Descartes' mathematical formulas are used frequently in geometry. His slope theory and other algebraic formulas related to the geometric plane are still the standard in mathematics and his ideas helped form the basis of modern calculus.
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It sounds like that Rene Descartes wanted to be a teacher and teach different types of subjects.
Rene Descartes valued rationality and human logic. Descartes is famous for his sentence, "I think, therefore I am." It was the mind that Descartes valued more than anything else.
Rene Descartes invented the Cartesian coordinate system and the idea of the x-y axis. He used the coordinate system to express equations and formulas visually through slopes and lines. He created a slope for the equation, rather than the equation for a slope.
Rene Descartes was a man (boy as young).
Rene Descartes discoveries helped benefit mankind in many ways. His influence in mathematics is still used today in engineering, science, and every day life. His 'Meditations on First Philosophy' is a standard text at most university philosophy departments today.