# Rene Descartes: Contributions & Achievements

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• 0:05 Renaissance Man
• 0:20 Mathematical Achievements
• 2:10 Philosophical Achievements
• 3:06 Cogito, Ergo Sum
• 4:32 Lesson Summary
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Lesson Transcript
Instructor: Mark Koscinski

Mark has a doctorate from Drew University and teaches accounting classes. He is a writer, editor and has experience in public and private accounting.

In this lesson, you will learn about Rene Descartes, a mathematical and philosophical genius. You will also learn about the most famous phrase in the history of philosophy.

## Renaissance Man

Rene Descartes made significant contributions in the fields of mathematics, philosophy, and optics in the 17th century. Descartes was a polymath or a Renaissance Man, meaning he was brilliant in every field.

## Mathematical Achievements

Descartes made many lasting contributions in the field of mathematics. His most significant achievement was the use of algebraic formulas to describe geometric figures, which formed a branch of mathematics known as analytical geometry. Every high school student becomes familiar with Descartes' work as it was the foundation of the Cartesian coordinate system. The system relies on the use of an x-, y- and z-axes to graphically portray a 3-dimensional shape such as a cube, resulting from an algebraic formula.

High school algebra students should also recognize some of Descartes' other achievements, such as standardized algebraic notation. For instance, it is very common to notate unknowns or variables in an equation with the letters x, y, and z. Constants in the equation are commonly represented with the letters a, b, and c. Therefore, in the equation F(x, y, z) = 2x + 3y + 4z, the value of F(x, y, z) is determined by three variables and three constants.

The unknowns in the equation are x, y, and z. A more general way of formulating the equation using letter for constants would be:

F(x, y, z) = ax + by + cz

In this version of the equation, the numbers are replaced by the constants a, b, and c. Descartes used this notation and we have used it ever since. He was also responsible for developing standard notation for exponents. For example, any number (x) raised to its third power (that is x times x times x) is notated as x^3. Descartes' work had profound influence on Isaac Newton, who later helped to discover calculus.

## Philosophical Achievements

Descartes is also regarded as the father of modern Western Philosophy. He adopted a radical skepticism, rejecting facts until he could be certain the facts were true. The Scholastic philosophers of the Middle Ages made little distinction between theology and philosophy. But Descartes identified philosophy with the natural sciences, a sharp break from his predecessors. He set the stage for the future development of philosophy outside of the constraints of theology.

In his book Rules for the Direction of the Mind written in 1629 but published posthumously in 1701, Descartes wrote his three rules for thinking:

1. The validity of all true judgments depends on reason alone.
2. Knowledge should be proven by the same rigor required in mathematics and geometry.
3. The mind should not be bound by tradition or authority, only by what can be observed and deduced by reason.

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