Short answers, pulled from the story.
René Descartes was a French philosopher, scientist, logician, and mathematician who lived from 1596 to 1650. He is called the father of modern philosophy because his methodic doubt shifted the debate from "what is true" to "of what can I be certain," raising human reason to the guarantor of truth. He is also credited as the father of analytic geometry.
"Cogito, ergo sum" means "I think, therefore I am," originally written in French as "Je pense, donc je suis." Descartes reasoned that if he doubted, something must be doing the doubting, so the very act of doubting proved his existence. It appears in his Discourse on the Method as his first indubitable principle.
Cartesian dualism is Descartes's doctrine that the universe contains two radically different substances: the mind or soul, defined as thinking, and the body, defined as unthinking matter. He held that the two are really distinct because each can exist apart from the other, yet are closely joined, so that a person feels pain rather than perceiving bodily damage purely by intellect. He singled out the pineal gland as the connector between soul and body.
Descartes developed analytic geometry together with Pierre de Fermat, using algebra to describe geometry, and the Cartesian coordinate system is named after him. Both men drew on the Greek mathematicians Pappus of Alexandria and Apollonius of Perga and on the symbolic algebra of François Viète. Their key step was using coordinates to study the relationship between geometry and algebra. Descartes also introduced using x, y, and z for unknowns and superscripts for exponents.
René Descartes died of pneumonia on the 11th of February 1650 in Stockholm, at the house of Pierre Chanut. He had moved to Sweden to tutor Queen Christina, who scheduled lessons three times weekly at 5 a.m. in her cold, draughty castle. He contracted pneumonia on the 1st of February 1650.
Descartes was first buried in a Stockholm churchyard where mainly orphans were interred, then his remains were taken to France in 1666 and buried in Saint-Étienne-du-Mont. He was reburied in 1819 in the Abbey of Saint-Germain-des-Prés, missing a finger and the skull. The skull held in the Musée de l'Homme in Paris may be a forgery, while one fragment of the original reached the University of Lund in 1691.