On November 10, 1619, a frail 23-year-old French mercenary shut himself in a heated stove room in Bavaria and had three vivid dreams, along with a phantom explosion now linked to exploding head syndrome. He emerged convinced he had found a unified mathematical method for understanding nature. This episode follows Rene Descartes from a sickly childhood and a law degree to his study of military engineering in the Dutch army, his chance meeting with Isaac Beeckman over a Dutch math puzzle in Breda, and his nomadic years living off bond income across a dozen Dutch addresses.

We also meet the human being behind the icy-rationalist myth: his relationship with Helena Jans van der Strom, the death of their daughter Francine at five, and his open weeping and defense of the passions. From there we unpack the method of doubt, the evil demon, the cogito, mind-body dualism and the pineal gland, his hydraulic account of reflexes, why splitting reality in two served as a shield for science after Galileo’s condemnation, and the Cartesian coordinate system that unified algebra and geometry. We end with his fatal 5 a.m. tutoring sessions for Queen Christina and the strange afterlife of his skull and finger.

• Why a 17th-century army camp was the best physics laboratory on Earth
• Replacing Aristotle’s purposeful matter with the cannonball view of mechanical physics
• I think, therefore I am: the one truth that survives the evil demon
• Animal spirits, hollow nerves, and the pineal gland as the mind’s joystick
• How the x and y axes and the letters x, y, z became the language of modern math