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Cartan, Elie - A remarkable class of analytic and geometric transformations



Type of Spiritual Experience


Élie Joseph Cartan (9 April 1869 – 6 May 1951) was an influential French mathematician who did fundamental work in the theory of Lie groups and their geometric applications. He also made significant contributions to mathematical physics, differential geometry, and group theory.

Élie Cartan was born in the village of Dolomieu, Isère, the son of a blacksmith. He attended the École Normale Supérieure in Paris in 1888 and obtaining his doctorate in 1894. He subsequently held lecturing positions in Montpellier and Lyon, becoming a professor in Nancy in 1903. He took a lecturing position at the Sorbonne in Paris in 1909, becoming professor there in 1912 until his retirement in 1940. He died in Paris after a long illness.

By his own rather understated account (found in his Notice sur les travaux scientifiques'), the main theme of Cartan's works (numbering 186 and published throughout the period 1893–1947) was the theory of Lie groups.

A description of the experience

An Essay on the Psychology of Invention in the Mathematical Field – Jacques Hadamard

In 1913, Elie Cartan, one of the first among French mathematicians, thought of a remarkable class of analytic and geometric transformations in relation to the theory of groups.  No reason was seen, at that time, for special consideration of those transformations except just their aesthetic character.

Then some fifteen years later, experiments revealed to physicists some extraordinary phenomena concerning electrons, which they could only understand by the help of Cartan’s ideas of 1913.

The source of the experience

Scientist other

Concepts, symbols and science items


Science Items

Activities and commonsteps