René Descartes was born on 31 March 1596 in La Haye en Touraine, France. His mother died shortly after his birth, and he was raised by his father, Joachim, a member of the Parlement of Rennes, along with his grandmother and great-uncle. Descartes attended the Jesuit Collège Royal Henry-Le-Grand in La Flèche, where he was introduced to mathematics and physics. He graduated in 1614 and studied law at the University of Poitiers, earning degrees in canon and civil law in 1616, as per his father's wishes.In 1618, Descartes joined the Protestant Dutch States Army as a mercenary, where he studied military engineering and mathematics. He met Isaac Beeckman, who influenced his mathematical pursuits. During his military service, he experienced a series of dreams that he interpreted as a divine revelation, leading him to develop his ideas on analytic geometry and the application of mathematics to philosophy. He left the army in 1620 and traveled through various countries before settling in France, where he began writing his first essay on method.Descartes returned to the Dutch Republic in 1628, where he continued his studies at the University of Franeker and Leiden University. He published his major works during this period, including the 'Discourse on the Method' in 1637, which outlined his philosophical approach and introduced the famous phrase 'Cogito, ergo sum' ('I think, therefore I am'). He also published 'La Géométrie,' which laid the groundwork for analytic geometry. His works gained attention, but he faced challenges, including the condemnation of Cartesian philosophy at the University of Utrecht in 1643.In 1649, Descartes accepted an invitation from Queen Christina of Sweden to tutor her and establish a scientific academy. He moved to Sweden in winter, where he faced harsh conditions. Descartes contracted pneumonia and died on 11 February 1650. His remains were initially buried in Stockholm but were later transferred to France in 1666. His philosophical and mathematical contributions, particularly in epistemology and the development of analytic geometry, have had a lasting impact on modern philosophy and science.Descartes's philosophical work emphasized the importance of doubt and reason as foundations for knowledge. He proposed a dualistic view of the mind and body, arguing that they are distinct substances that interact. His theories on emotions and the nature of the soul were articulated in 'The Passions of the Soul,' published in 1649. He also contributed to various fields, including physics, optics, and meteorology, proposing theories that challenged existing beliefs and laid the groundwork for future scientific inquiry.In mathematics, Descartes introduced the convention of using letters to represent unknowns and developed the Cartesian coordinate system, which revolutionized the relationship between algebra and geometry. His work influenced later mathematicians, including Isaac Newton, and provided a foundation for calculus. Descartes's mechanical philosophy sought to explain natural phenomena through mathematical principles, marking a significant shift in scientific thought.