One year before this, in 1843, Bonnet had written a paper on the convergence of series with positive terms.

From 1868 Bonnet assisted Chasles at the Ecole Polytechnique, and three years later he became a director of studies there.

Bonnet did important work on differential geometry, a topic that was also being investigated in France by Serret, Frenet, Bertrand and Puiseux.

Independently of Ferdinand Minding, Bonnet showed the invariance of the Gauss curvature of a surface under bending.

In modern terminology, the prize was offered for determining all possible local isometric embeddings in Euclidean 3-space of a surface with given Riemannian metric ("line element").