René Descartes revolutionized the pursuit of knowledge by applying the mathematical approach across various domains of inquiry. He pioneered analytic geometry and crafted a philosophical framework around mind-body dualism that remains influential. His work marked a decisive shift towards modernity in both science and philosophy.

Early Life

Born into an esteemed family among the French nobility in Touraine, René Descartes was destined for a life of intellectual inquiry. His father, Joachim, served as a counselor at the Parlement de Bordeaux. Tragically, Descartes lost his mother to tuberculosis shortly after his birth, resulting in a childhood marked by fragile health. This delicate condition persisted until he reached his twenties.

Despite these challenges, Joachim Descartes was committed to providing his son, whom he fondly called “his philosopher,” with an excellent education. At the age of ten, young René was enrolled at the Collège de La Flèche, a Jesuit institution founded under Henry IV's patronage.

At La Flèche, Descartes excelled in humanities and mathematics. At sixteen, his exploration of natural philosophy led him to a pivotal realization that would shape his future contributions; he noted that physics and metaphysics were riddled with uncertainty and inconsistent beliefs. In contrast, mathematics offered clarity and certainty, leading him to the conviction that its principles should be expanded to other areas of inquiry. This insight prompted him to reject the traditional educational systems in pursuit of more definitive knowledge.

Upon leaving college, Descartes moved to Paris at his father's behest. The city's social scene did not captivate him, and instead, he sought companionship among France’s most prominent intellectuals. At twenty-one, Descartes joined the military, though his engagement in active duty was minimal. His time was often spent writing about music and demonstrating his mathematical prowess by solving complex puzzles posed by his fellow soldiers.

In 1619, while stationed with a German regiment in Ulm, Descartes experienced a profound intellectual awakening in a series of dreams on November 10. He interpreted these dreams as a divine mandate to develop a unified science grounded in a novel approach to human reason, marking a turning point in his intellectual journey.

Life’s Work

Over the next decade, Descartes refined his method while traversing Europe, analyzing what he termed “the great book of the world.” He believed that systems of thought, particularly in science and philosophy, were better conceived by a single mind rather than through collective inputs. Seeking liberation from the biases acquired from previous scholars, Descartes aimed to lay his own groundwork for knowledge. This philosophy was first documented in his work, Rules for the Direction of the Mind, where he proposed a method of rational inquiry applicable to any pursuit of knowledge.

In 1633, Descartes completed The World, but upon learning of Galileo's condemnation for similar ideas, he chose to withhold its publication. The work mirrored Galileo's Copernican cosmology and the controversial notion that human understanding could rival divine knowledge. Later, Descartes published a series of treatises on mathematics and physical sciences, targeting educated but non-academic French readers. This collection included Discourse on Method, Geometry, Dioptric, and Meteors.

Discourse on Method succinctly outlined Descartes’s four-part method of doubt:

• Accept as true only what is irrefutably clear.
• Break down complex problems into manageable parts.
• Proceed from simple to complex knowledge systematically.
• Conduct comprehensive reviews to ensure nothing is overlooked.

This method, inspired by mathematics, was deductive and analytical, serving as a tool for innovation and discovery. Descartes’s work on geometry involved transforming curves into Cartesian coordinates, a breakthrough unattainable through traditional Euclidean methods.

Descartes’s innovative approach aligned with the intellectual shifts initiated by thinkers...