# Mathematician:René Descartes

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## Contents

## Mathematician

French mathematician and philosopher who is supposed to have invented the Cartesian coordinate system, and thence the field of analytic geometry.

In fact it has been suggested that he actually did nothing of the kind, but in fact built much of his own philosophical approach on the thinking of others.

Well-known for spending the morning lying in bed meditating.

A member of the informal Académie Parisienne.

## Nationality

French

## History

- Born: 31 March 1596, La Haye (now Descartes), Touraine, France.
- 1607: Attended Collège La Flèche, a school for young gentlemen established in 1604 by Henry IV (now Prytanée National Militaire)
- 1614: Graduated
- 1615-16: Studied at the University of Poitiers
- 1616: Moved to Paris, lived as a dandy
- 1618: Joined the Dutch States Army in Breda. Studied military engineering, as had been established by Simon Stevin
- 1619: Enrolled in the army of the Duke of Bavaria
- 10th November 1619: Made the decision to study mathematics, as a result of a personal epiphany in which the elements of analytic geometry coalesced
- November 1620: Visited Tycho Brahe in Prague and Johannes Kepler in Regensburg
- 1620: Left the army.
- 1625: Returned to Paris, renewed acquaintance with Marin Mersenne, an old school friend from Collège La Flèche
- 1628: Moved to Holland to live a solitary life
- 1649: Moved to Stockholm at the invitation of Queen Christina of Sweden.
- Died: 11 Feb 1650, Stockholm, Sweden

## Theorems and Definitions

- Cartesian coordinate system
- Cartesian Product
- Descartes's Rule of Signs
- Snell-Descartes Law (independently of Willebrord van Royen Snell)

Results named for **René Descartes** can be found here.

Definitions of concepts named for **René Descartes** can be found here.

## Publications

- 1618:
*Renati Descartes Musicae Compendium*(unpublished until after his death in 1650) - 1637:
*Discours de la méthode pour bien conduire sa raison et chercher la vérité dans les sciences*, including as appendices:*La Dioptrique*(on optics)*Les Météores*(on meteorology, one of the first attempts to put weather on a scientific basis)*La Géométrie*(his most important work, in which he is supposed to have joined algebra to geometry)

- 1641:
*Meditations on First Philosophy*

- 1644:
*Principia Philosophiae*, in four parts:*The Principles of Human Knowledge**The Principles of Material Things**Of the Visible World**The Earth*

- 1644:
*Meditations*

- 1701:
*Rules for the Direction of the Mind*(written around 1628)

*Le Monde, ou Traité de la Lumière*(completed 1633, published in part after his death -- it has survived only in fragments)

## Also known as

**Renatus Cartesius**

## Notable Quotes

*Cogito ergo sum*(I think therefore I am)

*Bene vixit qui bene latuit.*(He has lived well who has hidden well.)

*... as soon as my age permitted me to leave the control of my teachers, I completely gave up the study of letters. And resolving to seek no knowledge other than that which I could find in myself, or else in the great book of the world, I spent the rest of my youth in travel, visiting courts and armies, so as to mix with people of diverse temperaments and ranks, gathering various experiences, testing myself in the situations which fortune offered me, and above all, trying to learn from whatever came my way, so as to derive some profit from my experience.*- --
*Discours de la méthode pour bien conduire sa raison et chercher la vérité dans les sciences*: Part $\text I$

- --

*Those long chains of simple reasoning which geometers use to arrive at their most difficult conclusions made me believe that all things which are the objects of human knowledge are similarly interdependent; and that if we will only abstain from assuming something to be true which is not, and always follow the necessary order in deducing one thing from another, there is nothing so remote that we cannot reach it, nor so hidden that we cannot discover it.*- --
*Discours de la méthode pour bien conduire sa raison et chercher la vérité dans les sciences*: Part $\text {II}$

- --

*It is not possible that I could have in myself the idea of God, if God did not truly exist.*- --
*Meditations*

- --

*When writing about transcendental issues, be transcendentally clear.*

*I desire only tranquillity and repose.*- -- Quoted in 1937: Eric Temple Bell:
*Men of Mathematics*: Chapter $\text{III}$

- -- Quoted in 1937: Eric Temple Bell:

## Critical View

*To explain all nature is too difficult a task for any one man or even for any one age. 'Tis much better to do a little with certainty, and leave the rest for others that come after you, than to explain all things.*- -- Isaac Newton

*It is quite another thing to recognise [as in the use of co-ordinates] a general method and to follow to the end the idea which it represents. It is exactly this merit, whose importance every real mathematician knows, that was pre-eminently Descartes' in geometry; it was thus that he was led to what ... is his true discovery in the matter; namely, the application of the method of co-ordinates not only to translate into equations curves already defined geometrically, but, looking at the question from an exactly opposite point of view, to the*a priori*definition of more and more complicated curves and, hence more and more general ...**Directly, with Descartes himself, later, indirectly, in the return which the following century made in the opposite direction, it is the entire conception of the object of mathematical science that was revolutionised. Descartes indeed understood thoroughly the significance of what he had done, and he was right when he boasted that he had so far surpassed all geometry before him as Cicero's rhetoric surpasses the ABC.*- -- Jacques Salomon Hadamard
- -- Quoted in 1937: Eric Temple Bell:
*Men of Mathematics*: Chapter $\text{III}$

*Any qualified person who examines Descartes's treatise on geometry will soon convince himself that this work contains nothing about perpendicular axes, or the "Cartesian" coordinates of a point ... His*Geometry*was little read then and is less read now, and deservedly so, ... he wrote it more to boast than to explain, and somehow he managed to cow most of his contemporaries and successors into believing against the evidence that he had accomplished something worthwhile.*- -- 1992: George F. Simmons:
*Calculus Gems*

- -- 1992: George F. Simmons:

*How on earth did Descartes, who could not on*prima facie*evidence accept his own existence as real, believe that his thinking was? That was the beginning of the dark ages of European philosophy.*- -- Lin Yutang

## Sources

- 1937: Eric Temple Bell:
*Men of Mathematics*... (previous) ... (next): Chapter $\text{III}$: Gentleman, Soldier and Mathematician - 1958: P.J. Hilton:
*Differential Calculus*... (previous) ... (next): Chapter $1$: Introduction to Coordinate Geometry - 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): A List of Mathematicians in Chronological Sequence - 1989: Ephraim J. Borowski and Jonathan M. Borwein:
*Dictionary of Mathematics*... (previous) ... (next): Entry:**Descartes, René**(1596-1650) - 1991: David Wells:
*Curious and Interesting Geometry*... (previous) ... (next): A Chronological List Of Mathematicians - 1992: George F. Simmons:
*Calculus Gems*... (previous) ... (next): Chapter $\text {A}.11$: Descartes ($\text {1596}$ – $\text {1650}$) - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): A List of Mathematicians in Chronological Sequence - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next): Entry:**Descartes, René**(1596-1650) - 2008: David Joyner:
*Adventures in Group Theory*(2nd ed.) ... (previous) ... (next): Chapter $2$: 'And you do addition?': $\S 2.1$: Functions - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next): Entry:**Descartes, René**(1596-1650) - 2008: Ian Stewart:
*Taming the Infinite*... (previous) ... (next): Chapter $6$: Curves and Coordinates: Descartes - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next): Entry:**Descartes, René**(1596-1650)