Tuesday, March 31, 2009

March 31: René Descartes

René Descartes
March 31, 1596 – February 11, 1650

René Descartes was a French philosopher, mathematician, scientist, and writer who spent most of his adult life in the Dutch Republic. He has been dubbed the "Father of Modern Philosophy," and much of subsequent Western philosophy is a response to his writings, which continue to be studied closely to this day. In particular, his Meditations on First Philosophy continues to be a standard text at most university philosophy departments. Descartes' influence in mathematics is also apparent, the Cartesian coordinate system allowing geometric shapes to be expressed in algebraic equations being named for him. He is accredited as the father of analytical geometry. Descartes was also one of the key figures in the Scientific Revolution.

Descartes was a major figure in 17th century continental rationalism, later advocated by Hobbes, Baruch Spinoza and Gottfried Leibniz, and opposed by the empiricist school of thought consisting of Locke, Berkeley, and Hume. Leibniz, Spinoza and Descartes were all well versed in mathematics as well as philosophy, and Descartes and Leibniz contributed greatly to science as well. As the inventor of the Cartesian coordinate system, Descartes founded analytic geometry, the bridge between algebra and geometry, crucial to the discovery of calculus and analysis. His most famous statement is: Cogito ergo sum (I think, therefore I am).

Descartes' theory provided the basis for the calculus of Newton and Leibniz, by applying infinitesimal calculus to the tangent line problem, thus permitting the evolution of that branch of modern mathematics. This appears even more astounding considering that the work was just intended 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, better known under the shortened title Discourse on Method).

Descartes' rule of signs is also a commonly used method to determine the number of positive and negative zeros of a polynomial.

Descartes created analytic geometry, and discovered an early form of the law of conservation of momentum (the term momentum refers to the momentum of a force). He outlined his views on the universe in his Principles of Philosophy.

Descartes also made contributions to the field of optics. He showed by using geometric construction and the law of refraction (also known as Descartes' law) that the angular radius of a rainbow is 42 degrees (i.e. the angle subtended at the eye by the edge of the rainbow and the ray passing from the sun through the rainbow's centre is 42°). He also independently discovered the law of reflection, and his essay on optics was the first published mention of this law.

One of Descartes most enduring legacies was his development of Cartesian geometry which uses algebra to describe geometry. He also invented the notation which uses superscripts to show the powers or exponents, for example the 2 used in x^2 to indicate squaring.

1 comment:

  1. Wow! I didn't know he came up with so much of modern mathematics. Fascinating stuff!