Indefinite with Respect to Topics and Applications

Mathematics is indefinite with respect to topics. This is illustrated by the Modern Mathematics Movement, which brought about revolutionary changes to the mathematics curriculum. These changes were facilitated by an incoherent combination of political preoccupations, military interests, economic priorities, and intrinsic mathematical ideas. That mathematics is indefinite with respect to applications is illustrated by the radical change in research related to algorithms. The Entscheidungsproblem is a specific metamathematical problem, whose solution presupposed that the notion of algorithm was clearly specified. This specification was done by means of the Turing machine, a conception tremendously important in the development of computing. That mathematics is indefinite with respect to applications is also illustrated by the development of modern cryptography, which refers to cryptography based on computing. In the development of modern cryptography, number theory plays a huge role. Results from apparently harmless pure number theory have acquired massive economic and also military interests.