On Proofs (1600 - 1800)

"It is very difficult to write mathematics books today. If one does not take pains with the fine points of theorems, explanations, proofs and corollaries, then it won’t be a mathematics book; but if one does these things, then the reading of it will be extremely boring." (Johannes Kepler)

"There have been only Mathematicians who were able to find some proofs, that is to say some sure and certain reasons." (René Descartes)

"The essential quality of a proof is to compel belief." (Pierre de Fermat)

“But the most powerful proof of the reality of phenomena (a proof which is, indeed, sufficient by itself) is success in predicting future phenomena from those which are past and present, whether the prediction be founded upon the success, so far, of a reason or hypothesis, or upon custom so far observed.” (Gottfried W Leibniz, "De Modo Distinguendi phenomena realia ab imaginariis" [“On the Method of Distinguishing Real from Imaginary Phenomena”], cca. 1684)

“Mathematics in gross, it is plain, are a grievance in natural philosophy, and with reason: for mathematical proofs, like diamonds, are hard as well as clear, and will be touched with nothing but strict reasoning. Mathematical proofs are out of the reach of topical arguments; and are not to be attacked by the equivocal use of words or declaration, that make so great a part of other discourses, - nay, even of controversies.” (John Locke, 1690)

"As arithmetic and algebra are sciences of great clearness, certainty, and extent, which are immediately conversant about signs, upon the skillful use whereof they entirely depend, so a little attention to them may possibly help us to judge of the progress of the mind in other sciences, which, though differing in nature, design, and object, may yet agree in the general methods of proof and inquiry." (George Berkeley, "Alciphron: or the Minute Philosopher", 1732)

"Some facts can be seen more clearly by example than by proof.” (Leonard Euler)