The Miracle of Applied Mathematics

Mathematics has a great variety of applications in the physical sciences. This simple, undeniable fact, however, gives rise to an interesting philosophical problem: why should physical scientists find that they are unable to even state their theories without the resources of abstract mathematical th...

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Bibliographic Details
Published in:Synthese (Dordrecht) 2001-06, Vol.127 (3), p.265-277
Main Author: Colyvan, Mark
Format: Article
Language:English
Subjects:
20th century
Addition & subtraction
Aesthetics
Applied mathematics
Electric current
Electrons
History
History of science and technology
Mathematical puzzles
Mathematical sciences and techniques
Mathematicians
Mathematics
Philosophers
Philosophical realism
Philosophy of mathematics
Philosophy of science
Physical sciences
Physical theory
Physicists
Physics
Puzzles
Realism
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Summary:Mathematics has a great variety of applications in the physical sciences. This simple, undeniable fact, however, gives rise to an interesting philosophical problem: why should physical scientists find that they are unable to even state their theories without the resources of abstract mathematical theories? Moreover, the formulation of physical theories in the language of mathematics often leads to new physical predictions which were quite unexpected on purely physical grounds. It is thought by some that the puzzles the applications of mathematics present are artefacts of out-dated philosophical theories about the nature of mathematics. In this paper I argue that this is not so. I outline two contemporary philosophical accounts of mathematics that pay a great deal of attention to the applicability of mathematics and show that even these leave a large part of the puzzles in question unexplained.
ISSN:0039-7857
1573-0964
DOI:10.1023/a:1010309227321