Nanoscale devices such as simple nanoelectronic circuits can be designed to represent sets and set operations, and an array of such devices constitutes a universal mathematical processor, able to solve any problem that can be expressed in set theory. Nanologic will find most value for human-meaningful problems involving uncertainty, ambiguity, error, under-specified and over-specified systems, and for approximate analysis of combinatorially intractable problems, including mathematical theorems. Novel quantum computers which will have quantum bit memory space termed qubit for several computations at the same time, enable the use of fast quantum algorithms.