Quotable Mathematics

"A manifold, roughly, is a topological space in which some neighborhood of each point admits a coordinate system, consisting of real co...

"Logic sometimes makes monsters. For half a century we have seen a mass of bizarre functions which appear to be forced to resemble as l...

"One very important genus of complex ideas that we encounter everywhere are those in which the idea of collection (Inbegriff ) appears....

"A manifold, roughly, is a topological space in which some neighborhood of each point admits a coordinate system, consisting of real co...

"I see with much pleasure that you are working on a large work on the integral Calculus [...] The reconciliation of the methods which y...

"In the extension of space-construction to the infinitely great, we must distinguish between unboundedness and infinite extent; the for...

"Whereas the conception of space and time as a four-dimensional manifold has been very fruitful for mathematical physicists, its effect...

"If in the case of a notion whose specialisations form a continuous manifoldness, one passes from a certain specialisation in a definit...

"The object of pure mathematics is those relations which may be conceptually established among any conceived elements whatsoever by...

"Philosophers conceive of the passions which harass us as vices into which men fall by their own fault, and, therefore, generally derid...

"[...] a manifold is a set M on which 'nearness' is introduced (a topological space), and this nearness can be described at eac...

"Neither space nor time has any existence outside the system of evolving relationships that comprises the universe. Physicists refer ...

"If two well-defined manifolds M and N can be coordinated with each other univocally and completely, element by element (which, if poss...