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Descartes's Meditations on First Philosophy (1641) continues to be a standard text at most university philosophy departments. Descartes's influence in mathematics is equally apparent, being the namesake of the Cartesian coordinate system. He is credited as the father of analytic geometry—used in the discovery of infinitesimal calculus and ...
In the Netherlands, where Descartes had lived for a long time, Cartesianism was a doctrine popular mainly among university professors and lecturers.In Germany the influence of this doctrine was not relevant and followers of Cartesianism in the German-speaking border regions between these countries (e.g., the iatromathematician Yvo Gaukes from East Frisia) frequently chose to publish their ...
Frontispiece of Operum Mathematicorum Pars Prima (1657) by John Wallis, the first volume of Opera Mathematica including a chapter entitled Mathesis Universalis.. Mathesis universalis (from Greek: μάθησις, mathesis "science or learning", and Latin: universalis "universal") is a hypothetical universal science modelled on mathematics envisaged by Descartes and Leibniz, among a number of ...
Descartes, René – Discours de la méthode, 1692 – BEIC 1273122. Although mathematical methods of investigation have been used to establish meaning and analyse the world since Pythagoras, it was Descartes who pioneered the subject as epistemology, setting out Rules for the Direction of the Mind. He proposed that method, rather than ...
Rules 13–24 deal with what Descartes terms "perfectly understood problems", or problems in which all of the conditions relevant to the solution of the problem are known, and which arise principally in arithmetic and geometry. Rules 25–36 deal with "imperfectly understood problems", or problems in which one or more conditions relevant to the ...
René Descartes is credited as the father of analytical geometry, the bridge between algebra and geometry, crucial to the discovery of infinitesimal calculus and analysis. In the 17th century, Descartes introduced Cartesian co-ordinates which allowed the development of analytic geometry, bring the notation of equations to geometry.
In mathematics, reductionism can be interpreted as the philosophy that all mathematics can (or ought to) be based on a common foundation, which for modern mathematics is usually axiomatic set theory. Ernst Zermelo was one of the major advocates of such an opinion; he also developed much of axiomatic set theory.
Descartes was a substance dualist, and argued that reality was composed of two radically different types of substance: extended matter, on the one hand, and immaterial mind, on the other. Descartes argued that one cannot explain the conscious mind in terms of the spatial dynamics of mechanistic bits of matter cannoning off each other.