Cartan was the youngest child born to Anne Florentine Cottaz (1841–1927) and Joseph Antoine Cartan (1837–1917), who was the village
blacksmith. 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 (1869–1951) who became an acclaimed mathematician and sire of a family of mathematicians, notably his first son,
Henri Cartan, 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 ==