What is the relationship between programming and math?

Question

Possible duplicate:
Is programming == math?

Programmers seem to think that their work is quite mathematical.

I understand this when you try to optimize something in performance, find the most effective alotism, etc.

But this clearly seems false when you look at a store billing request or system software riddled with I / O calls.

So what is it? Is mathematical calculation and related programming?

Here I mean, in particular, the words of the philosopher Schopenhauer:

This arithmetic is the lowest of all mental actions, the fact is proved that it is the only one that can be achieved through a machine. Take, for example, the settlement machines that are so commonly used in England at present, and solely for the sake of convenience. But the whole analysis of finitorum et infinitorum is based on calculation. Therefore, we can “deeply feel the mathematician,” whom Lichtenberg did merrily, in that he says: “These so-called professors of mathematics took advantage of the simplicity of other people, achieved that it has a deep meaning that reminds theologians deeply aware of their holiness.”

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<CoolStuff> Y combinator

#lang scheme

;(define Y
;  (λ(p)
;    ( (λ(f)(f f)) (λ(f)(p (λ(x)((f f) x)))) )))

(define Y
  (λ(X)
    ((λ(f)
       (X (λ(arg) ((f f) arg))))
     (λ(f)
       (X (λ(arg) ((f f) arg)))))))

> ((Y (λ (n!)(λ (n)  (if (< n 2) 1 (* n (n! (- n 1))))))) 5)
120
>

</CoolStuff>

Answer 4

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Now, if you are wondering if programming is part of mathematics, then I think the answer is yes, if you also consider physics part of mathematics.