Quotable Mathematics

"While those whom devotion to abstract discussions has rendered unobservant of the facts are too ready to dogmatize on the basis of a f...

"Storytelling is the art of unfolding knowledge in a way that makes each piece contribute to a larger truth." (Philip Gerard, ...

"It is true that of far the greater part of things, we must content ourselves with such knowledge as description may exhibit, or analog...

"In every branch of knowledge the progress is proportional to the amount of facts on which to build, and therefore to the facility of o...

"The final truth about phenomena resides in the mathematical description of it; so long as there is no imperfection in this, our knowle...

"[…] it must be noticed that these diagrams do not naturally harmonize with the propositions of ordinary life or ordinary logic. […] Th...

"All knowledge that is not the real product of observation, or of consequences deduced from observation, is entirely groundless and ill...

"While the individual man is an insoluble puzzle, in the aggregate he becomes a mathematical certainty. You can, for example, never for...

"The realm of the particularity of each experienced item differs from the formal realm of concepts. [...] The power of paradigmatic tho...

"Any pattern of activity in a network, regarded as consistent by some observer, is a system, Certain groups of observers, who share a c...

"Self-organization can be defined as the spontaneous creation of a globally coherent pattern out of local interactions. Because of its ...

"Because the question for me was always whether that shape we see in our lives was there from the beginning or whether these random eve...

"Every generalisation is a hypothesis. Hypothesis therefore plays a necessary rôle, which no one has ever contested. Only, it should ...

"In order to supply the defects of experience, we will have recourse to the probable conjectures of analogy, conclusions which we will ...

"Isolated facts, those that can only be obtained by rough estimate and that require development, can only be presented in memoires; but...

"Facts are the mere dross of history. It is from the abstract truth which interpenetrates them, and lies latent among them, like gold i...

"The Laws of Nature are merely truths or generalized facts, in regard to matter, derived by induction from experience, observation, ari...

"Observation is so wide awake, and facts are being so rapidly added to the sum of human experience, that it appears as if the theorizer...

"As in the experimental sciences, truth cannot be distinguished from error as long as firm principles have not been established through...

"It is of the nature of true science to take nothing on trust or on authority. Every fact must be established by accurate observation, ...