19 May 2024

On Perfection (-1799)

"The mathematician is perfect only in so far as he is a perfect man, in so far as he senses in himself the beauty of truth; only then will his work be thorough, transparent, prudent, pure, clear, graceful, indeed elegant." (Plato, "Republic", cca. 375 BC)

"If in a discussion of many matters […] we are not able to give perfectly exact and self-consistent accounts, do not be surprised: rather we would be content if we provide accounts that are second to none in probability." (Plato, "Timaeus", cca. 360 BC)

"But Nature flies from the infinite, for the infinite is unending or imperfect, and Nature ever seeks an end." (Aristotle, "Generation of Animals", cca 4th century BC)

"[…] he who wishes to attain to human perfection, must therefore first study Logic, next the various branches of Mathematics in their proper order, then Physics, and lastly Metaphysics." (Moses Maimonides, "The Guide for the Perplexed", 1190)

"Sound is generated by motion, since it belongs to the class of successive things. For this reason, while it exists when it is made, it no longer exists once it has been made. […] All music, especially mensurable music, is founded in perfection, combining in itself number and sound." (Jean de Muris,"Ars novae musicae", 1319)

"Nature is not at variance with art nor art with nature, they both being the servants of his providence: art is the perfection of nature." (Sir Thomas Browne," Religio Medici", 1643)

"And thus many are ignorant of mathematical truths, not out of any imperfection of their faculties, or uncertainty in the things themselves, but for want of application in acquiring, examining, and by due ways comparing those ideas." (John Locke, "An Essay Concerning Human Understanding", 1689)

"There is nothing in Nature that does more show the piercing Force of Human Understanding, the sublimity of its Speculations and deep researchers, than true Astronomy. It raises our Minds above our Senses, and even in contradiction to them, shows us the true System of the World: the faculty of Reason by which we have made these great discoveries in the Heavens must needs be derived from Heaven, since no Earthly Principle can attain so great a Perfection." (John Keill, "An Introduction to the True Astronomy", 1721)

"For since the fabric of the universe is most perfect and the work of a most wise Creator, nothing at all takes place in the universe in which some rule of maximum or minimum does not appear." (Leonhard Euler, "De Curvis Elasticis", 1744)

"[...] one day the precision of the data might be brought to such perfection that the mathematician in his study would be able to calculate any phenomenon of chemical combination in the same way…as he calculates the movement of the heavenly bodies." (Antoine-Laurent Lavoisier, "Memories de l’Académie Royale des Sciences", 1782 [Published 1785])

"As long as algebra and geometry proceeded along separate paths, their advance was slow and their applications limited. But when these sciences joined company, they drew from each other fresh vitality and thenceforward marched on at a rapid pace toward perfection." (Joseph-Louis de Lagrange, "Leçons Élémentaires de Mathématiques", 1795)

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