**Pierre Bonnet** was a French mathematician who worked in the differential geometry of surfaces. He proved the Gauss-Bonnet theorem.

- His full name is Pierre Ossian Bonnet but he wrote all his papers and books under the name 'Ossian Bonnet', using 'Ossian' as his first name.
- His three sons, however, all sometimes used "Ossian-Bonnet" as their surname.
- We give more information about Bonnet's sons below.
- Ossian Bonnet's parents were Pierre Bonnet (born about 1785) and Magdelaine Messac (born about 1795).
- Bonnet attended the Collège in Montpellier, then in 1838 he entered the École Polytechnique in Paris.
- Bonnet published his first few papers in the Journal de Mathématiques Pures et Appliquées, the journal founded by Joseph Liouville in 1836 which is the second oldest mathematical journal in the world.
- After some thought, however, 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.
- They had three sons, Emile Pierre Ossian-Bonnet (1845-1901), Georges Pierre Alfred Ossian-Bonnet (1852-1912) and Gaston-Pierre Ossian-Bonnet.
- However between these two papers on series, Bonnet had begun his work on differential geometry in 1844 with the paper Sur quelques propriétés générales des surfaces et des lignes tracées sur les surfaces Ⓣ(On some general properties of surfaces and lines drawn on surfaces).
- This paper contains the famous Gauss-Bonnet theorem which gives a formula for the line integral of the geodesic curvature along a closed curve.
- Let us look at Bonnet's career before we return to look at his other mathematical work.
- Eugène Catalan, who was already working as an assistant tutor at he École Polytechnique, had been listed first for appointment to tutor in November 1844 but Bonnet was appointed to the tutor position leaving Catalan as an assistant tutor.
- Two admission examiners were appointed for the École Polytechnique in 1848, Charles Hermite and Joseph Serret with Abel Transon (1805-1876) and Bonnet as their deputies.
- There does appear to have been a certain tension between Bonnet and Catalan over the years.
- Bonnet later became a tutor in analysis at the École Polytechnique.
- We learn a little about Bonnet's teaching there by examining his book Leçons de mécanique élémentaire Ⓣ(Lessons in elementary mechanics) (1858).
- On the title page of the book, Bonnet is given as Doctor of Science.
- In 1853 Bonnet was appointed as a substitute professor of mathematical astronomy at the Collège de France standing in for Jacques Binet whose health had begun to deteriorate.
- In 1860 there was a vacancy for the Academy of Sciences and four candidates were ranked in the order Joseph Serret, Ossian Bonnet, Victor Puiseux and Eugène Catalan.
- Serret was elected and Bonnet had to wait two years, then he was elected to the Academy in 1862 to replace Biot.
- Bour won the prize with his paper Théorie de la déformation des surfaces Ⓣ(Theory of surface deformation) (1862), which is why we say Bonnet's election ahead of Bour was slightly surprising.
- Bonnet and Delfino Codazzi received honourable mentions for their submissions.
- Bonnet's entry was published as Mémoire sur la théorie des surfaces applicables sur une surface donnée Ⓣ(Dissertation on the theory of surfaces applicable to a given surface.).
- From 1868 Bonnet assisted Chasles at the École Polytechnique, and three years later he became a director of studies there.
- Bonnet acted as a substitute professor for Chasles at the university of Paris in 1871-72 and again 1874-77.
- In 1878 Bonnet succeeded Le Verrier to the chair at the Sorbonne, but he was dismissed from his director of studies position at the École Polytechnique in that year on account of false allegations about a scandal in his private life.
- M Ossian Bonnet, one of the most distinguished teachers of the school has just been dismissed from his job.
- In other words, M Ossian Bonnet, who is sixty years old, has a governess of about the same age as him, and the Ministry of War, which has the shyness and modesty of a young girl, could not any longer endure this scandal.
- As for the 'Siècle', it wrote gravely that M Ossian Bonnet is the victim of an infamous plot hatched by the Jesuits.
- Anyway, it seems that the version of 'Temps' is the only true one, with this corrective which is very important: M Ossian Bonnet has never put his interests above those of his housekeeper.
- Against the Minister and the Director of the School rose 'en masse' the colleagues of M Bonnet and his fellow members from the Faculty of Science.
- In 1883 Bonnet succeeded Liouville as a member of the Bureau des Longitudes.
- Bonnet did important work on differential geometry in addition to Joseph Serret, Jean Frenet, Joseph Bertrand and Victor Puiseux who all worked in France on this topic.
- Bonnet made major contributions introducing the notion of geodesic curvature.
- Independently of Ferdinand Minding, Bonnet showed the invariance of the geodesic curvature under bending.
- Bonnet also published on cartography, algebra, rational mechanics and mathematical physics.

Born 22 December 1819, Montpellier, France. Died 22 June 1892, Paris, France.

View full biography at MacTutor

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive