René Descartes (IPA: [r?ne.dek??t], March 31, 1596 – February 11, 1650), 
also known as Cartesius, worked as a philosopher and mathematician. 
While most notable for his groundbreaking work in philosophy, he has 
achieved wide fame as the inventor of the Cartesian coordinate 
system, which influenced the development of modern calculus.

Descartes, sometimes called the founder of modern philosophy and the 
Father of Modern Mathematics, ranks as one of the most important and 
influential thinkers in modern western history. He inspired both his 
contemporaries and later generations of philosophers, leading them 
to form what we know today as continental rationalism, a philosophical 
position in 17th and 18th century Europe.

Descartes' life

Descartes (1596-1650) was born in La Haye, Indre-et-Loire, France. At the 
age of eight he entered the Jesuit College Royal Henry-Le-Grand at La 
Flèche. After graduation he studied at the University of Poitiers, 
graduating with a Baccalauréat and Licence in law in 1616.

Descartes never practiced law however, and in 1618 he entered the service 
of Prince Maurice of Nassau, leader of the United Provinces of the 
Netherlands, with the intention of following a military career. Here he 
met Isaac Beeckman, and composed a short treatise on music entitled 
Compendium Musicae. In 1619, he travelled in Germany, and on November 
10 had a vision of a new mathematical and scientific system. In 1622 
he returned to France, and during the next few years spent time in Paris 
and other parts of Europe. Descartes was present at the siege of La 
Rochelle by Cardinal Richelieu in 1627.

In 1628 he composed Rules for the Direction of the Mind, and left for 
Holland, where he lived until 1649, changing his address frequently. In 
1629 he began work on The World. In 1633, Galileo was condemned and 
Descartes abandoned plans to publish The World. In 1635, Descartes' 
daughter Francine was born. She was baptized on August 7, 1635 and 
died in 1640. Descartes published Discourse on Method, with Optics, 
Meteorology and Geometry in 1637. In 1641, Meditations on First 
Philosophy was published, with the first six sets of Objections and 
Replies. In 1642 the second edition of Meditations was published with 
all seven sets of Objections and Replies, followed by Letter to Dinet. 
In 1643, Cartesian philosophy was condemned at the University of 
Utrecht, and Descartes began his long correspondence with Princess 
Elizabeth of Bohemia. Descartes published Principles of Philosophy 
and visited France in 1644. In 1647 he was awarded a pension by the 
King of France, published Comments on a Certain Broadsheet and began 
work on The Description of the Human Body. He interviewed Frans 
Burman at Egmond-Binnen in 1648, resulting in Conversation with Burman. 
In 1649 he went to Sweden on invitation of Queen Christina, and his 
Passions of the Soul, which he dedicated to Princess Elizabeth, were 
published.

René Descartes died of pneumonia on February 11, 1650 in Stockholm, 
Sweden, where he had been invited as a teacher for Queen Christina of 
Sweden. Accustomed to working in bed till noon, he may have suffered 
a detrimental effect on his health due to Christina's demands for early 
morning study. As a Catholic in a Protestant nation, he was interred in 
a graveyard mainly used for unbaptized infants, in Adolf Fredrikskyrkan 
in Stockholm. Later his remains were taken to France from Sweden and 
buried in the Church of St. Genevieve-du-Mont in Paris. A memorial 
erected in the 18th century remains in the Swedish church.

During the French Revolution, his remains were disinterred for 
burial in the Panthéon, among the great French thinkers. The village 
in the Loire Valley where he was born was renamed La Haye - Descartes.

In 1667, after his death, the Roman Catholic Church placed his works 
on the Index of Prohibited Books.

Significance

Often regarded as the first "modern" thinker for providing a 
philosophical framework for the natural sciences as these began to 
develop, Descartes in his Meditations on First Philosophy attempts 
to arrive at a fundamental set of principles that one can know as 
true without any doubt. To achieve this, he employs a method called 
Methodological Skepticism: he doubts any idea that can be doubted.

He gives the example of dreaming: in a dream, one's senses perceive 
things that seem real, but do not actually exist. Thus one cannot 
rely on the data of the senses as necessarily true. Or, perhaps an 
"evil genius" exists: a supremely powerful and cunning being who 
sets out to try to deceive Descartes from knowing the true nature 
of reality. Given these possibilities, what can one know for certain?

Initially, Descartes arrives at only a single principle: if I am 
being deceived, then surely "I" must exist. Most famously, this is 
known as cogito ergo sum, ("I think, therefore I am"). (These words 
do not appear in the Meditations, although he had written them in 
his earlier work Discourse on Method).

Therefore, Descartes concludes that he can be certain that he exists. 
But in what form? You perceive your body through the use of the 
senses; however, these have previously proved unreliable. So 
Descartes concludes that at this point, he can only say that he is 
a thinking thing. Thinking is his essence as it is the only thing 
about him that cannot be doubted.

To further demonstrate the limitations of the senses, Descartes 
proceeds with what is known as the Wax Argument. He considers a 
piece of wax: his senses inform him that it has certain 
characteristics, such as shape, texture, size, color, smell, and so 
forth. However, when he brings the wax towards a flame, these 
characteristics change completely. However, it seems that it is still 
the same thing: it is still a piece of wax, even though the data of 
the senses inform him that all of its characteristics are different. 
Therefore, in order to properly grasp the nature of the wax, he cannot 
use the senses: he must use his mind. Descartes concludes:

"Thus what I thought I had seen with my eyes, I actually grasped solely 
with the faculty of judgment, which is in my mind."

In this manner Descartes proceeds to construct a system of knowledge, 
discarding perception as unreliable and instead admitting only 
deduction as a method. Halfway through the Meditations he also 
claims to prove the existence of a benevolent God, who, being 
benevolent, has provided him with a working mind and sensory system, 
and who cannot desire to deceive him, and thus, finally, he 
establishes the possibility of acquiring knowledge about the world 
based on deduction and perception.

Mathematicians consider Descartes of the utmost importance for his 
discovery of analytic geometry. Up to Descartes's times, geometry, 
dealing with lines and shapes, and algebra, dealing with numbers, 
appeared as completely different subsets of mathematics. Descartes 
showed how to translate many problems in geometry into problems in 
algebra, by using a coordinate system to describe the problem.

Descartes's theory provided the basis for the calculus of Newton 
and Leibniz, and thus for much of modern mathematics. This appears 
even more astounding when one keeps in mind that the work was just 
meant as an example to his Discours de la méthode pour bien conduire 
sa raison, et chercher la verité dans les sciences (Discourse on 
the Method to Rightly Conduct the Reason and Search for the Truth 
in Sciences, known better under the shortened title Discours de 
la méthode).