General Relativity and Gravitation

, Volume 43, Issue 12, pp 3657–3664 | Cite as

The reasonable effectiveness of mathematics in the natural sciences

  • Alex Harvey
Research Article


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 Realism. The crucial element is the extraordinary predictive capacity of mathematical structures descriptive of physical theories.


Philosophy of science History of science 


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© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Visiting ScholarNew York UniversityNew YorkUSA

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