Tortolini was born on 19 November 1808, in Rome and studied literature and philosophy at the Pontifical Gregorian University, especially under Don Andrea Caraffa (1789–1845) who was a mathematical physicist.

A year later, in 1836, Tortolini was appointed to the chair of mechanics and hydraulics at the University of Rome where, in 1837, he obtained by competition the professorship of introductory higher calculus.

At the Pontifical Roman Seminary, his alma mater, he assumed the professorship of mathematical physics in 1846 and began directing the publication of Propaganda Fide, founded in 1626.

He devoted his life to raising the standards of scientific education on the peninsula at a time when Italy as a newly formed European power in 1860 needed a cultural presence on par with France, Germany, and England.

This journal gathered and disseminated the work of the most notable scholars of the exact sciences in order to revive a love for higher educational studies in Italy and to bring to notice to other nations the scientific activity of the peninsula.

By publishing his own research abroad, he underscored his belief in the importance of the internationalization of mathematical results and made contact with differing cultures reflecting the views and standards of rigor promoted by foreign editors.

Among the foreign authors who published in his journal were Arthur Cayley, Carl Gustav Jakob Jacobi, J. J. Sylvester and the Irishman William Roberts.

This was the last year of the Annali’s publication as broader geopolitical trends called for a more focused new journal of pure mathematics to witness the opening stages of what would become the unification of Italy by 1861.

The new Annali saw contributions from Alfred Clebsch, Elwin Christoffel, Paul Gordan, Camille Jordan, Cayley, Charles Hermite, Rudolf Sturm, Carl Neumann, Hermann Schwarz and Georg Friedrich Bernhard Riemann.

Aside from Betti, Tortolini was one of the few Italian contemporaries to tap into foreign journals and by doing so established a rapport with the finest minds of his time including Carl Friedrich Gauss, Joseph Louis Lagrange, Cauchy, Riemann, Luigi Bianchi, Tullio Levi-Civita, Charles Hermite, Niels Abel, Peter Gustav Lejeune Dirichlet, Sir William Thomson, Augustus De Morgan, J. J. Sylvester, Gabriel Lamé, and Eugenio Beltrami.