Descartes - History of Math

Descartes, father of modern philosophy, one of the key figures in the scientific revolution of the 17th century and one of the first of the modern school of mathematics who laid many of the foundations for calculus and algebra. He was born on the 31st of March 1596 in a small French town. As a young man, he was a mercenary for many countries, both Protestant and Catholic alike, but after meeting with the Dutch scientist and philosopher Isaac Beekman, who gave him his interest in mathematics and new physics, he came to the decision that his real destiny in life was to pursue true wisdom and science. Back in France, the young Descartes soon realized that the key to philosophy, with all its vagueness, was to build the foundations on the unchangeable facts of math. To realize his heretical ideas furthermore, he moved from the highly conservative Catholic France to a more liberal society in the Netherlands, in which Descartes would spend the majority of his adult life and where he achieved the goals of merging geometry and algebra. In the year 1637, he published his mathematical and philosophical book called Discourse de la méthode or Discourse on Method. One part of the book in particular, La Geometrie, is today seen as a huge step forward in the history of math. Going after early movements, seeing to use symbols and expressions in mathematics, La Geometrie gave us what has become widely known as the standard for algebraic notation, which uses lowercase a, b, and c for known values and x, y, and z for unknown values. It was the first book that could resemble a modern algebra textbook, using symbols we know and love today. Cartesian coordinates. In La Geometrie, Descartes first claimed that every point in two dimensions can be interpreted by two numbers on a plane, with one value giving the points horizontal location and another value the vertical location. This has become known today as Cartesian coordinates, a huge staple in modern math. He used perpendicular lines or axes crossing at a point called the origin to measure the horizontal x and vertical y locations, both having positive and negative values, therefore dividing the plane into four quadrants. An equation can be visualized on the plane by plotting on it the solution set of the equation. For example, the simple equation y equals x yields a straight line connecting together the points 0, 0, 1, 1, 2, 2, etc. The equation y equals 2x gives us a line with steeper slope connecting points 0, 0, 1, 2, 2, 4, etc. More complex equations involving x, 2, x, 3, etc. plot many different types of curves on the plane. Descartes' earth-shattering work allowed for the conversion of geometry into algebra and vice versa. With it, a pair of equations can now be solved either geometrically or algebraically. This allowed for the development of Newton's and Leibniz's discoveries of calculus later on. It also gave us the possibility of working with geometries of higher dimensions, impossible to visualize physically, an idea which has become crucial to modern physics and technology, which changed mathematics forever. Descartes' rule of science. Analytic geometry is far from Descartes' most crucial addition to mathematics. He also created a rule of science method for finding the number of positive or negative real roots of a polynomial, popularized a superscript notation for showing powers or exponents, for example 24 showed 2 times 2 times 2 times 2, and reinvented Thabit Ibn Khoura's formula for amicable numbers. Despite all his influence in the creation of modern mathematics, Descartes is best known today as a philosopher who advocated dualism and rationalism. His philosophy was made up of a method of doubting everything then reforging knowledge from the ground up, and he's especially well known for the famous statement cogito ergo sum or I think therefore I am. Descartes also played a role in the advancement of modern physics, a role that's been generally underappreciated until very recently. He gave us the first modern system of laws of nature and the conservation principle of motion, made many advancements in optics in the study of refraction and reflection of light, and created the most popular theory of planetary motion of the late 1600s. His contributions to the scientific method was faced with heavy opposition by the catholic officials of the time. His game-changing ideas made him a very controversial figure and he died in Sweden in 1650 with many of his works being prohibited by the catholic church later on. It was only until relatively recently that his genius was truly known to the world. Without his contribution to mathematics, much of what we learn about algebra and geometry in Ms. Clyde's class would be wildly different and it wouldn't have as great of an understanding of such fascinating knowledge. We felt like diving into the history of math would give us a better understanding of how modern mathematics came to be and also give us some insight to just what precalc might look like next year. History felt like it would be a fun thing to explore and research and that it could be taught easily in a video. This project enhanced our understanding of how modern graphs, on which we base much of our learning in Ms. Clyde's, came to be and how they are and were used in the world. Descartes in particular had a huge influence on math, which is one of the reasons why we chose him.