Quotable Mathematics

"A Markov process is a stochastic process in which present events depend on the past only through some finite number of generations. In...

"In the initial stages of research, mathematicians do not seem to function like theorem-proving machines. Instead, they use some sort o...

"For group theoretic reasons the most impressive paradoxical decompositions occur in dimension at least three, but there are also inter...

"The reason why new concepts in any branch of science are hard to grasp is always the same; contemporary scientists try to picture the ...

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

"The function of man’s highest faculty, his reason, consists precisely of the continuous limitation of infinity, the breaking up of inf...

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

"Nothing is accomplished all at once, and it is one of my great maxims, and one of the most completely verified, that Nature makes no l...

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

"It is no great wonder if in long process of time, while fortune takes her course hither and thither, numerous coincidences should spon...

"If we are not content with the dull accumulation of experimental facts, if we make any deductions or generalizations, if we seek for a...

"The steady progress of physics requires for its theoretical formulation a mathematics which get continually more advanced. […] it was ...

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