On a traditional view, the primary role of a mathematical proof is to warrant the truth of the
resulting theorem. This view fails to explain why it is very often the case that a new proof of a …

Three different ways in which systems of axioms can contribute to the discovery of new
notions are presented and they are illustrated by the various ways in which lattices have …

There is not much that can be said for all $ x $ and for all $ n $ about the sum\[\sum_ {k= 1}^
n\frac {1}{|\sin k\pi x|}.\] However, for this and similar sums, series, and products, we can …

Richard Dedekind was born into a well-off family in Braunschweig (in the Duchy of
Brunswick, now Germany) on 6 October 1831 and died in his hometown on 12 February …

By the middle of the nineteenth century, it had become clear to mathe-maticians that the
study of finite field extensions of the rational numbers is indispensable to number theory …