1. About Betti, the mathematical school of Pisa, and more in general about Italian mathematics after the Unity, see U. Bottazzini, Va’ pensiero. Immagini della Matematica nell’Italia dell’Ottocento, Bologna, Il Mulino, 1994.
2. On F. Brioschi see U. Bottazzini, Francesco Brioschi and the “Annali di Matematica”, in C.G. Lacaita, A. Silvestri (eds.), Francesco Brioschi e il suo tempo (1824–1897), Milano, Angeli, 2000, pp. 71–84; A. Brigaglia, Brioschi, Cremona e l’insegnamento della Geometria nel Politecnico, ibidem, pp. 403–418.
3. On F. Casorati see U. Bottazzini, Alla scuola di Weierstrass, in Va’ pensiero, op. cit., pp. 195–218; A. Gabba, Il carteggio Brioschi-Casorati, in C.G. Lacaita, A. Silvestri (eds.), Francesco Brioschi e il suo tempo (1824–1897), op. cit., pp. 419–429.
4. See L. Cremona, Introduzione ad una teoria geometrica delle curve piane, Mem. Accad. Sci. Bologna, 12 (1861), pp. 305–436; Preliminari di una teoria geometrica delle superficie, Mem. Accad. Sci. Bologna, n.s., 6 (1867), pp. 91–136 e 7 (1867), pp. 29–78.
5. As a young man, Beltrami was very active, given his Risorgimento ideals. As a result of these in 1856 he had to suspend his studies at the University of the Pavia before graduation and start working as a humble clerk. After the Kingdom of Italy was founded, Brioschi had him appointed without a public examination (on Cremona’s recommendation) as visiting professor in algebra and analytical geometry at the University of Bologna in 1862. Beltrami could at last devote himself to research and teaching, swinging for two decades between the Universities of Pisa, Rome and Pavia. He finally decided to settle in Rome, where he succeeded Brioschi as president of the Accademia nazionale dei Lincei. On Beltrami, see R. Tazzioli, Beltrami e i matematici “relativisti”. La meccanica in spazi curvi nella seconda metà dell’Ottocento, Bologna, Pitagora Editrice, 2000.