as a distance, duration or temperature. Here, ''continuous'' means that values can have arbitrarily small variations. Every real ...
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 mathematician who made important contributions to number theory, abstract algebra (particularly ring theory), and the axiomatic foundations of arithmetic. His ...
.


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 University of Rome may refer to: * Sapienza University of Rome, founded in 1303 * Università Cattolica del Sacro Cuore, Rome satellite campus opened 1961 * University of Rome Tor Vergata, founded in 1982 * Roma Tre University Roma Tre Universi ...
(1869). The following year the
Papal State The Papal States ( ; it, Stato Pontificio, ), officially the State of the Church ( it, Stato della Chiesa, ; la, Status Ecclesiasticus;), were a series of territories in the Italian Peninsula under the direct sovereign rule of the pope fro ...
fell and so Gregorio was called by his father to the city of his birth, Lugo di Romagna. Subsequently he attended courses at
University of Bologna The University of Bologna ( it, Alma Mater Studiorum – Università di Bologna, UNIBO) is a public research university in Bologna, Italy. Founded in 1088 by an organised guild of students (''studiorum''), it is the oldest university in continuo ...
during the year 1872 - 1873, then transferred to the
Scuola Normale Superiore di Pisa The Scuola Normale Superiore in Pisa (commonly known in Italy as "la Normale") is a public university in Pisa and Florence, Tuscany, Italy, currently attended by about 600 undergraduate and postgraduate (PhD) students. It was founded in 1810 wi ...
. In 1875 he graduated in
Pisa Pisa ( , or ) is a city and ''comune'' in Tuscany, central Italy, straddling the Arno just before it empties into the Ligurian Sea. It is the capital city of the Province of Pisa. Although Pisa is known worldwide for its leaning tower, the cit ...
in physical sciences and mathematics with a thesis on
differential equation In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, an ...
s, entitled "On Fuches's Research Concerning Linear Differential Equations". During his various travels he was a student of the mathematicians
Enrico Betti Enrico Betti Glaoui (21 October 1823 – 11 August 1892) was an 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 equations, giv ...
, Eugenio Beltrami,
Ulisse Dini Ulisse Dini (14 November 1845 – 28 October 1918) was an Italian mathematician and politician, born in Pisa. He is known for his contribution to real analysis, partly collected in his book "''Fondamenti per la teorica delle funzioni di variabil ...
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, complex analysis, non-Euclidean geometry, and on the associations between geometry and group ...
.


Studies on absolute differential calculus

In 1877 Ricci-Curbastro obtained a scholarship at the
Technical University of Munich The Technical University of Munich (TUM or TU Munich; german: Technische Universität München) is a public research university in Munich, Germany. It specializes in engineering, technology, medicine, and applied and natural sciences. Establis ...
, 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 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 ...
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 systematically used to make communication possible between groups ...
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 and most influential physicists of all time. Einstein is best known for developing the theory ...
'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 or pseudo-Riemannian metric on a manifold. It can be considered, broadly, as a measur ...
which would have a crucial role within that theory.


Influences

The advent of tensor calculus in dynamics goes back to Lagrange, 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 an ambient space. Examples include the mathematical models that describe the swinging of a ...
, and to
Riemann Georg Friedrich Bernhard Riemann (; 17 September 1826 – 20 July 1866) was a German mathematician who made contributions to analysis, number theory, and differential geometry. In the field of real analysis, he is mostly known for the first rig ...
, 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 Lipschitz 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 on a manifold by means of a differ ...
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 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 ...
- 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 The Academy of Sciences of the Institute of Bologna (''Accademia delle Scienze dell'Istituto di Bologna'') is an academic society in Bologna, Italy, that was founded in 1690 and prospered in the Age of Enlightenment. Today it is closely associated ...
- Reale Accademia di Bologna - from 1922. *The
Pontifical Academy of Sciences The Pontifical Academy of Sciences ( it, Pontificia accademia delle scienze, la, Pontificia Academia Scientiarum) is a Academy of sciences, scientific academy of the Vatican City, established in 1936 by Pope Pius XI. Its aim is to promote the ...
- 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 An asteroid is a minor planet of the inner Solar System. Sizes and shapes of asteroids vary significantly, ranging from 1-meter rocks to a dwarf planet almost 1000 km in diameter; they are rocky, metallic or icy bodies with no atmosphere. ...
, 13642 Ricci, is named after him.


Publications

* *


See also

*
Ricci flow In the mathematical fields of differential geometry and geometric analysis, the Ricci flow ( , ), sometimes also referred to as Hamilton's Ricci flow, is a certain partial differential equation for a Riemannian metric. It is often said to be ana ...


References

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