Pierre Ossian Bonnet (; 22 December 1819,
Montpellier
Montpellier (, , ; oc, Montpelhièr ) is a city in southern France near the Mediterranean Sea. One of the largest urban centres in the region of Occitania (administrative region), Occitania, Montpellier is the prefecture of the Departments of ...
– 22 June 1892,
Paris
Paris () is the capital and most populous city of France, with an estimated population of 2,165,423 residents in 2019 in an area of more than 105 km² (41 sq mi), making it the 30th most densely populated city in the world in 2020. S ...
) was a French
mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems.
Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change.
History
On ...
. He made some important contributions to the
differential geometry
Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and multili ...
of surfaces, including the
Gauss–Bonnet theorem
In the mathematical field of differential geometry, the Gauss–Bonnet theorem (or Gauss–Bonnet formula) is a fundamental formula which links the curvature of a surface to its underlying topology.
In the simplest application, the case of a ...
.
Biography
Early years
Pierre Bonnet attended the Collège in Montpellier. In 1838 he entered the
École Polytechnique
École may refer to:
* an elementary school in the French educational stages normally followed by secondary education establishments (collège and lycée)
* École (river), a tributary of the Seine flowing in région Île-de-France
* École, Savoi ...
in Paris. He also studied at the
École Nationale des Ponts et Chaussées
École may refer to:
* an elementary school in the French educational stages normally followed by secondary education establishments (collège and lycée)
* École (river), a tributary of the Seine flowing in région Île-de-France
* École, Savoi ...
.
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
The British Indian Ocean Territory (BIOT) is an Overseas Territory of the United Kingdom situated in the Indian Ocean, halfway between Tanzania and Indonesia. The territory comprises the seven atolls of the Chagos Archipelago with over 1,000 ...
. He defeated Bour for this position. From 1868 Bonnet assisted
Chasles 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
Urbain Jean Joseph Le Verrier FRS (FOR) H FRSE (; 11 March 1811 – 23 September 1877) was a French astronomer and mathematician who specialized in celestial mechanics and is best known for predicting the existence and position of Neptune usin ...
to the chair at the Sorbonne, then in 1883 he succeeded
Liouville
Joseph Liouville (; ; 24 March 1809 – 8 September 1882) was a French mathematician and engineer.
Life and work
He was born in Saint-Omer in France on 24 March 1809. His parents were Claude-Joseph Liouville (an army officer) and Thérèse ...
as a member of the Bureau des Longitudes.
Bonnet did important work on differential geometry, a topic that was also being investigated in France by
Serret
Serret is a surname. Notable people with the surname include:
*Dulce MarÃa Serret (1898–1989), Cuban pianist and music teacher
*Joseph Alfred Serret (1819–1885), French mathematician
*Marie-Ernestine Serret (1812–1884), French painter and p ...
,
Frenet,
Bertrand
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Places
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and
Puiseux. Here Bonnet made major contributions to the concept of curvature. In particular, he published a formula relating the surface integral of the Gauss curvature to the Euler characteristic of the surface and the line integral of the geodesic curvature of its boundary; this result is now known as the
Gauss–Bonnet theorem
In the mathematical field of differential geometry, the Gauss–Bonnet theorem (or Gauss–Bonnet formula) is a fundamental formula which links the curvature of a surface to its underlying topology.
In the simplest application, the case of a ...
.
Gauss
Johann Carl Friedrich Gauss (; german: Gauß ; la, Carolus Fridericus Gauss; 30 April 177723 February 1855) was a German mathematician and physicist who made significant contributions to many fields in mathematics and science. Sometimes refer ...
was known to have previously discovered a special case of this fundamental result, but had never published it.
Independently of
Ferdinand Minding
Ernst Ferdinand Adolf Minding (russian: link=no, Фердинанд Готлибович Миндинг; – ) was a German-Russian mathematician known for his contributions to differential geometry. He continued the work of Carl Friedrich Ga ...
, Bonnet showed the invariance of the Gauss curvature of a surface 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. 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").
See also
*
Topics named after Carl Friedrich Gauss
Carl Friedrich Gauss (1777–1855) is the eponym of all of the topics listed below.
There are over 100 topics all named after this German mathematician and scientist, all in the fields of mathematics, physics, and astronomy. The English eponymo ...
References
*
External links
*
{{DEFAULTSORT:Bonnet, Pierre Ossian
1819 births
1892 deaths
Members of the French Academy of Sciences
University of Paris faculty
Differential geometers
École Polytechnique alumni
École Normale Supérieure faculty
19th-century French mathematicians
Members of the Göttingen Academy of Sciences and Humanities