Gregorio RicciCurbastro
Gregorio RicciCurbastro  

Born 

12 January 1853
Died  6 August 1925 
(aged 72)
Nationality  Italian 
Alma mater  Scuola Normale Superiore di Pisa 
Known for 
Tensor calculus Ricci calculus 
Scientific career  
Fields  Mathematics 
Doctoral advisor 
Ulisse Dini Enrico Betti 
Doctoral students  Tullio LeviCivita 
Gregorio RicciCurbastro (Italian: [ɡreˈɡɔːrjo ˈrittʃi kurˈbastro]; 12 January 1853 – 6 August 1925) was an Italian mathematician born in Lugo di Romagna.^{[1]} He is most famous as the inventor of tensor calculus, but also published important works in other fields.
With his former student Tullio LeviCivita, he wrote his most famous single publication,^{[2]} a pioneering work on the calculus of tensors, signing it as Gregorio Ricci. This appears to be the only time that RicciCurbastro used the shortened form of his name in a publication, and continues to cause confusion.
RicciCurbastro also published important works in other fields, including a book on higher algebra and infinitesimal analysis,^{[3]} and papers on the theory of real numbers, an area in which he extended the research begun by Richard Dedekind.^{[4]}
Contents
Biography
Youth
Completing privately his high school studies at only sixteen years of age he enrolled on the course of philosophymathematics at Rome University (1869). The following year the Papal State fell and so Gregorio was called by his father to the city of his birth, Lugo. Subsequently he attended courses at Bologna, but after only one year he enrolled at the Scuola Normale Superiore di Pisa.
In 1875, he graduated in Pisa 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, Eugenio Beltrami, Ulisse Dini and Felix Klein.
Studies on absolute differential calculus
In 1877 RicciCurbastro obtained a scholarship at the Technische Hochschule of Munich, 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 LeviCivita 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 Einstein'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 RicciCurbastro's nephew. In this context RicciCurbastro identified the socalled Ricci tensor 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, 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 on the quadratic forms. In fact, it was essentially Christoffel’s idea of covariant differentiation^{[5]} that allowed RicciCurbastro to make the greatest progress.^{[6]}
Recognition
RicciCurbastro 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 Ravennaarea land drainage and the Lugo aqueduct.
An asteroid, 13642 Ricci, is named after him.
Publications
 RicciCurbastro, Gregorio (1898), Lezioni sulla teoria delle superficie (in Italian), Verona: Drucker ^{[7]}
See also
Notes
 ^ LeviCivita, Tullio (1926), "Commemorazione del socio nazionale prof. Gregorio RicciCurbastro" [Commemoration of national member Gregorio RicciCurbastro read by member T. LeviCivita at the meeting of 3 January 1926], Mem. Accad. Lincei (in Italian), 1 (8): 555–564
 ^ Ricci, Gregorio; LeviCivita, Tullio (March 1900). "Méthodes de calcul différentiel absolu et leurs applications" [Methods of the absolute differential calculus and their applications]. Mathematische Annalen (in French). Springer. 54 (1–2): 125–201. doi:10.1007/BF01454201.
 ^ RicciCurbastro, Gregorio (1918), Lezioni di Analisi algebrica ed infinitesimale (1926 ed.), Padova: Tip. Universitaria
 ^ RicciCurbastro, Gregorio (1897), "Della teoria dei numeri reali secondo il concetto di Dedekind", Gior. di Matem., 35: 22–74
 ^ Christoffel, E.B. (1869), "Ueber die Transformation der homogenen Differentialausdrücke zweiten Grades", Journal für die reine und angewandte Mathematik, B. 70: 46–70
 ^ RicciCurbastro, Gregorio (1887), "Sulla derivazione covariante ad una forma quadratica differenziale" [On the covariant differentiation with respect to a quadratic differential form], Rend. Acc. Lincei (in Italian), 3 (4): 15–18
 ^ James, George Oscar (1899). "Review: Lezioni sulla Teoria delle Superficie, by Gregorio Ricci" (PDF). Bull. Amer. Math. Soc. 7 (8): 359–360. doi:10.1090/s000299041901008166.
References
 Tonolo, Angelo (1954), "Commemorazione di Gregorio RicciCurbastro nel primo centenario della nascita" (PDF), Rendiconti del Seminario Matematico della Università di Padova (in Italian), 23: 1–24
 Goodstein, Judith R. (2018). Einstein’s Italian mathematicians : Ricci, LeviCivita, and the birth of general relativity. American Mathematical Society. ISBN 9781470428464.
External links
 Gregorio RicciCurbastro at the Mathematics Genealogy Project
 O'Connor, John J.; Robertson, Edmund F., "Gregorio RicciCurbastro", MacTutor History of Mathematics archive, University of St Andrews.