The Department of Mathematics traces its roots to the glorious tradition of the school of mathematics which was formed in Pisa near the time of Italian unity. It was the first Italian school of mathematics and has long remained the true source of mathematical research in Italy. Its birth was favored by the presence of the Scuola Normale Superiore and also by the close scientific contacts which Bernhard Riemann, during his long stays in Pisa (between 1863 and 1865), established with Enrico Betti and Eugenio Beltrami. These two mathematicians, along with their mentor Ottaviano Fabrizio Mossotti, were the initiators of the school in Pisa. Their work was continued by their many pupils, both direct and indirect. Among them, besides Ulisse Dini, who became a professor at the age of 21, one can cite Eugenio Bertini, ecc,ecc, Luigi Fantappie', and Mauro Picone. All these illustrious mathematicians were trained in Pisa, almost all of them at the Scuola Normale Superiore.
Leonida Tonelli, after whom the department is named, was, in fact, trained in Bologna under the tutelage of Cesare Arzelà, who was, in turn, a student of Ulisse Dini at Pisa. Tonelli taught in Pisa for many years. After his premature death in 1946, it fell to his students to carry forward his demanding heredity during the extremely difficult years following the end of the second world war. One of these, Alessandro Faedo, for many years rector of the University of Pisa, was largely responsible for the subsequent flowering of Pisan mathematics. It began with his bringing to Pisa Federico Cafiero, a student of Renato Cacciopoli, and reached its peak in the 1960's with the arrival of Aldo Andreotti, Jacopo Barsotti, Enrico Bombieri, Sergio Campanato, Gianfranco Capriz, Ennio De Giorgi, Giovanni Prodi, Guido Stampacchia, and Edoardo Vesentini. The mathematicians that now constitute the faculty of the Department are, in large part, the progeny of these outstanding mathematicians.