"Reflexion is careful and laborious thought, and watchful attention directed to the agreeable effect of one's plan. Invention, on the other hand, is the solving of intricate problems and the discovery of new principles by means of brilliancy and versatility." (Marcus Vitruvius Pollio, "De architectura" ["On Architecture"], cca. 15 BC)
"Reasoning draws a conclusion and makes us grant the conclusion, but does not make the conclusion certain, nor does it remove doubt so that the mind may rest on the intuition of truth, unless the mind discovers it by the path of experience." (Roger Bacon, "Opus Major", 1267)
"In the discovery of hidden things and the investigation of hidden causes, stronger reasons are obtained from sure experiments and demonstrated arguments than from probable conjectures and the opinions of philosophical speculators of the common sort […]" (William Gilbert, "De Magnete", 1600)
"To invent is to discover that we know not, and not to recover or resummon that which we already know." (Francis Bacon, Advancement of Learning", 1605)
"It cannot be that axioms established by argumentation should avail for the discovery of new works, since the subtlety of nature is greater many times over than the subtlety of argument. But axioms duly and orderly formed from particulars easily discover the way to new particulars, and thus render sciences active." (Francis Bacon, "Novum Organum", 1620)
"The entire method consists in the order and arrangement of the things to which the mind's eye must turn so that we can discover some truth." (René Descartes, "Rules for the Direction of the Mind", 1628)
"We do not yet pretend to have discovered all things, or that what we have discovered can receive no addition; and therefore, pray let us agree, there are yet many things to be done in the ages to come." (Bernard Le Bovier de Fontenelle, "Conversations on the Plurality of Worlds", 1686)
"For the understanding, like the eye, judging of objects only by its own sight, cannot but be pleased with what it discovers, having less regret for what has escaped it, because it is unknown." (John Locke, "An Essay Concerning Human Understanding", 1689)
Quotes and Resources Related to Mathematics, (Mathematical) Sciences and Mathematicians
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