There are two labyrinths of the human mind: one concerns the composition of the continuum, and the other the nature of freedom, and both spring from the same source—the infinite. —Baron von Leibniz...

An example of a basic and powerful theorem in arithmetic combinatorics is the sum product theorem of Jean Bourgain, Nets Katz, and Terence Tao. It is an elementary but fundamental quantitative combinatorial fact about the way addition and multiplication work in finite sets of integers. Its generalizations have wide applications to algebra, number theory, theoretical computer science, and most recently to group theory.

There are two labyrinths of the human mind: one concerns the composition of the continuum, and the other the nature of freedom, and both spring from the same source—the infinite. —Baron von Leibniz...