Pierre Ossian Bonnet was a French

France

The French Republic , The French Republic , The French Republic , (commonly known as France , is a unitary semi-presidential republic in Western Europe with several overseas territories and islands located on other continents and in the Indian, Pacific, and Atlantic oceans. Metropolitan France...

 mathematician

Mathematician

A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....

. He made some important contributions to the differential geometry of surfaces, including the Gauss-Bonnet theorem.

Early years

Pierre Bonnet attended the Collège in Montpellier. In 1838 he entered the Ecole Polytechnique

École Polytechnique

The École Polytechnique is a state-run institution of higher education and research in Palaiseau, Essonne, France, near Paris. Polytechnique is renowned for its four year undergraduate/graduate Master's program...

 in Paris. He also studied at the École Nationale des Ponts et Chaussées

École Nationale des Ponts et Chaussées

Founded in 1747, the École nationale des ponts et chaussées , often referred to as les Ponts, is the world's oldest civil engineering school...

.

Middle years

In graduating he was offered a post as an engineer. After some thought Bonnet decided on a career in teaching and research in mathematics instead.

Turning down the engineering post had not been an easy decision since Bonnet was not well off financially. He had to do private tutoring so that he could afford to accept a position at the Ecole Polytechnique in 1844.

One year before this, in 1843, Bonnet had written a paper on the convergence of series with positive terms. Another paper on series in 1849 was to earn him an award from the Brussels Academy. However between these two papers on series, Bonnet had begun his work on differential geometry in 1844.

Bonnet was elected to the Academy of Sciences in 1862 to replace Biot. He defeated Bour for this position. From 1868 Bonnet assisted Chasles

Michel Chasles

Michel Floréal Chasles was a French mathematician.He was born at Épernon in France and studied at the École Polytechnique in Paris under Siméon Denis Poisson. In the War of the Sixth Coalition he was drafted to fight in the defence of Paris in 1814...

 at the Ecole Polytechnique, and three years later he became a director of studies there. In addition to this post he also taught at the Ecole Normale Supérieure.

In 1878 Bonnet succeeded Le Verrier to the chair at the Sorbonne, then in 1883 he succeeded Liouville as a member of the Bureau des Longitudes.

Bonnet did important work on differential geometry. In addition Serret, Frenet

Jean Frédéric Frenet

Jean Frédéric Frenet was a French mathematician, astronomer, and meteorologist. He was born and died in Périgueux, France....

, Bertrand

Joseph Louis François Bertrand

Joseph Louis François Bertrand was a French mathematician who worked in the fields of number theory, differential geometry, probability theory, economics and thermodynamics....

 and Puiseux

Pierre Puiseux

Pierre Henri Puiseux was a French astronomer.Born in Paris, son of Victor Puiseux, he was educated at the Ecole Normale Supérieure before starting work as an astronomer at the Paris Observatory in 1885....

 worked in France on this topic. Bonnet made major contributions introducing the notion of geodesic curvature. A formula for the line integral of the geodesic curvature along a closed curve is known as the Gauss-Bonnet theorem. Gauss

Carl Friedrich Gauss

Johann Carl Friedrich Gauss was a German mathematician and scientist who contributed significantly to many fields, including number theory, statistics, analysis, differential geometry, geodesy, geophysics, electrostatics, astronomy and optics.Sometimes referred to as the Princeps mathematicorum...

 published a special case.

Independently of Ferdinand Minding

Ferdinand Minding

Ferdinand Minding was a German–Russian mathematician known for his contributions to differential geometry. He continued the work of Gauss concerning differential geometry of surfaces, especially its intrinsic aspects. Minding considered questions of bending of surfaces and proved the invariance of...

, Bonnet showed the invariance of the geodesic curvature under bending. Between 1844 and 1867 he published a series of papers on the differential geometry of surfaces. In 1859 he submitted an important memoir for the Grand Prize of the Paris Academy. The prize was to find all surfaces of a given linear element.

See also

• Topics named after Carl Friedrich Gauss