[Haskell-cafe] is proof by testing possible?

muad muad.dib.space at gmail.com
Mon Nov 9 17:22:00 EST 2009

I have come across an example:

> However, the following proof of the lovely identity:
> sum . map (^3) $ [1..n] = (sum $ [1..n])^2  is perfectly rigorous. 
> Proof: True for n = 0, 1, 2, 3, 4 (check!), hence true for all n. QED.
> In order to turn this into a full-fledged proof, all you have to do is
> mumble the following incantation:
> Both sides are polynomials of degree ≤ 4, hence it is enough to check the
> identity at five distinct
> values. 

from http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimPDF/enquiry.pdf

Now this sort of idea surely applies to more than just number theory?
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