Anna Cartan
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Anna Cartan (15 May 1878 – 1923) 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 ...
, teacher and textbook author who was a student of Marie Curie and Jules Tannery.


Early years

Cartan was the youngest child born to Anne Florentine Cottaz (1841–1927) and Joseph Antoine Cartan (1837–1917), who was the village
blacksmith A blacksmith is a metalsmith who creates objects primarily from wrought iron or steel, but sometimes from #Other metals, other metals, by forging the metal, using tools to hammer, bend, and cut (cf. tinsmith). Blacksmiths produce objects such ...
. Anna had an elder sister Jeanne-Marie (1867–1931) who became a dressmaker, a brother Léon (1872–1956) who became a blacksmith working in his father's smithy, and a middle brother
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 ...
(1869–1951) who became an acclaimed mathematician and sire of a family of mathematicians, notably his first son,
Henri Cartan Henri Paul Cartan (; 8 July 1904 – 13 August 2008) was a French mathematician who made substantial contributions to algebraic topology. He was the son of the mathematician Élie Cartan, nephew of mathematician Anna Cartan, oldest brother of c ...
, who later became influential in the field. Anna's brother, Élie Cartan, later recalled that the family was very poor and his childhood had passed under "blows of the anvil, which started every morning from dawn," and that "his mother, during those rare minutes when she was free from taking care of the children and the house, was working with a spinning wheel."


Mathematics career

As the family was poor, it would have been very unusual for any of the children to attend college, but in 1901, partly under Élie's influence, Anna Cartan entered '' École normale supérieure de jeunes filles'' in
Sèvres Sèvres (, ) is a French Communes of France, commune in the southwestern suburbs of Paris. It is located from the Kilometre zero, centre of Paris, in the Hauts-de-Seine department of the Île-de-France region. The commune, which had a populatio ...
near
Paris Paris () is the Capital city, capital and List of communes in France with over 20,000 inhabitants, largest city of France. With an estimated population of 2,048,472 residents in January 2025 in an area of more than , Paris is the List of ci ...
, France. Anna chose to pursue mathematics to become a secondary school teacher. Among the courses she attended were those led by
Marie Curie Maria Salomea Skłodowska-Curie (; ; 7 November 1867 – 4 July 1934), known simply as Marie Curie ( ; ), was a Polish and naturalised-French physicist and chemist who conducted pioneering research on radioactivity. She was List of female ...
(who taught
physics Physics is the scientific study of matter, its Elementary particle, fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge whi ...
there from 1900 to 1906) and
Jules Tannery 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. H ...
. One of her friends was the
scientist A scientist is a person who Scientific method, researches to advance knowledge in an Branches of science, area of the natural sciences. In classical antiquity, there was no real ancient analog of a modern scientist. Instead, philosophers engag ...
and
women's rights Women's rights are the rights and Entitlement (fair division), entitlements claimed for women and girls worldwide. They formed the basis for the women's rights movement in the 19th century and the feminist movements during the 20th and 21st c ...
activist Eugénie (Feytis) Cotton who would become director of the school in 1936. Another friend was Marthe Baillaud, the niece of Jules Tannery. Anna completed her studies in mathematics in 1904 and taught the subject at the high school in
Poitiers Poitiers is a city on the river Clain in west-central France. It is a commune in France, commune, the capital of the Vienne (department), Vienne department and the historical center of Poitou, Poitou Province. In 2021, it had a population of 9 ...
, France from 1904 to 1906, and then she taught in
Dijon Dijon (, ; ; in Burgundian language (Oïl), Burgundian: ''Digion'') is a city in and the Prefectures in France, prefecture of the Côte-d'Or Departments of France, department and of the Bourgogne-Franche-Comté Regions of France, region in eas ...
from 1906 to 1908. In 1908, Cartan received a one-year scholarship established by a French philanthropist Albert Kahn to travel around the world to allow her to "enrich her skills and future education by direct knowledge of the world." Among the places she visited were the United States (New York, St. Louis, Chicago, Boston and Niagara Falls), Quebec, Mexico and Cuba. After the tour, she returned to Dijon and taught there until 1916. Then she taught at the Jules Ferry high school in Paris and, until 1920, at the Sèvres application school, annexed to the normal school. In 1912 and 1913, Cartan wrote two books on
arithmetic Arithmetic is an elementary branch of mathematics that deals with numerical operations like addition, subtraction, multiplication, and division. In a wider sense, it also includes exponentiation, extraction of roots, and taking logarithms. ...
and
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 ...
for girls, and later she co-authored with her brother Élie two more textbooks for both boys and girls. Cartan died of cancer in 1923.


Works

*''Arithmetic and geometry, first year, secondary education for young girls'', by Anna Cartan, 1912 and 1921. *''Arithmetic, secondary education for young girls, second year'', by Anna Cartan, 1913 and 1918. *''Arithmetic, secondary education, boys and girls, classes of 4th and 3rd'', by Anna Cartan and Élie Cartan, 1928 and 1931. *''Arithmetic, secondary education, boys and girls, grades 6 and 5'', by Anna Cartan and Élie Cartan, 1926.


References

{{DEFAULTSORT:Cartan, Anna 1878 births 1923 deaths French mathematicians French women mathematicians