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Re: WAS-- Re: Hanson 2006, Mortimer, Baeker response

On Fri, 23 Jun 2006 22:23:56 +0200 Andreas Johansson <andreasj@gmail.com>
> On 6/23/06, Phil Bigelow <bigelowp@juno.com> wrote:
> >
> > The construction, testing, and potential falsification of 
> mathematical
> > theorems and mathematical proofs follows the scientific method, so 
> I
> > don't see why it isn't a science, too.
> Except theorems aren't constructed, tested and falsified that way. 
> A
> theorem isn't a best explanation of data; it's something that's, 
> given
> the axioms, is *true*.

Have mathematical theorems ever been declared to be "true", but later
falsified or put into a category of uncertainty by either another theorem
or because one of the axioms doesn't always follow the theorem?

I'm not claiming that this has ever happened, I'm just curious.  But if
it has happened, then it sure looks like familiar scientific methodology
to me.