Quotable Mathematics

"Mathematical induction […] is an entirely different procedure. Although it, too, leaps from the knowledge of particular cases to knowl...

"To say that observations of the past are certain, whereas predictions are merely probable, is not the ultimate answer to the question ...

"Whatever lies beyond the limits of experience, and claims another origin than that of induction and deduction from established data, i...

"Induction applied to the physical sciences is always uncertain, because it rests on the belief in a general order of the universe,...

"Mathematical induction […] is an entirely different procedure. Although it, too, leaps from the knowledge of particular cases to knowl...

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

"The only possible way to conceive universal is by induction, since we come to know abstractions by induction. But unless we have sense...

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

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

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

"Tectology, or the theory of structure in organisms, is the comprehensive science of individuality among living natural bodies, which u...

"Mathematics is a science of Observation, dealing with reals, precisely as all other sciences deal with reals. It would be easy to show...

"A line, as defined by geometers, is wholly unconceivable. We can reason about a line as if it had no breadth; because we have a power,...

"Analogies prove nothing, that is quite true, but they can make one feel more at home." (Sigmund Freud, Neue Folge der Vorlesunge...

"All perception of truth is the detection of an analogy [...]" (Henry D Thoreau, 1851) "Reasoning from analogy is often mos...

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

"Nature is a network of happenings that do not unroll like a red carpet into time, but are intertwined between every part of the world;...

"To say that observations of the past are certain, whereas predictions are merely probable, is not the ultimate answer to the question ...

"Discoveries are not generally made in the order of their scientific arrangement: their connexions and relations are made out gradually...

”[…] the chief reason in favor of any theory on the principles of mathematics must always be inductive, i.e., it must lie in the fact that t...