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The Philosophy of Mathematical Practice$
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Paolo Mancosu

Print publication date: 2008

Print ISBN-13: 9780199296453

Published to Oxford Scholarship Online: February 2010

DOI: 10.1093/acprof:oso/9780199296453.001.0001

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Mathematics and Physics: Strategies of Assimilation

Mathematics and Physics: Strategies of Assimilation

(p.417) 16 Mathematics and Physics: Strategies of Assimilation
The Philosophy of Mathematical Practice

Alasdair Urquhart

Oxford University Press

The main topic of this chapter is the problem posed to the mathematical community by the non-rigorous methods used by physicists in investigating mathematical problems. These methods are often highly successful in finding concrete results, but cannot be justified by standard methods. The chapter illustrates methods used by mathematicians in assimilating such non-rigorous techniques by reference to areas such as the umbral calculus of Blissard, Dirac's delta function, and the use of infinitesimals in calculus. It concludes with an example of an area where assimilation is currently incomplete, the replica method in statistical physics.

Keywords:   umbral calculus, infinitesimals, replica method, rigour, assimilation, Blissard, Dirac's delta function

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