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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, mathematical structure, structure, space, Mathematica ...
. He is most famous as the discoverer of tensor calculus. With his former student Tullio Levi-Civita, 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 tens ...
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 areas of mathematics, 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 mathem ...
and infinitesimal analysis, and papers on the theory of
real number In mathematics, a real number is a number that can be used to measurement, measure a ''continuous'' one-dimensional quantity such as a distance, time, duration or temperature. Here, ''continuous'' means that values can have arbitrarily small var ...
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 (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 from ...
fell and so Gregorio was called by his father to the city of his birth,
Lugo di Romagna Lugo ( rgn, Lùgh) is a town and ''comune'' in the northern Italian region of Emilia-Romagna, in the province of Ravenna. History A settlement in where is now the city is mentioned for the first time in 782 AD, but the names Lucus appears only in ...
. Subsequently he attended courses at University of Bologna during the year 1872 - 1873, then transferred to the Scuola Normale Superiore di Pisa. 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 ...
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 the mathematicians Enrico Betti, Eugenio Beltrami, Ulisse Dini and Felix Klein.


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 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 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 theor ...
'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 which would have a crucial role within that theory.


Influences

The advent of tensor calculus in dynamics goes back to
Lagrange Joseph-Louis Lagrange (born Giuseppe Luigi Lagrangiadynamical system In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water i ...
, and to Riemann, 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 Lipschitz, Lipshitz, or Lipchitz, is an Ashkenazi Jewish (Yiddish/German-Jewish) surname. The surname has many variants, including: Lifshitz (Lifschitz), Lifshits, Lifshuts, Lefschetz; Lipschitz, Lipshitz, Lipshits, Lopshits, Lipschutz (Lipschütz ...
on the quadratic forms. In fact, it was essentially Christoffel's idea of covariant differentiation 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 The Pontifical Academy of Sciences ( it, Pontificia accademia delle scienze, la, Pontificia Academia Scientiarum) is a scientific academy of the Vatican City, established in 1936 by Pope Pius XI. Its aim is to promote the progress of the math ...
- 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 Solar System#Inner solar system, 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 o ...
,
13642 Ricci Year 1364 ( MCCCLXIV) was a leap year starting on Monday (link will display the full calendar) of the Julian calendar. Events January–December * February 15 – Joint kings Magnus Eriksson and Haakon Magnusson of Sweden are both ...
, is named after him.


Publications

* *


See also

* Ricci flow


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