This section is all about the history of math-famous people, events, ideas, concepts, and other stuff. Right now there is only one report (although it is rather lengthily), but many more are to follow. This section will be frequently updated with new sections, so keep looking back. Anyway, the first report is about the life and deeds of René Descartes. So here it is:

Introduction

René Descartes was a French philosopher, scientist and mathematician. He was born in La Haye, Tourane which was a former province of France, in 1596. His father, Joachim Descartes was the son of a minor nobleman. Descartes' mother died when he was only one year old.

When Descartes was eight he went to the Jesuit school of La Flèche, where he was taught mathematics and Scholastic philosophy, plus all the usual studies. After completing his studies at La Flèche, René studied law at the University of Poitiers, though he never got to practice it. In 1618 Descartes entered the service of Prince Maurice of Nassau, leader of the United Provinces of the Netherlands, with the intention of following a military career. Though Descartes served in other armies after this, his attention had already been attracted to the philosophical and mathematical problems to which he would devote the remainder of his life.

Mathematics

René Descartes made many notable contributions to mathematics. In 1618 Descartes journeyed to Holland, where he met Isaac Beeckman, a thirty year-old student of medicine who was astounded at the range of Descartes' scientific curiosity. Over the next few weeks Descartes showed Beeckman how to apply algebra and mathematics to many problems. He showed him how mathematics could be applied to a more precise spacing and tuning of lute stings, proposed algebraic formula to determine the raise in water level when a heavy object was placed in water, drew a geometric graph that showed how to predict the accelerating speed of a pencil falling in a vacuum at any time during a two hour period, and showed how a spinning top stays upright and how this could be used to help man become airborne. Beeckman's journal showed us that by the end of 1618, Descartes was already applying algebraic equations to solve geometric problems, and that it was then, not later as many sources say, that he invented analytical geometry.

One day during the winter while he was in the army, Descartes decided to escape the cold by shutting himself up in a stove. While there he had dreams with flashing lights and thunder, in which it seems some spirit was revealing to him a new philosophy. This was the way that a geometric proposition can be transferred into algebraic terms, using a vertical axis, a and a horizontal axis, b. Any position to the left or right of the vertical axis can be shown as some function on a and b. This let the geometric equations be manipulated in new ways that were impossible using a mass of geometric tangents. Five days before his twenty-third birthday Descartes wrote a letter to Beeckman in which he told him that there was no problem in geometry that cannot be expressed using axes, lines and curves.

Before Descartes all of the sciences and mathematical fields had been thought of as separate entities. He had seen that if math was a "science of discontinuous quantities", and geometry was a "science of continuous quantities" the barriers that had been perceived to separate them collapse, creating analytical geometry. Descartes also realized that arithmetic and algebra were not just sciences of numbers, but sciences of propositions, which justified the use of irrational numbers and opened up vast new mathematical possibilities. After this Descartes universalized this principle in the first of his "Rules for Guidance of the Mind" : "For inasmuch as all the sciences are naught but human wisdom, which remains one and the same, however different the thoughts to which it is applied, and which is no more changed by these objects and the light of the sun by the variety of things it illuminates... one must therefore convince himself that all the sciences are linked together and that it is easier to learn them all as one than to isolate them from each other." In this statement Descartes said that math and all of the sciences were interrelated and are easier to treat as a whole than break apart and learn individual little pieces. Descartes reinforced the commonness of all the sciences in his fourth rule, in which he stated that mathematics can be applied to all measurable things : "Without its mattering that this measure be sought for in numbers, figures, stars, sounds or any other object, and thus one observes that there must be some general science explaining everything that one can look for regarding order and measurement without application to a particular matter, and that this science is called universal mathematics." The universal mathematics that Descartes described has since been applied to optics, astronomy, meteorology, acoustics, chemistry, architecture, physics, engineering, accounting, and warfare, all of which Descartes foresaw, plus electronics, cybernetics, microbiology, genetics, economics, and even politics, which he didn't.

Descartes made other lesser known contributions to mathematics. He was the first to use the first letters of the alphabet to represent known quantities, and the last letters to represent unknown ones. He also invented the method of using exponents, such as x2 to represent the powers of a number. Descartes also formulated a rule known as Descartes' rule of signs, for finding the positive and negative roots of an algebraic equation.

Philosophy

In Descartes Discourses on Method, he said that he would reject everything that is held to be true, all doctrines and previous ideas, and doubt everything. Since he doubted everything Descartes could not proceed until he had one fact that is universally held to be true. This fact was his proof of his own existence- in French, "Je pense, donc, je suis," or in Latin, "Cogito, ergo sum," in English, "I think, therefore, I am." Descartes then judged the truthfulness of other ideas in proportion to this fact. His new method - novum organum, was to analyze the parts of complex ideas and show them as simple, clear ideas. By building on small parts, Descartes could show a complex argument or idea.

Science

Though Descartes was primarily a philosopher and mathematician, he devoted the end of his life to solving various physical problems using his philosophies. In his study of optics he discovered the fundamental law of reflection- that the angle of incidence equals the angle of reflection. Descartes dissected various animal heads to see in what form imagination and memory exists. He studied reflexes and explained by what mechanism the eye blinks when a blow is approaching. Descartes developed a theory of human emotions: the external cause of the emotion sets off a response and generates a corresponding emotion at the same time (eg. we see a dangerous animal approaching, which sets off an automatic response, such as flight, and causes the corresponding emotion: fear). Descartes' studies led him to believe that the entire universe, except for God and the rational mind, operated on mechanical principles.

Conclusion

René Descartes was a revolutionary mathematician and philosopher who merged all of the ancient Greek sciences into one, making a universal mathematics that has and will be applied to many situations. This use of thoughts from other sciences enabled others to expand by leaps and bounds. Descartes proved his own existence in the phrase, "I think, therefore, I am," and then using this absolute truth Descartes developed a way to prove other statements using the truth values of their components. So in many ways, Descartes helped bring human thought to the point it is today.

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