René Descartes was born in France in the year 1596. Like many great Renaissance thinkers of his time, Descartes was interested in many things, notably mathematics, science, and philosophy. He liked to lay in bed until late in the morning, and it was during these times that he did his most productive work. As a child, school had made Descartes understand how little he knew; the only subject which was satisfactory, in his eyes, was mathematics. Only mathematics, Descartes felt, is certain, so 'all must be based on mathematics'. This idea became the foundation for his way of thinking, and was to form the basis for all his works. After finishing university, Descartes travelled for years, eventually settling down in Holland, where he began work on a major treatise on physics. This work was near completion when news that Galileo was condemned to house arrest reached him. (Galileo's revolutionary ideas had angered those in authority). Descartes, perhaps wisely, decided not to risk publication, and moved on to other studies, particularly mathematics. One of his most well-known contributions to the field of mathematics was his work in analytical geometry. He was able to use algebra to prove ideas that before his time had only been demonstrated with diagrams and explanation. In particular, he used analytic geometry to describe the shapes of various polynomial functions, and the solutions to polynomial equations of degree higher than two. He also showed that the points in which two curves intersect can be determined by finding the roots common to their two equations. These are topics which are studied in high school mathematics courses today. Descartes was able to work with algebra in geometric figures because of his 'discovery' that position could be plotted on a coordinate grid made from two perpendicularly intersecting number lines, where any point could be located using a unique ordered pair (x , y). This grid is named in his honour. It is said (probably with no more truth than the story about Newton discovering the laws of gravity by watching an apple fall) that Descartes invented the coordinate grid while watching a fly crawl around on the ceiling tiles above his head, while he lay in bed. Junior High math students can try a quiz that practices plotting points on such a grid. Descartes invented the system of using the first letters of the alphabet to represent known quantities, and the last letters to represent unknowns. For example, in the quadratic equation ax2 + bx + c = 0, the letters a, b, and c represent known values (coefficients), while x represents the unknown solution to the equation. He also introduced the method for writing powers that we are familiar with. As an example, if you want to write 4 x 4 x 4, you can use 43. Descartes also investigated Euler's relation   v + f - e = 2,   the equation that describes how the number of verticies, faces, and edges of a convex polyhedron are related. In the example at the left, the prism has 8 faces, 12 verticies, and 18 edges. The rule states that, just as for this figure where 8 + 12 - 18 = 2, the three values must always equal 2, for any convex polyhedron. In the area of science, Descartes did work in optics, astronomy and meteorology, but his work here was flawed, and nowhere near as impressive as his results in mathematics and philosophy. His most famous philosophical work dealt with the concept of 'existence'. In his investigation of reality, Descartes decided his first step would be to discover some fact that was indisputable. He realized that there was one thing he never doubted -- that he existed. "I think," he wrote, "therefore I am." (in Latin: cogito, ergo sum). It didn't matter to Descartes whether this thinking was part of a dream or a hallucination, or even if he was crazy. The fact that thought was going on proved that he existed, because there had to be a thinker. Having established that he existed, Descartes advanced his arguments for the existence of God. The first of these was that he had the idea of a Perfect Being in his imperfect mind. But he reasoned that an imperfect mind couldn't come up with the idea of a Perfect Being, so there must actually be a Perfect Being (God) who gave him the idea! The second argument was this: If God is perfect -- as we imagine Him to be -- then He must exist, because if he didn't exist, He wouldn't be perfect. (If this argument strikes you as a bit strange, you are not alone. Most philosophers regard it as more of a play on words than as a philosophical proof.) From his conclusion that a perfect God exists, Descartes argued that God would not deceive his created beings, so the things we experience around us must also be real. While other philosophers had argued that God exists by saying the universe must have a creator, Descartes took the argument the other way. The world must exist, he argued, because God exists. Descartes believed that all material bodies, including the human body, are machines that operate by mechanical principles. In his physiological studies, he dissected animal bodies to show how their parts move. He argued that, because animals have no souls, they do not think or feel; thus vivisection, which Descartes pioneered, is permissible. In 1649 Queen Christina of Sweden persuaded Descartes to go to Stockholm. However, the Queen, being interested in mathematics, wanted to draw tangents at 5 a.m., and Descartes broke the habit of his lifetime of getting up at 11 o'clock. After only a few months in the cold northern climate, walking to the palace for 5 o'clock every morning, he died of pneumonia. Resources