**Gregorio Ricci-Curbastro** was an Italian mathematician best known for the invention of tensor calculus.

- In 1869 Ricci-Curbastro entered the University of Rome with the intention of studying mathematics and philosophy.
- When Ricci-Curbastro began his studies in Rome, although the Kingdom of Italy had been created a few years earlier, Rome was not part of that Kingdom being part of the Papal States in which Ricci was born and brought up.
- Ricci-Curbastro studied at Rome for one year from 1869 to 1870 and then returned to his parents home where he remained for two years before beginning a second university career.
- As well as attending lectures by Betti in Pisa, Ricci-Curbastro also attended lectures by Dini.
- In 1875 Ricci-Curbastro was awarded a doctorate for his thesis On Fuchs's research concerning linear differential equations.
- A perceptive reader will have noticed that both of these first two works by Ricci-Curbastro were based on works by German, rather than by Italian, mathematicians.
- Ricci-Curbastro now competed for a scholarship and he won one which allowed him to spend the year 1877-78 abroad.
- As well as Klein, Brill worked at the Technische Hochschule in Munich and Ricci-Curbastro attended lectures by both these famous mathematicians.
- Returning to Pisa in 1879, Ricci-Curbastro became Dini's assistant.
- Ricci-Curbastro's early work was in mathematical physics, particularly on the laws of electric circuits and differential equations.
- However, it was a paper of Christoffel, published in Crelle's Journal in 1868, which was the main influence on Ricci-Curbastro to begin his investigations in 1884 on quadratic differential forms.
- Much of Ricci-Curbastro's work after 1900 was done jointly with his student Levi-Civita.
- In the paper, applications are given by Ricci-Curbastro and Levi-Civita to the classification of the quadratic forms of differentials and there are other analytic applications; they give applications to geometry including the theory of surfaces and groups of motions; and mechanical applications including dynamics and solutions to Lagrange's equations.
- Ricci-Curbastro's absolute differential calculus became the foundation of tensor analysis and was used by Einstein in his theory of general relativity.
- Ricci-Curbastro received many honours for his outstanding contributions, although one would have to say that the importance of his work was not fully understood at the time when he produced it, but rather it was realised some time later.

Born 12 January 1853, Lugo, Papal States (now Italy). Died 6 August 1925, Bologna, Italy.

View full biography at MacTutor

Origin Italy, Physics

**Oâ€™Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive