René Descartes

Born: 31 March 1596 in La Haye (now Descartes),Touraine, France

Died: 11 Feb 1650 in Stockholm, Sweden

René Descartes was a philosopher whose work, La géométrie, includes his application of algebra to geometry from which we now have Cartesian geometry.

Descartes was educated at the Jesuit college of La Flèche in Anjou. He entered the college at the age of eight years, just a few months after the opening of the college in January 1604. He studied there until 1612, studying classics, logic and traditional Aristotelian philosophy. He also learnt mathematics from the books of  Clavius. While in the school his health was poor and he was granted permission to remain in bed until 11 o'clock in the morning, a custom he maintained until the year of his death.

School had made Descartes understand how little he knew, the only subject which was satisfactory in his eyes was mathematics. This idea became the foundation for his way of thinking, and was to form the basis for all his works.

Descartes spent a while in Paris, apparently keeping very much to himself, then he studied at the University of Poitiers. He received a law degree from Poitiers in 1616 then enlisted in the military school at Breda. In 1618 he started studying mathematics and mechanics under the Dutch scientist Isaac Beeckman, and began to seek a unified science of nature. After two years in Holland he travelled through Europe. Then in 1619 he joined the Bavarian army.

From 1620 to 1628 Descartes travelled through Europe, spending time in Bohemia (1620), Hungary (1621), Germany, Holland and France (1622-23). He spent time in 1623 in Paris where he made contact with  Mersenne, an important contact which kept him in touch with the scientific world for many years. From Paris he travelled to Italy where he spent some time in Venice, then he returned to France again (1625).

By 1628 Descartes tired of the continual travelling and decided to settle down. He gave much thought to choosing a country suited to his nature and chose Holland. It was a good decision which he did not seem to regret over the next twenty years.

Soon after he settled in Holland Descartes began work on his first major treatise on physics, Le Monde, ou Traité de la Lumière. This work was near completion when news that  Galileo was condemned to house arrest reached him. He, perhaps wisely, decided not to risk publication and the work was published, only in part, after his death. He explained later his change of direction saying:-

... in order to express my judgement more freely, without being called upon to assent to, or to refute the opinions of the learned, I resolved to leave all this world to them and to speak solely of what would happen in a new world, if God were now to create ... and allow her to act in accordance with the laws He had established.

In Holland Descartes had a number of scientific friends as well as continued contact with  Mersenne. His friendship with Beeckman continued and he also had contact with  Mydorge, Hortensius,  Huygens and Frans van Schooten (the elder).

Descartes was pressed by his friends to publish his ideas and, although he was adamant in not publishing Le Monde, he wrote a treatise on science under the title Discours de la méthod pour bien conduire sa raison et chercher la vérité dans les sciences. Three appendices to this work were La Dioptrique, Les Météores, and La Géométrie. The treatise was published at Leiden in 1637 and Descartes wrote to  Mersenne saying:-

I have tried in my Dioptrique and my Météores to show that my Méthod is better than the vulgar, and in my Géométrie to have demonstrated it.

The work describes what Descartes considers is a more satisfactory means of acquiring knowledge than that presented by  Aristotle's logic. Only mathematics, Descartes feels, is certain, so all must be based on mathematics.

La Dioptrique is a work on optics and, although Descartes does not cite previous scientists for the ideas he puts forward, in fact there is little new. However his approach through experiment was an important contribution.

Les Météores is a work on meteorology and is important in being the first work which attempts to put the study of weather on a scientific basis. However many of Descartes' claims are not only wrong but could have easily been seen to be wrong if he had done some easy experiments. For example Roger  Bacon had demonstrated the error in the commonly held belief that water which has been boiled freezes more quickly. However Descartes claims:-

... and we see by experience that water which has been kept on a fire for some time freezes more quickly than otherwise, the reason being that those of its parts which can be most easily folded and bent are driven off during the heating, leaving only those which are rigid.

Despite its many faults, the subject of meteorology was set on course after publication of Les Météores particularly through the work of  Boyle,  Hooke and  Halley.

La Géométrie is by far the most important part of this work. In  Scott summarises the importance of this work in four points:-

He makes the first step towards a theory of invariants, which at later stages derelativises the system of reference and removes arbitrariness.

Algebra makes it possible to recognise the typical problems in geometry and to bring together problems which in geometrical dress would not appear to be related at all.

Algebra imports into geometry the most natural principles of division and the most natural hierarchy of method.

Not only can questions of solvability and geometrical possibility be decided elegantly, quickly and fully from the parallel algebra, without it they cannot be decided at all.

Some ideas in La Géométrie may have come from earlier work of  Oresme but in  Oresme's work there is no evidence of linking algebra and geometry.  Wallis in Algebra (1685) strongly argues the the ideas of La Géométrie were copied from  Harriot.  Wallis writes:-

... the Praxis was read by Descartes, and every line of Descartes' analysis bears token of the impression.

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