Jean-Gaston Darboux FAS MIF FRS

FRSE Fellowship of the Royal Society of Edinburgh (FRSE) is an award granted to individuals that the Royal Society of Edinburgh, Scotland's national academy of science and Literature, letters, judged to be "eminently distinguished in their subject". ...

(14 August 1842 – 23 February 1917) 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, mathematical structure, structure, space, Mathematica ...

Life

According to his birth certificate, he was born in

Nîmes Nîmes ( , ; ; Latin: ''Nemausus'') is the Prefectures in France, prefecture of the Gard Departments of France, department in the Occitania (administrative region), Occitanie Regions of France, region of Southern France. Located between the Med ...

France France, officially the French Republic, is a country located primarily in Western Europe. Overseas France, Its overseas regions and territories include French Guiana in South America, Saint Pierre and Miquelon in the Atlantic Ocean#North Atlan ...

on 14 August 1842, at 1 am. However, probably due to the midnight birth, Darboux himself usually reported his own birthday as 13 August, ''e.g.'' in his filled form for Légion d'Honneur. His parents were François Darboux, businessman of mercery, and Alix Gourdoux. The father died when Gaston was 7. His mother undertook the mercery business with great courage, and insisted that her children receive good education. Gaston had a younger brother, Louis, who taught mathematics at the Lycée Nîmes for almost his entire life. He studied at the Nîmes Lycée and the

Montpellier Montpellier (; ) 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 France, department of ...

Lycée before being accepted as the top qualifier at the

École normale supérieure École or Ecole may refer to: * an elementary school in the French educational stages normally followed by Secondary education in France, secondary education establishments (collège and lycée) * École (river), a tributary of the Seine flowing i ...

in 1861, and received his

PhD A Doctor of Philosophy (PhD, DPhil; or ) is a terminal degree that usually denotes the highest level of academic achievement in a given discipline and is awarded following a course of graduate study and original research. The name of the deg ...

there in 1866. His thesis, written under the direction of

Michel Chasles Michel Floréal Chasles (; 15 November 1793 – 18 December 1880) was a French mathematician. Biography 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 Coal ...

, was titled ''Sur les surfaces orthogonales''. During his studies at the ENS, he also took lectures in

Sorbonne University Sorbonne University () is a public research university located in Paris, France. The institution's legacy reaches back to the Middle Ages in 1257 when Sorbonne College was established by Robert de Sorbon as a constituent college of the Unive ...

and

Collège de France The (), formerly known as the or as the ''Collège impérial'' founded in 1530 by François I, is a higher education and research establishment () in France. It is located in Paris near La Sorbonne. The has been considered to be France's most ...

Darboux as a student of the Ecole Normale

In 1870, he co-founded the journal ''Bulletin des sciences mathématiques et astronomiques'', called "Darboux's Journal" by his contemporary mathematicians. The publishing house was the Henry Gauthier-Villars et Cie Éditeurs, located in Paris. In 1872, Darboux married the Beauvaisian milliner Amélie ''Célina'' Carbonnier (1848-1911), daughter of Charles Louis Carbonnier, tailor, and Marie Victorine Anastase Hènocq. He and Célina had two children, Jean-''Gaston'' (1870-1921), who was born at the time of the Siege of Paris and later became a marine zoologist at the Faculty of Science in Marseille, and Anaïs Berthe ''Lucie'' (1873-1970). He participated in the foundation of the École normale supérieure de jeunes filles in 1880, an institute that aimed at training female educators and ran parallel to the

on rue d'Ulm. Its first director was Julie Favre. In 1884, Darboux was elected to the

Académie des Sciences The French Academy of Sciences (, ) is a learned society, founded in 1666 by Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French Scientific method, scientific research. It was at the forefron ...

. Darboux made several important contributions to

geometry Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician w ...

and

mathematical analysis Analysis is the branch of mathematics dealing with continuous functions, limit (mathematics), limits, and related theories, such as Derivative, differentiation, Integral, integration, measure (mathematics), measure, infinite sequences, series ( ...

(see, for example, linear PDEs). He was a

biographer Biographers are authors who write an account of another person's life, while autobiographers are authors who write their own biography. Biographers Countries of working life: Ab=Arabia, AG=Ancient Greece, Al=Australia, Am=Armenian, AR=Ancient Rome ...

Henri Poincaré Jules Henri Poincaré (, ; ; 29 April 185417 July 1912) was a French mathematician, Theoretical physics, theoretical physicist, engineer, and philosophy of science, philosopher of science. He is often described as a polymath, and in mathemati ...

and he edited the Selected Works of

Joseph Fourier Jean-Baptiste Joseph Fourier (; ; 21 March 1768 – 16 May 1830) was a French mathematician and physicist born in Auxerre, Burgundy and best known for initiating the investigation of Fourier series, which eventually developed into Fourier analys ...

. Among his students were

Émile Borel Félix Édouard Justin Émile Borel (; 7 January 1871 – 3 February 1956) was a French people, French mathematician and politician. As a mathematician, he was known for his founding work in the areas of measure theory and probability. Biograp ...

Élie Cartan Élie Joseph Cartan (; 9 April 1869 – 6 May 1951) was an influential French mathematician who did fundamental work in the theory of Lie groups, differential systems (coordinate-free geometric formulation of PDEs), and differential geometry. He ...

Édouard Goursat Édouard Jean-Baptiste Goursat (21 May 1858 – 25 November 1936) was a French mathematician, now remembered principally as an expositor for his ''Cours d'analyse mathématique'', which appeared in the first decade of the twentieth century. It s ...

Émile Picard Charles Émile Picard (; 24 July 1856 – 11 December 1941) was a French mathematician. He was elected the fifteenth member to occupy seat 1 of the Académie française in 1924. Life He was born in Paris on 24 July 1856 and educated there at th ...

, Gheorghe Țițeica and Stanisław Zaremba. In 1900, he was appointed the Academy's permanent secretary of its Mathematics section. In 1902, he was elected to the

Royal Society The Royal Society, formally The Royal Society of London for Improving Natural Knowledge, is a learned society and the United Kingdom's national academy of sciences. The society fulfils a number of roles: promoting science and its benefits, re ...

and the

American Philosophical Society The American Philosophical Society (APS) is an American scholarly organization and learned society founded in 1743 in Philadelphia that promotes knowledge in the humanities and natural sciences through research, professional meetings, publicat ...

; in 1916, he received the

Sylvester Medal The Sylvester Medal is a bronze medal awarded by the Royal Society for the encouragement of mathematical research, and accompanied by a £1,000 prize. It was named in honour of James Joseph Sylvester, the Savilian chair of geometry, Savilian Prof ...

from the Society. In 1908, he was a plenary speaker at the

International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the IMU Abacus Medal (known before ...

Rome Rome (Italian language, Italian and , ) is the capital city and most populated (municipality) of Italy. It is also the administrative centre of the Lazio Regions of Italy, region and of the Metropolitan City of Rome. A special named with 2, ...

. He continued to contribute to the French ''Bulletin des sciences mathématiques'', even after 1916.

Named in his honour

There are many things named after him: * Darboux basis * Darboux chart * Darboux cyclide * Darboux cubic * Darboux derivative * Darboux equation *

Darboux frame In the differential geometry of surfaces, a Darboux frame is a natural moving frame constructed on a surface. It is the analog of the Frenet–Serret frame as applied to surface geometry. A Darboux frame exists at any non- umbilic point of a ...

Darboux integral In real analysis, the Darboux integral is constructed using Darboux sums and is one possible definition of the integral of a function. Darboux integrals are equivalent to Riemann integrals, meaning that a function is Darboux-integrable if and onl ...

* Darboux net invariants * Darboux or Goursat problem * Darboux transformation * Darboux vector * Darboux's problem * Darboux's theorem in

symplectic geometry Symplectic geometry is a branch of differential geometry and differential topology that studies symplectic manifolds; that is, differentiable manifolds equipped with a closed, nondegenerate 2-form. Symplectic geometry has its origins in the ...

* Darboux's theorem in

real analysis In mathematics, the branch of real analysis studies the behavior of real numbers, sequences and series of real numbers, and real functions. Some particular properties of real-valued sequences and functions that real analysis studies include co ...

, related to the

intermediate value theorem In mathematical analysis, the intermediate value theorem states that if f is a continuous function whose domain contains the interval , then it takes on any given value between f(a) and f(b) at some point within the interval. This has two imp ...

* Darboux's formula * Christoffel–Darboux identity * Christoffel–Darboux formula * Euler–Darboux equation * Darboux–Froda's theorem *

Euler–Poisson–Darboux equation In mathematics, the Euler–Poisson–Darboux(EPD) equation is the partial differential equation : u_+\frac=0. This equation is named for Siméon Poisson, Leonhard Euler, and Gaston Darboux. It plays an important role in solving the classical w ...

Euler-Poisson-Darboux Equation -- from Wolfram MathWorld
at mathworld.wolfram.com * Laplace–Darboux transformations

Notes

References

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External links

* * * {{DEFAULTSORT:Darboux, Gaston 1842 births 1917 deaths 19th-century French mathematicians 20th-century French mathematicians French geometers Differential geometers Members of the French Academy of Sciences Corresponding members of the Saint Petersburg Academy of Sciences Foreign members of the Royal Society Foreign associates of the National Academy of Sciences École Normale Supérieure alumni People from Nîmes Lycée Louis-le-Grand teachers Members of the Royal Society of Sciences in Uppsala International members of the American Philosophical Society

Life

Named in his honour

See also

Notes

References

External links