# Professor Gregorio Ricci Curbastro (1853 – 1925)

**«Unfortunately there seems to be no photographic proof of the only encounter between Albert Einstein and Gregorio Ricci Curbastro: we can only imagine the cordial and satisfying handshake between the histrionic genius from Ulm and the taciturn gentleman from Lugo. Each had a considerable debt of gratitude towards the other: without Ricci Curbastro’s calculus, almost certainly – if not certainly – Einstein would never have been able to substantiate his most fortunate scientific thoughts. On the other hand, with the emergence of general relativity, the cream of the crème of mathematicians and theoretical physicists throughout most of the globe began to study, use, and develop that calculation that was ever so potent and ever so effective, yet, which remained for so long in the shadows. »**

At the heart of Einstein’s general theory of relativity, a jewel among the most gleaming in twentieth century science, lies the work of an Italian mathematician, Gregorio Ricci Curbastro. Albert Einstein, after being the victim of a tried and true “scientist’s block”, found in Ricci Curbastro’s tensor calculus the algorithmic apparatus, which allowed him to transform a fleeting intuition into a solid physical theory. That famous theory that represents the perfect balance between the physics genius of Einstein and the power, synthesis, and elegance of mathematics created by Ricci Curbastro. In the twenties, the success of the general relativity theory offered the tensor calculus theory – until then, considered so complicated as to be superfluous – a chance to avenge itself and its creator. However, while the world turned Einstein into a sort of superstar, Ricci Curbastro persevered in the privacy of a lifetime, keeping away from the limelight.

(From **Il Genio and il Gentiluomo, Einstein e il matematico italiano che salvò la teoria della relatività** by Fabio Toscano, published by Sironi Editore Milano, 2004).

**Gregorio Ricci Curbastro (Lugo, January 12th, 1853 – Bologna, August 6th, 1925)**

Born in Lugo di Romagna (Ravenna), his father was Antonio Ricci Curbastro, an engineer known throughout the province of Ravenna, and his mother was Livia Vecchi. Both he and his brother, Domenico were, before entering university, schooled privately at home by teachers who led them through a targeted and detailed course of instruction. At sixteen, Gregorio begins philosophical mathematical studies at the University of Rome. Called back to Lugo by his father in 1870, after Rome became the capital of Italy, in 1872 he enrolled at the University of Bologna, attending for two-years, and then transferred to the Normale University of Pisa, which was already a very important center for mathematical research at the time. Here, Ricci Curbastro met Enrico Betti and Ulisse Dini, attending conferences and learning more on the mathematical developments of that era, which were crucial to his research and direction. In fact, already in 1875, he was awarded his first doctorate thanks to research he carried out on linear differential equations.

After graduation, he won a scholarship to study at the Technische Hochschule in Munich. There he met Felix Klein (president) and Alexander von Brill. Ricci Curbastro participated in their conferences and won both their respect. It must be said that Klein was not the “motivated” mathematician in the style of Ricci Curbastro, as were instead Lipschitz, Christoffel, and Rienmann. The latter gave Ricci Curbastro the input for an in-depth study on “Riemannian” geometry.

When he returned to Pisa, he worked as special assistant to Ulisse Dini, his professor. In 1880, he became visiting professor of mathematics at the University of Padua. He created the Absolute Differential Calculus and immediately realized the importance that his work could have on mathematical physics and on the theory of elasticity and the theory of heat. This was work that was worthy of awards and that allowed him, with good reason, to compete twice for the Premio Reale di Matematica (Mathematics Award), but unfortunately without success, probably because he still had not seen, at that time, the real-world applications for these mathematical models. Despite the lack of recognition, Ricci Curbastro continued his studies, and attracted the attention of other young mathematicians who quickly found themselves in full collaboration with him, including Tullio Levi Civita, who then became his valuable collaborator, with a strong intuition.

Within a few years from then, the two mathematicians published together. It was the year 1900, in the “Mathematische Annalen”, and the article was: “Méthodes de Calcul Differentiel Absolu et leurs Application”, an extensive report on the Absolute Differential Calculus.

Albert Einstein was at an “impasse” in developing the theory of general relativity, due to several equations that could not adhere to the space-time theory. In essence, this was related to understanding the possibility of creating a differential calculus on a non-Euclidean space-time structure.

Einstein did not know that this type of calculation had already been initiated by Gregorio Ricci Curbastro and further developed by Levi Civita in Italy. So much so that Einstein wrote to his friend and mathematician, Marcel Grossmann: “Help me, or I’ll go crazy.” It was precisely Grossmann who led Einstein towards the solutions of tensor calculus.

When Einstein completed the “construction” of his famous theory, he stated in a paper: “No one who has really understood this theory can escape its beauty. This is a triumph in the methods of general differential calculus.”

Gregorio Ricci Curbastro actively participated in political life, both in his hometown, as well as in Padua, and contributed with his projects to the reclamation of the Ravenna region and the construction of the aqueduct in Lugo. Here, at his childhood home, a commemorative plaque is affixed that reads: “He gave to science the absolute differential calculus, an essential tool for the theory of general relativity, a new vision of the universe.”

The Science High School of Lugo, where several of his manuscripts are preserved, is also dedicated to him.

Ricci Curbastro received many honors for his contributions, although you could say that the importance of his work was not fully understood by the Italian mathematical community during the time he developed, but only later, especially thanks to the application of his methods by Einstein.

He was honored with admission to various Academies, including the Istituto Veneto di Scienze, Lettere ed Arti (Venetian Institute of Arts and Sciences) (1892), of which he became president in 1916-19. He was also a member of the Accademia dei Lincei (Lincean Academy) from 1899, the Accademia di Padova (Academy of Padua) from 1905, the Accademia delle Scienze di Torino (Academy of Sciences of Turin) from 1918, the Società dei Quaranta (Academy of the Forty) from 1921, the Reale Accademia di Bologna (Royal Academy of Bologna) from 1922, the Accademia Pontificia (Pontifical Academy) from 1925, and the Accademia Galileiana di Scienze, Lettere ed Arti (Galilean Academy of Arts and Sciences), of which he was President from 1920 to 1922.

He was also deputy mayor of Padua, having refused the post as Mayor.