Quotable Mathematics

"We may assume the existence of an aether; only we must give up ascribing a definite state of motion to it, i. e. we must by abstractio...

"The discovery of Minkowski […] is to be found […] in the fact of his recognition that the four-dimensional space-time continuum of the...

"Diagrams are information graphics that are made up primarily of geometric shapes, such as rectangles, circles, diamonds, or triangles,...

"Arithmetic and number theory study patterns of number and counting. Geometry studies patterns of shape. Calculus allows us to handle p...

"According to the special theory there is a finite limit to the speed of causal chains, whereas classical causality allowed arbitrarily...

"Probability is a mathematical discipline with aims akin to those, for example, of geometry or analytical mechanics. In each field we m...

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

"Arithmetical symbols are written diagrams and geometrical figures are graphic formulas." (David Hilbert, Bulletin of the American...

"The culture of the geometric imagination, tending to produce precision in remembrance and invention of visible forms will, therefore, ...

"It is well known that geometry presupposes not only the concept of space but also the first fundamental notions for constructions in s...