René Descartes René Descartes was an influential 15 th century French philosopher, mathematician, and scientist. He is most famously remembered today for his assertion I think, therefore I am. His work in philosophy set the stage for an understanding of epistemology known as Cartesianism. His work in mathematics is directly responsible for the field of analytic geometry and indirectly responsible for the invention of calculus. In addition to his incredible scientific insight, Descartes was a humble man and had many friends. He valued travel and was worldlier than most famous mathematicians. Descartes was born in La Haye en Touraine (an area that would later be renamed after him) in 1596. Descartes mother, Jeanne, and his would-be sibling died during childbirth when René was only one year old. His father, Joachim, was a councilor in the Parliament of Brittany in Rennes. Descartes was brought up not by his father, but by his maternal grandmother. At the age of 10 he was sent to a Jesuit college where he was trained for a career in military engineering. Descartes was said to be a sickly child, and it was here he convinced his teachers that he needed to sleep in until 11 in the morning (a habit he would hold for the rest of his life). At 18 He moved on to Poitiers, where he earned his law degree. It s thought that Descartes earned this degree to appease his father, as it was expected that he too would join Parliament. He was conflicted about this arrangement and ultimately came to the decision to pursue his passions. He writes about this time in Discourse: I entirely abandoned the study of letters, resolving to seek no knowledge other than that which could be found in myself or else in the great book of the world. I spent the rest of my
youth travelling, visiting courts and armies, mixing with people of diverse temperaments and ranks, gathering various experiences, testing myself in the situations which fortune offered me, and at all times reflecting on whatever came my way so as to derive some profit from it. Two years later he travelled to the city of Breda in the Netherlands where he was taught mathematics and military architecture from the physicist Isaac Beeckman. It s during this period in 1618 that he writes his first work Compendium of Music, though it would not be published until 1650. Descartes spent the next 9 years of his life travelling across Europe. During his time in Bohemia he invents analytic geometry and his universal method of deductive reasoning (which he would later formalize in Discourse on the Method). In 1622 he moves to Paris where he spends his time gambling, fencing, going to the theatre, and socializing. It s in Paris that he becomes friends with the poets Jean Loius Guez de Balzac, and Theophile de Viau, the mathematician Claude Mydorge, and Father Marin Mersenne. Mersenne had many friends in the intellectual world and helped Descartes garner a reputation before he even published any of his work. Descartes was notorious for hiding from his friends in order to think or do work. In 1628 Descartes fled to the Netherlands where, by his own account, he would be free from religious persecution for his ideas, from the distractions of Paris, and from his friends. He took this freedom and solitude as an opportunity to think. He lived in 18 different places across the Netherlands for the next 16 years. In 1635 Descartes illegitimate daughter Francine was born to a woman named Helena Jans. Unfortunately, Francine died to scarlet fever at the age of five. This undoubtedly caused Descartes a great deal of pain, and was perhaps the saddest
chapter of his life. It was throughout his time in the Netherlands that he published all his greatest works: Discourse on the Method, The World, Meditations, Principles of Philosophy, and Passions of the Soul. Between 1644 and 1648 he returned to France numerous times to oversee some translations of his work and meet with friends and colleagues. In 1648 a friend of Descartes procured for him an invitation from Queen Christina of Sweden (one of the most powerful monarchs in Europe at the time). René was invited to join her court and tutor her in mathematics and philosophy. He reluctantly accepted the offer in 1649 and moved to Sweden where he would serve the 22 year-old-queen. Despite her knowledge of his lifelong sleeping habits, she routinely forced him to awake at five in the morning to give her philosophy lessons. In the winter of 1650, Descartes contracted pneumonia and died at the age of 53 due to the cold climate and cruel sleep schedule. Descartes massive influence on modern philosophy stems mostly from his Discourse on the Method. In it, Descartes attempts to address skepticism surrounding knowledge. Earlier philosophers had posed convincing arguments that nothing was truly knowable. He challenges himself and the reader to leverage their power of reason and doubt to find that which is truly knowable. He does this by presenting four precepts. First, doubt absolutely anything of which you cannot be absolutely certain. Second, divide each problem into as many parts as necessary. Third, solve the simplest problems first to work towards solving more complex ones. Fourth, thoroughly review everything to ensure there are no mistakes in the process. The first edict casts doubt on everything observed by the senses. The senses are wholly unreliable as they often deceive us (as in dreams or hallucinations or even illusions). Since they
cannot be trusted with absolute certainty, they are doubted absolutely. As a result, it seems that we can truly know nothing. Descartes proves that we can indeed still know things despite this dilemma. Cogito ergo sum. I think, therefore I am. Descartes points out that in order to cast doubt in the first place, something (that is, our self) must exist to cast that doubt. We can be assured of our own existence simply by our own ability to question it. This small intuition can seem inconsequential at first, but it demonstrates a new approach to knowledge that still resonates with philosophers today. Descartes then provides an argument for the existence of God: The idea of a perfect God is as vivid and clear as other truths such as reason, doubt, numbers and geometric shapes. It is more perfect to exist than to not exist. Because God is perfect, he must exist. Since God exists and is perfect, he is not a deceiver, and the power of reason which he granted us can be trusted. Critics of this argument have pointed out that Descartes uses reason to reach the conclusion that God exists and reason can be trusted. This potential logical mistake has been dubbed the Cartesian Circle as a result. Although Descartes is best known for his contributions to philosophy, his contributions to mathematics are severely understated. In The Geometry, an appendix to his Discourse, he introduces possibly his most important contribution to mathematics: that geometry and
algebra were inextricably linked. Algebra could be used to solve geometric problems quickly and elegantly. This discovery, analytic geometry, led to the Cartesian coordinate system that is a vital tool in modern mathematics. Another important discovery that Descartes unveils is his method for finding normals (and tangents, equivalently) for algebraic curves based on the concept of double intersection. It leverages the fact that the radius of a circle is normal to the circle itself. First, find a circle that intersects the curve only once. This can be done by setting the discriminant to zero to force a single root. Once you have the radius of this circle at the point of intersection, you have the slope of the normal line and equivalently the tangent line. This method is thought to have been influential to Newton s invention of calculus. There are a handful of other important concepts outlined in The Geometry. His convention of using x, y, and z to represent unknown quantities and a, b, and c for constants has become the norm. He pioneered the modern notation for exponents. He even included a rudimentary attempt at the theory of invariants. His technique of determining the upper bound of positive or negative roots of a polynomial (known today as Descartes rule of signs) is still taught in schools. These contributions only scratch the surface of Descartes contributions. His mathematics revolutionized the way we think about geometry and algebra, and served as possibly Newton s greatest influence. His philosophy on existence (both his own and God s) still serve as important guidelines in the field of epistemology, and he often regarded as the father
of modern philosophy. For a man who described his mind as average, he certainly accomplished a lot in his short life.
Works Cited Burman, R. (2010). Descartes: An Introduction. Naxos AudioBooks. Katz, V. (2008). A History of Mathematics. Pearson. Watson, Richard A. René Descartes. Encyclopædia Britannica, Encyclopædia Britannica, inc., 27 Jan. 2017, www.britannica.com/biography/rene-descartes. Accessed 15 Sept. 2017. The Geometry of Rene Descartes. The Geometry of Rene Descartes Mathematical Association of America, www.maa.org/publications/periodicals/convergence/the-geometry-ofrene-descartes. Accessed 15 Sept. 2017.