Quotable Mathematics

"Each of us carries within us a worldview, a set of assumptions about how the world works - what some call a paradigm - that forms the ...

" Mathematics provides a good part of the cultural context for the worlds of science and technology. Much of that context lies not only...

"A model is a useful (and often indispensable) framework on which to organize our knowledge about a phenomenon. […] It must not be over...

"The framing of hypotheses is, for the enquirer after truth, not the end, but the beginning of his work. Each of his systems is invente...

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

"What I am offering, is not a scientific theory, but a method; the first step in the construction of a model is to describe the dynamic...

"Economics is a science of thinking in terms of models joined to the art of choosing models which are relevant to the contemporary worl...

"We form in the imagination some sort of diagrammatic, that is, iconic, representation of the facts, as skeletonized as possible. The i...

"All crises begin with the blurring of a paradigm and the consequent loosening of the rules for normal research […] Or finally, the cas...

“One measure of the depth of a physical theory is the extent to which it poses serious challenges to aspects of our worldview that had previ...

“Some people believe that a theorem is proved when a logically correct proof is given; but some people believe a theorem is proved only when...

"As the objects of abstract geometry cannot be totally grasped by space intuition, a rigorous proof in abstract geometry can never be b...