**René Descartes** (1596-1650) is a French philosopher, physicist and mathematician, theorist of rationalism. Published in 1637, Son *Discourse on Method *is his most important work. In mathematics, he developed algebraic writing and founded analytical geometry. Descartes will influence opposing philosophical currents, such as Malebranche's mysticism or Diderot's rationalism.

## Short biography of René Descartes

Born in 1596, Descartes is originally from La Haye-en-Touraine (now renamed Descartes). Coming from the upper middle class, he is the son of an adviser to the Rennes parliament. Raised at the Jesuit college of La Flèche, he quickly distinguished himself for his taste for philosophy, mathematics and law. He obtained a law degree from the University of Poitiers but refused to pursue this path. He began a military career under the orders of the Dutch Maurice de Nassau then Maximilian of Bavaria and took part in the first campaigns of the Thirty Years' War.

From 1625 to 1628 he frequented the scientific and literary circles of Paris, but refused to settle there and returned to settle in the Netherlands, where he devoted himself to his work as a philosopher and scholar. there he successively published his discourse on method (1637), his Metaphysical Meditations (1641), his principles of philosophy (1644) and his treatise on the passions of the soul (1648). Invited by Queen Christine to the Swedish court in 1649, he died shortly after in Stockholm, leaving behind a rich and innovative work.

## Cartesian thinking

The thought of Descartes, known as "Cartesian", mixes science and philosophy. For him, all sciences are subordinate to a universal science: the mathesis universalis, universal science of order and measure. He published in 1637 the *Discourse on the method (Discourse on the method to conduct one's reason well and seek the truth in science)*, his most important work.

His approach stems from both metaphysical idealism and experimental materialism. This is how, in his famous Speech, he developed “methodical doubt”. “I think, therefore I am” constitutes the starting point of all reflection and affirms the power of logical reasoning; it allows man to know the laws of nature and to describe the functioning of the world and of the human body. Descartes wrote many philosophical works {Meditations; the Passions of the soul, ...) and treatises on mathematics and physics {Dioptics, Meteors, Geometry, the Treatise on the World, which, developing ideas close to those of Galileo, was not published because of his conviction in 1633).

Cartesian thought has exerted a great influence on modern philosophy. Diderot, Pascal, Leibniz, Mallebranche and Spinoza will draw largely on the work of Descartes to develop new issues and reflections.

## A method used in mathematics and geometry

The basis of the Cartesian method is strict obedience to the rule of evidence: "never receive anything as true that I obviously did not know it to be such". Any rational scientific process must begin with the simplest notions in order to arrive, by deductive means, at the most complex notions which depend on the first. Mathematics follows this method and therefore is the ideal model that should be applied to all sciences. Descartes requires the use of the last letters of the alphabet to denote unknown values (x, y, z) and of the first letters for known values (a, b, c). It also introduces superscript notation (x2) to express the power of a number.

In geometry, its contributions are fundamental. It was he who established that Euclidean geometry is based on an arithmetic structure, that of real numbers. At the same time and independently of Pierre de Fermat, Descartes contributes to the creation of analytical geometry (which allows equations to be associated with curves and geometric figures). It thus develops the Cartesian coordinates (abscissa and ordinate). In geometric optics, Descartes discovered the law of refraction of light. In mechanics, Descartes was the first to state the principle of inertia.

### For further

*- Discourse on method, by René Descartes. Pocket GF, 2016.*

*- Metaphysical Meditations, by René Descartes. pocket book, 1990.*

*- Descartes: Biography, by Geneviève Rodis-Lewis. Calmann-Lévy, 1995.*