Gen Relativ Gravit (2011) 43:3657–3664 DOI 10.1007/s10714-011-1248-9 RESEARCH ARTICLE The reasonable effectiveness of mathematics in the natural sciences Alex Harvey Received: 12 July 2011 / Accepted: 21 July 2011 / Published online: 10 August 2011 © Springer Science+Business Media, LLC 2011 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—mathe- matics is just the manipulation of formulas and rules invented for the purpose; Intu- itionism—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 Realism. The crucial element is the extraordinary predictive capacity of mathematical structures descriptive of physical theories. Keywords Philosophy of science · History of science 1 Introduction In an essay which appeared in his collection, Symmetries and Reflections, Wigner [1] explored the connection between mathematics and science. He wondered that, “…the enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and that there is no rational explanation for this.” It is a great pleasure to dedicate this paper to Josh Goldberg, long a valuable member of the commuunity of General Relativists, and a good friend. A. Harvey (B ) Visiting Scholar, New YorkUniversity, New York,NY, USA e-mail: ah30@nyu.edu 123