19th-century French mathematicians

Jules Tannery (24 March 1848 – 11 December 1910) was a French mathematician, who notably studied under Charles Hermite and was the PhD advisor of Jacques Hadamard. Tannery's theorem on interchange of limits and series is named after him. He was a brother of the mathematician and historian of science Paul Tannery.
Under Hermite, he received a doctorate in 1874 for his thesis Propriétés des intégrales des équations différentielles linéaires à coefficients variables.
Tannery was an advocate for mathematics education, particular as a means to train children in logical consequence through synthetic geometry and mathematical proofs.Tannery discovered a surface of the fourth order of which all the geodesic lines are algebraic. He was not an inventor, however, but essentially a critic and methodologist. He once remarked, "Mathematicians are so used to their symbols and have so much fun playing with them, that it is sometimes necessary to take their toys away from them in order to oblige them to think."
He notably influenced Pierre Duhem, Paul Painlevé, Jules Drach, and Émile Borel to take up science.
His efforts were mainly directed to the study of the mathematical foundations and of the philosophical ideas implied in mathematical thinking.
Tannery was "an original thinker, a successful teacher, and a writer endowed with an unusually clear, brilliant and attractive style."

Louis Jean-Baptiste Alphonse Bachelier (French: [baʃəlje]; 11 March 1870 – 28 April 1946) was a French mathematician at the turn of the 20th century. He is credited with being the first person to model the stochastic process now called Brownian motion, as part of his doctoral thesis The Theory of Speculation (Théorie de la spéculation, defended in 1900).
Bachelier's doctoral thesis, which introduced the first mathematical model of Brownian motion and its use for valuing stock options, was the first paper to use advanced mathematics in the study of finance. His Bachelier model has been influential in the development of other widely used models, including the Black-Scholes model.
Bachelier is considered as the forefather of mathematical finance and a pioneer in the study of stochastic processes.

Charles Edmond Alfred Riquier (19 November 1853, Amiens – 17 January 1929, Caen) was a French mathematician.Riquier matriculated in 1873 at the École Normale Supérieure (ENS) where he received his agrégé in mathematics in 1876. He taught from 1876 to 1878 at the Lycée de Brest and then from 1878 to 1886 at the Lycée de Caen and from 1886 to 1924 at the Université de Caen, where he retired as a professor emeritus.
After a brief leave of absence from the Lycée de Caen, Riquier received his doctorate in mathematics in 1886 from ENS at Paris with dissertation Extension à l’hyperespace de la méthode de M. Carl Neumann pour la résolution de problèmes relatifs aux fonctions de variables réelles à laplacien nul. His thesis committee consisted of Hermite (as chair), Darboux, and Picard.In 1910 he was awarded the Poncelet Prize. In 1920 he was elected to the French Academy of Sciences as the successor to Hieronymus Zeuthen. (Eugène Fabry was elected Riquier's successor in 1931.)
Riquier, Maurice Janet, Joseph Miller Thomas, Joseph Fels Ritt, and Ellis Kolchin were among the greatest pioneers of differential algebra and symbolic computation for systems of partial differential equations.

Paul Matthieu Hermann Laurent (2 September 1841 in Luxembourg City – 19 February 1908 in Paris, France) was a French mathematician. Despite his large body of works, Laurent series expansions for complex functions were not named after him, but after Pierre Alphonse Laurent.

Maurice Lévy (February 28, 1838, in Ribeauvillé – September 30, 1910, in Paris) was a French engineer and member of the Institut de France.
Lévy was born in Ribeauvillé in Alsace. Educated at the École Polytechnique, where he was a student of Adhémar Jean Claude Barré de Saint-Venant, and the École des Ponts et Chaussées, he became an engineer in 1863. During the Franco-Prussian War (1870–1871), he was entrusted by the Government of National Defense with the control of part of the artillery. During the next decade he held several educational positions, becoming professor at the École Centrale in 1875, member of the commission of the geodetic survey of France in 1879, and professor at the Collège de France in 1885.

Ernest Jean Philippe Fauque de Jonquières (born Carpentras, France 3 July 1820; died Mousans-Sartoux, France 12 August 1901) was a French mathematician and naval officer who made several contributions in geometry.
Jonquières attended the naval school at Brest, and later joined the French Navy. in 1841 he became a lieutenant, and from 1849 to 1850 he served on the staff of the Admiral in Paris. During this time, Jonquières became a close associate of Michel Chasles, whose works he had studied. During his subsequent time at sea, he continued his mathematical studies, and won a part of the Grand Prix of the French Academy of Sciences in 1862.
In 1865, Jonquières became a captain and was sent to Saigon to organize a French agricultural and industrial exhibition. He played an important role in the development of current Vietnam as a French colony. Later, he was head of the local naval depot and its maps and plans. In 1874, Jonquières was made Vice-Admiral. He retired in 1885.

Marie Georges Humbert (7 January 1859 Paris, France – 22 January 1921 Paris, France) was a French mathematician who worked on Kummer surfaces and the Appell–Humbert theorem and introduced Humbert surfaces. His son was the mathematician Pierre Humbert. He won the Poncelet Prize of the Académie des Sciences in 1891.
He studied at the École Polytechnique. He was the brother-in-law of Charles Mangin.

Georges-Henri Halphen (French: [ʒɔʀʒ ɑ̃ʁi alfɛn]; 30 October 1844, Rouen – 23 May 1889, Versailles) was a French mathematician. He was known for his work in geometry, particularly in enumerative geometry and the singularity theory of algebraic curves, in algebraic geometry. He also worked on invariant theory and projective differential geometry.

Louis Marcel Brillouin (French pronunciation: [lwi maʁsɛl bʁijwɛ̃]; 19 December 1854 – 16 June 1948) was a French physicist and mathematician.
Born in Saint-Martin-lès-Melle, Deux-Sèvres, France, his father was a painter who moved to Paris when Marcel was a boy. There he attended the Lycée Condorcet. The Brillouin family returned to Saint-Martin-lès-Melle during the Franco-Prussian War of 1870 to escape the fighting. There he spent time teaching himself from his grandfather's philosophy books. After the war, he returned to Paris and entered the École Normale Supérieure in 1874 and graduated in 1878. He became a physics assistant to Éleuthère Mascart (his future father-in-law) at the Collège de France, while at the same time working for his doctorates in mathematics and physics, which he gained in 1880 and 1882, respectively. Brillouin then held successive posts as assistant professor of physics at universities in Nancy, Dijon and Toulouse before returning to the École Normale Supérieure in Paris in 1888. Later, he was Professor of Mathematical Physics at the Collège de France from 1900 to retirement in 1931.
In 1911 he was one of only six French physicists invited to the first Solvay Conference. He was awarded the Prix La Caze for 1912.
Brillouin was elected to the Académie des Sciences in 1921. He was an officer of the Legion of Honour.During his career he was the author of over 200 experimental and theoretic papers on a wide range of topics which include the kinetic theory of gases, viscosity, thermodynamics, electricity, and the physics of melting conditions. Most notably he:

built a new model of the Eötvös balance,
wrote on Helmholtz flow and the stability of aircraft,
worked on a theory of the tides.Brillouin died in Paris (16 June 1948). His son Léon Brillouin, also had a prominent career in physics.

Joseph Valentin Boussinesq (pronounced [ʒɔzɛf valɑ̃tɛ̃ businɛsk]; 13 March 1842 – 19 February 1929) was a French mathematician and physicist who made significant contributions to the theory of hydrodynamics, vibration, light, and heat.