Born in Piazza Armerina, the son of Giovanni and Angioletta Bocciarelli, he graduated from the Università degli Studi di Genova, earning his laurea degree in 1949 under the direction of Enzo Martinelli.

[21][22] In 1954 he was awarded the Ottorino Pomini prize by the Unione Matematica Italiana, jointly with Gabriele Darbo: the judging commission was composed by Giovanni Sansone (as the president), Alessandro Terracini, Beniamino Segre, Giuseppe Scorza-Dragoni, Carlo Miranda, Mario Villa and Enzo Martinelli (as the secretary).

[28] According to Martinelli, Rizza is also a skilled organizer:[29] his ability in organizational tasks is also acknowledged and praised by Schreiber (1973, p. 1), who also alludes the positive opinions of colleagues and students alike about his involvement in research, teaching and administrative duties at the mathematics department of the University of Parma.

Few years later, he extended Cauchy's integral formula to every monogenic function F on a commutative normed real algebra A*,[33] isomorphic to a given complex algebra A:[34] precisely, he proves the formula where All'estensione, tutt'altro che banale, allo spazio R2n dei metodi di Martinelli per dimostrare la (3), è dedicata una Memoria [8] di Giovanni Battista Rizza, il quale, sempre nell'ipotesi ρ(x1, y1,..., xn, yn) ∈ Cω, perviene a stabilire la (3) per n qualsiasi.

Anche questo lavoro, per quanto redatto in lingua inglese e pubblicato su una delle principali riviste matematiche, non ha nella letteratura attuale, la notorietà che meriterebbe.