>> Show me one single mathematical result which was *proven* to be true,
>> and verified independently by a large number of mathematicians, and
>> subsequently turned out to actually be false.
> 
> The most obvious answer I can provide (but I don't know how many 
> confirmed the proof) is Fermat's Last Theorem - at least from my read, it 
> was proven for n=3 in the 10th century, but the proof was later 
> invalidated.
> 
> A correct proof was later constructed in the mid-20th century, again, 
> from what I understand.

See, now from what I understand,

1. Fermat claimed to have a proof, but to this day nobody knows what it was.

2. In the intervining several centuries, various proofs have been put 
forward. Some special cases were successfully proven. Some proofs put 
forward were quickly shown to be incorrect.

3. Recently a group of related mathematical proofs finally settled the 
matter.

I am not aware - despite possessing a book detailing the entire history 
of Fermat's Last Theorum - of any proof that was widely held to be 
correct for a long time before being found wrong. All the incorrect 
proofs were discovered to be incorrect fairly quickly.

It's easy for one person to make a mistake. (I saw a very neat example 
of this actually...) It's rather rarer for a large body of 
mathematicians to all fail to spot a flaw. Usually once a theorum gets a 
propper peer review, you can state the validity or otherwise of the 
proof with a pretty high degree of confidence. [Depending on how complex 
the proof is, of course...]

One of the reasons the Four Colour Map "proof" is not widely accepted is 
that it's just about impossibly to peer review it properly. Obviously 
the authors think it's correct, but nobody can easily check it, so it 
could actually be balony. [Regardless of whether the thing it's trying 
to prove is actually correct or not.]

>> And I suppose next you'll be telling me that some day, some future
>> technology might enable us to find a sequence of chess moves whereby a
>> bishop can get from a black square to a white square, despite it being
>> trivially easy to mathematically prove the impossibility of this...
> 
> You're still missing my point....

You're still missing *my* point. :-P

>>> And yet you agreed with another post in this thread that said that
>>> something was possible.  Look at the refocusing capabilities of some of
>>> the tools for that to reconstruct detail in blurred images.  Blurring
>>> is lossy compression, yet being able to recover that data isn't
>>> impossible; that's been proven.
>> Hey, guess what? Blurring isn't compression. It might *look* like it is,
>> but it isn't.
> 
> My point is that there's plenty of examples where raw data is lost but it 
> can be reconstructed.

Blurring doesn't actuallly "lose" nearly as much data as you'd think. 
That's why it can be mostly reversed.

>> Sure. And no doubt some day we'll discover that 2+2 isn't actually 4. I
>> won't hold by breath for that though. :-P
> 
> Well, who knows?  There are ancient civilizations that had no concept of 
> zero.  The introduction of imaginary numbers didn't come along until the 
> late 1500s.  Up until that point, sqrt(-1) was undefined.
> 
> Who knows what we don't know about mathematics even today?

If I were you, I'd be far more worried about the sky falling - it's 
about as logically plausible...

-- 
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*

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