René Descartes is a French philosopher, scientist, and mathematician, considered as the “Father of Modern Philosophy.”^{1} He was awarded the title in recognition of his enormous contributions to math and philosophy, as well as his status as a pioneer of the rationalist school of thought. Rene Descrates was the first to emphasize Skepticism as a crucial component of the scientific method. He is, therefore, regarded by many as one of the greatest philosophers in history. ^{1,2,3}

Descartes lived in an era before the Age of Enlightenment, which flourished in Europe during the late 17th and early 18th centuries and was characterized by revolutionary ideas in politics, personal freedom, and religion. Descartes’ legacy would be his influence on those who contributed to the scientific, political, and social revolutions that characterized this age of reason, despite the fact that he was not a direct participant.^{4}

He is also known as the “father of analytical geometry” because of his outstanding contributions in the field of geometry.^{5} Descartes’ seminal work on geometry, “*La Géométrie*,” was published in 1637. His most significant contribution was bridging the gap between algebra and geometry. He is, therefore, widely regarded as the pioneering mathematician who established modern geometry as the basis for the creation of analysis and calculus.^{3,5}

The Cartesian coordinate system, the cornerstone of analytical geometry, was created by him. It also offers geometric explanations for various other areas of mathematics, including group theory, multivariate calculus, differential geometry, complex analysis, and linear algebra.^{ }^{6,7}

He developed analytical geometry, a significant conceptual advancement that connected the previously distinct sciences of algebra and geometry. Descartes demonstrated that he could solve geometric puzzles that were previously intractable by transforming them into easier algebraic puzzles. He used the letters *x* and *y *to denote the horizontal and vertical directions, respectively. Since analytic geometry serves as the basis for the majority of contemporary branches of geometry, it finds extensive application in the fields of engineering, physics, rocketry, space science, aviation, and spaceflight. Therefore, this concept is essential to modern math and other disciplines. ^{5 6,7}

Descartes also created a method known as the “rule of signs” for counting a polynomial’s positive or negative real roots. In addition to rediscovering the amiable pair and Thabit ibn Qurra’s general formula for agreeable numbers, he popularized the superscript notation for displaying powers or exponents.^{ }^{6,7}

Cartesian coordinate system, Analytic geometry, Cartesian product, Defect, Fibred category, Descartes’ rule of signs, Descartes’ theorem, Pullback Theorem, and Cartesian Coordinate System are just a few of his many contributions to math. He also wrote articles on physiology, cosmology, coordinate geometry, optics, and philosophy.^{8}

He also had a significant role in the advancement of contemporary physics, a position that, until recently, was typically underappreciated and understudied.^{,9} Most significantly, he developed the first uniquely contemporary formulation of natural laws and a motion conservation concept. This was like a precursor to the law of conservation of mechanical momentum. He also made significant contributions to optics and the study of light reflection and refraction with his work “*Dioptrique*.”^{3} He discovered the Snell-Descartes law of refraction, also known as the law of refraction. He used it to demonstrate that a rainbow’s angular radius is 42 degrees. One of his many contributions that deserves special mention is the most well-known planetary motion theory of the late 17th century.^{5,9}

The modern study of the mind was given structure in the 17th century by René Descartes. In his day, Descartes was regarded as one of the greatest mathematicians, the creator of a new, all-encompassing theory of nature, and the proponent of a novel philosophy. His natural philosophy was increasingly recognized and discussed in the years after his passing. Aspects of his research, particularly his theories on physiology, as well as his quest to study the knower to determine the likelihood and breadth of human knowledge, were still relevant in the 18th century.^{2,3}

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**References:**

*Descartes, Rene | Internet Encyclopedia of Philosophy*. (n.d.). Retrieved December 21, 2022, from https://iep.utm.edu/rene-descartes/*Rene Descartes | Biography, Ideas, Philosophy, ‘I Think, Therefore I Am,’ & Facts | Britannica*. (n.d.). Retrieved December 21, 2022, from https://www.britannica.com/biography/Rene-Descartes*René Descartes (1596 – 1650) – Biography – MacTutor History of Mathematics*. (n.d.). Retrieved December 21, 2022, from https://mathshistory.st-andrews.ac.uk/Biographies/Descartes/*René Descartes – World History Encyclopedia*. (n.d.). Retrieved December 21, 2022, from https://www.worldhistory.org/Rene_Descartes/*René Descartes | Famous Mathematicians*. (n.d.). Retrieved December 21, 2022, from https://famous-mathematicians.com/rene-descartes/*René Descartes – Biography, Facts and Pictures*. (n.d.). Retrieved December 21, 2022, from https://www.famousscientists.org/rene-Descartes/*Rene Descartes and His Contribution to Mathematics – ValiantCEO*. (n.d.). Retrieved December 21, 2022, from https://valiantceo.com/rene-descartes-and-his-contribution-to-mathematics/*Contribution Of Rene Descartes To Mathematics Philosophy Essay*. (n.d.). Retrieved December 21, 2022, from https://www.ukessays.com/essays/philosophy/contribution-of-rene-descartes-to-mathematics-philosophy-essay.php*Rene Descartes*. (2022). The Story of Mathematics – A History of Mathematical Thought from Ancient Times to the Modern Day. Retrieved on December 22, 2022 from https://www.storyofmathematics.com/17th_descartes.html/