Giovanni Ceva was educated in a Jesuit college in Milan, then studied at the university of Pisa. He taught at Pisa before being appointed Professor of mathematics at the University of Mantua in 1686, a post he held for the rest of his life. When appointed in 1686 Giovanni Ceva served the Gonzagas rulers. However in 1708 Austria annexed the duchy and began to construct heavy fortifications. Giovanni Ceva quickly moved to support the new Austrian regime.

For most of his life Giovanni Ceva worked on geometry. He discovered one of the most important results on the synthetic geometry of the triangle between Greek times and the 19th Century. The theorem states that lines from the vertices of a triangle to the opposite sides are concurrent precisely when the product of the ratio the sides are divided is 1. He published this in De lineis rectis (1678).

Ceva also rediscovered and published Menelaus's theorem. He also studied applications of mechanics and statics to geometric systems. Although he wrongly concluded that the periods of oscillation of two pendulums was in the same ratio as their lengths, he later corrected the error.

Ceva published Opuscula mathematica in 1682. In Geometria Motus (1692) he, to some extent, anticipated the infinitesimal calculus. De Re Nummeraria in 1711 is one of the first works in mathematical economics; it attempts to solve the conditions of equilibrium for the monetary system of a state like Mantua.

Ceva also did important work on hydraulics. On this topic he published Opus hydrostaticum (1728). He held official positions in Mantua and used his knowledge of hydraulics to argue successfully against a project which proposed to divert the river Reno into the river Po.