Quotable Mathematics

"Every quantity whose value depends on one or more other quantities is called a function of these latter, whether one knows or is i...

"It is sometimes possible to infer a great deal about a dynamical system simply by finding its equilibrium states and determining which...

"A function acts like a set of rules for turning some numbers into others, a machine with parts that we can manipulate to accomplish an...

"Mathematicians study their problems on account of their intrinsic interest, and develop their theories on account of their beauty....

"I see with much pleasure that you are working on a large work on the integral Calculus [...] The reconciliation of the methods which y...

"Thus, differential calculus has all the exactitude of other algebraic operations." (Pierre-Simon Laplace, "A Philosophical E...

"The body of mathematics to which the calculus gives rise embodies a certain swashbuckling style of thinking, at once bold and dramatic...

"An equilibrium is defined to be stable if all sufficiently small disturbances away from it damp out in time. Thus stable equilibria ar...

"Since [...] nature is a principle of motion and mutation [...] it is necessary that we should not be ignorant of what motion is [...] ...

"Ideas are substitutions which require a secondary process when what is symbolized by them is translated into the images and experience...

"The theory of which we have just given an overview may be considered from a point of view apt to set aside the obscure in what it pres...