Lo siguiente lo encontré en Wikipedia, lo pongo en inglés porque me pareció más completa la información que la versión en español.
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Mathematical legacy
One of Descartes' most enduring legacies was his development of Cartesian or analytic geometry, which uses algebra to describe geometry. He "invented the convention of representing unknowns in equations by x, y, and z, and knowns by a, b, and c". He also "pioneered the standard notation" that uses superscripts to show the powers or exponents; for example, the 4 used in x4 to indicate squaring of squaring. He was first to assign a fundamental place for algebra in our system of knowledge, and believed that algebra was a method to automate or mechanize reasoning, particularly about abstract, unknown quantities. European mathematicians had previously viewed geometry as a more fundamental form of mathematics, serving as the foundation of algebra. Algebraic rules were given geometric proofs by mathematicians such as Pacioli, Cardan, Tartaglia and Ferrari. Equations of degree higher than the third were regarded as unreal, because a three dimensional form, such as a cube, occupied the largest dimension of reality. Descartes professed that the abstract quantity a2 could represent length as well as an area. This was in opposition to the teachings of mathematicians, such as Vieta, who argued that it could represent only area. Although Descartes did not pursue the subject, he preceded Leibniz in envisioning a more general science of algebra or "universal mathematics," as a precursor to symbolic logic, that could encompass logical principles and methods symbolically, and mechanize general reasoning.
Descartes' work provided the basis for the calculus developed by Newton and Leibniz, who applied infinitesimal calculus to the tangent line problem, thus permitting the evolution of that branch of modern mathematics. His rule of signs is also a commonly used method to determine the number of positive and negative roots of a polynomial.
Descartes discovered an early form of the law of conservation of mechanical momentum (a measure of the motion of an object), and envisioned it as pertaining to motion in a straight line, as opposed to perfect circular motion, as Galileo had envisioned it. He outlined his views on the universe in his Principles of Philosophy.
Descartes also made contributions to the field of optics. He showed by using geometric construction and the law of refraction (also known as Descartes's law or more commonly Snell's law, who discovered it 16 years earlier) that the angular radius of a rainbow is 42 degrees (i.e., the angle subtended at the eye by the edge of the rainbow and the ray passing from the sun through the rainbow's centre is 42°). He also independently discovered the law of reflection, and his essay on optics was the first published mention of this law.
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Esta es una de las bases de cómo veo el comportamiento de los supuestos y percepciones humanas.
Ya verán más adelante a qué me refiero...
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