Monge, who was born at Beaune in France, was trained as a draftsman at Mézières, where he later became professor of mathematics (1768). During the French Revolution he served on the committee that formulated the metric system (1791), became minister of the navy and the colonies (1792–93), and played a vital part in organizing the defense of France against the counterrevolutionary armies. He contributed significantly to the founding of the Ecole Polytechnique in 1795. Monge met Napoleon in 1796 and saw active service in Napoleon's army during the Egyptian campaign (1798–1801).

Monge's major mathematical achievements were the invention of descriptive geometry and the application of the techniques of analysis to the theory of curvature. The latter ultimately led to the revolutionary work of Georg Riemann on geometry and curvature.

Following Napoleon's fall from power in 1815, Monge was expelled from the French Academy and deprived of all his honors.