Abstract
In 1637, Descartes revolutionized geometry : by associating three coordinates with each point in space, he laid the foundations for algebraic geometry. This geometry is known as " commutative " : the product of two quantities does not depend on the order of the terms, and A x B = B x A. This is a fundamental property on which the entire mathematical edifice depends. But at the beginning of the 20th century, the discovery of the quantum world turned everything on its head. The geometrical space of states of a microscopic system - an atom, for example - is enriched by new properties, which are no longer commutative. All mathematical tools must therefore be adapted. This new geometry, known as non-commutative , has become essential to physics research, and has been developed by Alain Connes.
