Quotable Mathematics

"Reductionism (ultimately, the empirical explanability of everything and a cornerstone of science), has uses that are appropriate, and ...

"There is, indeed, a specific fault in our system of science, and in the resultant understanding of the natural world. […] This fault i...

"The more science enters into our lives, the more it must be 'humanized', and there is no better way to humanize it than to...

"Very often a strange attractor is a fractal object, whose geometric structure is invariant under the time evolution maps."  (Davi...

"But it is a third geometry from which quantity is completely excluded and which is purely qualitative; this is analysis situs. In this...

"The circle in the moon which divides the dark and the bright portions is least when the cone comprehending both the sun and th...

"In the initial stages of research, mathematicians do not seem to function like theorem-proving machines. Instead, they use some sort o...

"General or point set topology can be thought of as the abstract study of the ideas of nearness and continuity. This is done in the...

"[...] hence upon the principle that even for an infinite totality of sets there are always mappings that associate with every set one ...

"For group theoretic reasons the most impressive paradoxical decompositions occur in dimension at least three, but there are also inter...