Pierre Ossian Bonnet

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Pierre Ossian Bonnet (1819–1892) was a French mathematician who helped shape the geometry of surfaces. He was born in Montpellier and studied at the Collège in Montpellier, the École Polytechnique in Paris, and the École Nationale des Ponts et Chaussées. Although offered an engineering job, he chose a career in teaching and research in mathematics, helped by private tutoring to make ends meet, and joined the École Polytechnique in 1844.

Bonnet published on series in 1843 and 1849, but from 1844 he focused on differential geometry. He was elected to the French Academy of Sciences in 1862. He later held several important positions: assisting Chasles at the École Polytechnique from 1868 and becoming director of studies there about three years later; teaching at the École Normale Supérieure; taking the chair at the Sorbonne in 1878; and joining the Bureau des Longitudes in 1883.

His major work was in the differential geometry of surfaces, especially on curvature. He is best known for the Gauss–Bonnet theorem, which connects the total curvature of a surface to its Euler characteristic and the curvature along its boundary. He also showed that Gauss curvature remains unchanged when a surface is bent, independently of Ferdinand Minding. Between 1844 and 1867 he published many papers on this topic. In 1859 he submitted an important memoir for the Grand Prize of the Paris Academy about determining all possible local isometric embeddings of a surface with a given metric in Euclidean 3-space.