"Modesty was not a condition from which Descartes suffered."
René Descartes was a French philosopher, scientist, logician, and mathematician, widely considered a seminal figure in the emergence of modern philosophy and science during the Renaissance era. Mathematics was paramount to his method of inquiry, and he connected the previously separate fields of geometry and algebra into analytic geometry.
"Doubt is the origin of wisdom and Latin: Dubium sapientiae initium. This has been attributed to Descartes, including here previously, but no original attribution has been found. Descartes Meditationes de prima philosophia has been cited as the source of Dubium sapientiae initium, but this quote is not found in this work."
"[E]arly analytic geometers—Descartes in particular—did not accept that geometry could be based on numbers or algebra. Perhaps the first to take the idea of arithmetizing geometry seriously was Wallis..."
"An optimist may see a light where there is none, but why must the pessimist always run to blow it out?"
"He has given us only some beautiful beginnings, without getting to the bottom of things. ...he is still far from the true analysis and the general art of discovery. For I am convinced that his mechanics is full of errors, that his physics goes too fast, that his geometry is too narrow, and that his metaphysics is all these things."
"Functions are the bread and butter of modern scientists, statisticians, and economists. Once many repeated... experiments and observations produce the same functional interrelationships, those may acquire the... status of laws of nature—mathematical descriptions... Descartes ideas... opened the door for a systematic mathematization of everything—the very essence of the notion that God is a mathematician. ...[B]y establishing the equivalence of two perspectives of mathematics (algebraic and geometric) previously considered disjoint, Descartes expanded the horizons of mathematics and paved the way to the modern era of analysis, which allows [us] to comfortably cross from one mathematical discipline to another."
"René Descartes played his part in the world as a man in a mask. The phrase is his own. It implied no conscious duplicity but a certain apartness rendering him incapable of taking his share unreservedly in the game of life. His attitude was that of an unimpassioned spectator. He looked on and learned while others struggled for the stakes. A born recluse, he remained solitary even in the throng of social intercourse. ...The transport felt by Bacon at the glorious vision of a future in which the harvest he had sown would be reaped was not shared by Descartes. He indeed held himself to be the sower and the reaper in one. Calmly, and with settled conviction, he claimed to have virtually expounded all the phenomena of nature. He had crossed the frontier of the new world of knowledge; those who desired to follow him needed only to purge their eyes with the euphrasy of methodic doubt in order to obtain those crystal-clear intuitions from which, by sure reasoning, universal science could be deduced. ...He was a mathematician of first rate originality and power. ...Unfortunately, however, he was misled by false analogies of thought; he sought to universalise what was by its nature special and restricted; and thus pursued the flitting vision of a deceptive unity in knowledge. As the upshot, he gave to his philosophy a pseudo-mathematical character, and sacrificed the solid achievement of much by aiming at the illusory certainty of everything."