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This article attempts to address the problem of the applicability of mathematics in physics by considering the (narrower) question of what make the so-called special functions of mathematical physics special. It surveys a number of answers to this question and argues that neither simple pragmatic answers, nor purely mathematical classificatory schemes are sufficient. What is required is some connection between the world and the way investigators are forced to represent the world. 1. Introduction2. Some responses to the question3. Idealization4. Airy's equation5. Stokes on the Airy integral6. Asymptotic expansions and special functions7. Special functions and the world8. Conclusion: special functions and the philosophy of mathematics Introduction Some responses to the question Idealization Airy's equation Stokes on the Airy integral Asymptotic expansions and special functions Special functions and the world Conclusion: special functions and the philosophy of mathematics

On the Specialness of Special Functions (The Nonrandom Effusions of the Divine Mathematician)