The Reasonable Effectiveness of Mathematics in the Physical Sciences

Abstract: Mathematics and its relation to the physical universe have been the topic of speculation since the days of Pythagoras. Several different views of the nature of mathematics have been considered: Realism - mathematics exists and is discovered; Logicism - all mathematics may be deduced through pure logic; Formalism - mathematics is just the manipulation of formulas and rules invented for the purpose; Intuitionism - mathematics comprises mental constructs governed by self evident rules. The debate among the several schools has major importance in understanding what Eugene Wigner called, "The Unreasonable Effectiveness of Mathematics in the Natural Sciences." In return, this `Unreasonable Effectiveness' suggests a possible resolution of the debate in favor of it Realism. The crucial element is the extraordinary predictive capacity of mathematical structures descriptive of physical theories.