> Depends on what you mean by "proof", we sentence people to prison based on
> proof of their crime.  Not all proof is mathematical.  And mathematical
> proof is only relative to the axioms.

I think that this is one of those cases where the term is overloaded.
I would argue that, for most people, proof has a strong connotation of
"case closed". Mathematical proof is the only domain where this is
actually true. Everywhere else it is relative: it means sufficient
evidence for some course of action to be taken. I suspect that judges
and lawyers like the term because it makes everyone sleep better at
night. I never see contemporary scientists using the term, only
science journalists. Again, this makes sense: the general public likes
to feel that science is settling matters. I think it is anti-pedagogic
to talk about scientific theories being "proven", because it conveys
the wrong idea about what science is and what science does. For a
serious scientist, nothing is ever settled and no cases are closed.
There are strong hypothesis at a given time, there are effective
models for certain domains, and one does the best one can with them.
The lack of this "case closed" attitude is precisely what makes
science such a magnificent endeavour, and why it shines so bright
above the certainties of the religious fundamentalists and the
ideologues.

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