Quotable Mathematics

"The mathematician as the naturalist, in testing some consequence of a conjectural general law by a new observation, addresses a questi...

"Cultivate that kind of knowledge which enables us to discover for ourselves in case of need that which others have to read or be told ...

"In the discovery of hidden things and the investigation of hidden causes, stronger reasons are obtained from sure experiments and demo...

"In the study of Nature conjecture must be entirely put aside, and vague hypothesis carefully guarded against. The study of Nature begi...

"It is sometimes said that mathematics is not an experimental subject. This is not true! Mathematicians often use the evidence of lots ...

"All knowledge, the sociologist could say, is conjectural and theoretical. Nothing is absolute and final. Therefore all knowledge is re...

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

"It is best to prove things by actual experiment; then you know; whereas if you depend on guessing and supposing and conjecturing, you ...

"One of the most intimate of all associations in the human mind is that of cause and effect. They suggest one another with the utmost r...

"Pedantry and sectarianism aside, the aim of theoretical physics is to construct mathematical models such as to enable us, from the use...

"A proof in mathematics is a compelling argument that a proposition holds without exception; a disproof requires only the demonstration...

"[Number theory] produces, without effort, innumerable problems which have a sweet, innocent air about them, tempting flowers; and yet…...

"A scientist, whether theorist or experimenter, puts forward statements, or systems of statements, and tests them step by step. In the ...

"Mathematics is not placid, static and eternal. […] Most mathematicians are happy to make use of those axioms in their proofs, although...

"[…] mystery is an inescapable ingredient of mathematics. Mathematics is full of unanswered questions, which far outnumber known theore...

"It is through proof that human mathematicians transcend the limitations of their humanity. Proofs link human mathematicians to truths ...