Episode #9 of the course “Greatest Mathematicians”
“I think; therefore I am” is far from René Descartes only contribution to our world. The father of modern philosophy was also one of the greatest mathematicians of all time. The general term we apply to the collection of Descartes’ works is analytical geometry. This has provided centuries of mathematicians after him a way to visualize algebraic functions.
Born in France in 1596, Descartes spent most of his life in the Dutch Republic, now called the Netherlands or Holland. He was sickly for most of his life, but he still managed to study philosophy, law, mathematics, and physics. He traveled extensively and passed away in Stockholm, Sweden in 1650.
Descartes built on the foundation laid by Euclid, Apollonius, and Archimedes by connecting the analytical tools of algebra to geometric representation. He developed the Cartesian coordinates, the X, Y axis on a two-dimensional plane that is ingrained in textbooks today. Nearly 400 years later, this system is still at the core of geometry. He also pioneered standard notation, that is, using superscripts to show powers or exponents. Descartes also provided a precursor to German mathematician Wilhelm Leibniz’s work on symbolic logic. Descartes, and later Leibniz, thought that symbols and mathematics could encompass logical principles and methods better than standard speech, thereby providing greater reasoning and clarity in communication.
Descartes’ creation of the rectangular coordinates system—or Cartesian coordinate system—is the tool in which we can visualize algebraic functions. Dubbed as the father of analytical geometry, he provided the bridge between algebra and geometry, a crucial step to the discovery of infinitesimal calculus and analysis.
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