Quotable Mathematics

"After all the progress I have made in these matters, I am still not happy with Algebra, because it provides neither the shortest ways ...

"A surface is a topological space in which each point has a neighbourhood homeomorphic to the plane, ad for which any two distinct poin...

"A continuous function preserves closeness of points. A discontinuous function maps arbitrarily close points to points that are not clo...

"A special role is played in the theory of metric spaces by the class of open spheres within the class of all open sets. The main featu...

"From the point of view of general topology, homeomorphic spaces are the same. That is to say, the properties that interest us are ...

"Speaking roughly, a homology theory assigns groups to topological spaces and homomorphisms to continuous maps of one space int...

"I consider it as one of the most important steps made by Analysis in the last period, that of not being bothered any more by imaginary...

"Topology is the study of topological properties and, especially, topological invariants of figures." (Maurice Frechet & Ky Fa...

"From its beginning critical point theory has been concerned with mutual relations between topology and geometric analysis, including d...

"It is possible that analysis in the large may eventually reduce to topology, but not until topology has been greatly broadened. It i...

"After all the progress I have made in these matters, I am still not happy with Algebra, because it provides neither the shortest ways ...

"String theory promises to take a further step beyond that taken by Einstein's picture of force subsumed within curved space and ti...

"Systems, acting dynamically, produce (and incidentally, reproduce) their own boundaries, as structures which are complementary (necess...

"Homology theory introduces a new connection between invariants of manifolds. Continuing the 'physical' analogy, we say...

"Until now, physical theories have been regarded as merely models with approximately describe the reality of nature. As the models impr...

"In mathematics, logic, linguistics, and other abstract disciplines, the systems are not assigned to objects. They are defined by an en...

"At first glance the theory of numbers is deprived of any geometricity. But this is actually not the case. At the contemporary ...

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