Structure and Effectiveness

Mathematics, which has been called “unreasonably effective”, sometimes develops on its own, with problems and goals stemming from its own subject matter, and sometimes develops in tandem with other disciplines. In the latter case, mathematical structures may be articulated in response to the needs of other theories in natural science or may actually reveal directions in which the development of physical theories should proceed. No one doubts that such ventures – at least since the “scientific revolution” that began at the end of the Renaissance – have been successful. In fact, the spurt in the development of mathematics around this time is sometimes said to have made this revolution possible…