On Simplicity IX

"By the word simplicity, is not always meant folly or ignorance; but often, pure and upright Nature, free from artifice, craft or deceitful ornament." (Benjamin Franklin,  Poor Richard's Almanack, 1733-1758)

"Simplicity and precision ought to be the characteristics of a scientific nomenclature: words should signify things, or the analogies of things, and not opinions." (Sir Humphry Davy, Elements of Chemical Philosophy", 1812)

"Discoveries are not generally made in the order of their scientific arrangement: their connexions and relations are made out gradually; and it is only when the fermentation of invention has subsided that the whole clears into simplicity and order. " (William Whewell, "An Elementary Treatise on Mechanics" Vol. I, 1819)

"Simplicity is naturally agreeable to a mind of limited powers, but to an infinite mind all things are simple." (William S Jevons, "The Principles of Science: A Treatise on Logic and Scientific Method", 1874)

"[…] it is an error to believe that rigor in the proof is the enemy of simplicity." (David Hilbert, [Paris International Congress] 1900)

"Besides it is an error to believe that rigour is the enemy of simplicity. On the contrary we find it confirmed by numerous examples that the rigorous method is at the same time the simpler and the more easily comprehended. The very effort for rigor forces us to find out simpler methods of proof." (David Hilbert, "Mathematical Problems", Bulletin of the American Mathematical Society Vol. 8, 1902)

"There is one, but only one branch which may claim certainty; in which experts have not seriously disagreed, - Mathematics. […] Mathematics possesses also the second desideratum, - Simplicity. It begins, as is well known, with few and uncomplicated definitions and postulates, and proceeds, step by step, to quite elaborate cases. […] Mathematics possesses also the third desideratum, - Applicability of the skill acquired." (Jacob W A Young, "The Teaching of Mathematics", 1907)

"A theory is the more impressive the greater the simplicity of its premises is, the more different kinds of things it relates, and the more extended its area of applicability." (Albert Einstein, "Autobiographical Notes", 1949)

"Whether mathematical simplicity is God’s affair or our, the fact remains that this feature more than any other remains the mainspring of progress in the physical sciences." (Paul C W Davies, "The Edge of Infinity", 1981)

"To criticize mathematics for its abstraction is to miss the point entirely. Abstraction is what makes mathematics work. If you concentrate too closely on too limited an application of a mathematical idea, you rob the mathematician of his most important tools: analogy, generality, and simplicity. Mathematics is the ultimate in technology transfer." (Ian Stewart, "Does God Play Dice: The New Mathematics of Chaos", 2002)