Quotable Mathematics

"A collective appropriate for the application of the theory of probability must fulfil two conditions. First, the relative frequencies ...

"All the theories and hypotheses of empirical science share this provisional character of being established and accepted ‘until further...

“Science does not begin with facts; one of its tasks is to uncover the facts by removing misconceptions.” (Lancelot L Whyte, “Accent on Form...

"[…] we are far from having exhausted all the applications of analysis to geometry, and instead of believing that we have approached ...

"Entia non sunt multiplicanda praeter necessitatem. That is to say; before you try a complicated hypothesis, you should make quite sure...

"We may assume the superiority ceteris paribus [other things being equal] of the demonstration which derives from fewer postulates or h...

"Thought often leads us far beyond the imaginable without thereby depriving us of the basis for our conclusions. Even if, as it appears...

"The concepts which now prove to be fundamental to our understanding of nature- a space which is finite; a space which is empty, so tha...

"A proof only becomes a proof after the social act of ‘accepting it as a proof’." (Yuri I Manin, "A Course in Mathematical Lo...

"Logic moves in one direction, the direction of clarity, coherence, and structure. Ambiguity moves in the other direction, that of flui...