>> 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.
> 
> Absence of evidence is not evidence of absence. ;-)

It *is* evidence. It isn't proof, but it is evidence.

Somebody having a proof that everybody thought was right but actually 
turned out to be wrong would make for pretty dramatic reading in a book 
which is basically a dramatisation of the history of FLT. Of course, the 
researchers could have missed something though...

>> Blurring doesn't actuallly "lose" nearly as much data as you'd think.
>> That's why it can be mostly reversed.
> 
> Again, 10 years ago, doing this was thought to be impossible.

Emphasis: Thought.

There is a difference between something being "thought" and something 
being mathematically "proven". A very significant difference.

Cryptographers "thought" that public key cryptography was impossible, 
and where astonished when somebody actually invented it. However, note 
that nobody ever *proved* that PKC was impossible, people just *assumed* 
it would be. Very Big Difference.

>> If I were you, I'd be far more worried about the sky falling - it's
>> about as logically plausible...
> 
> I don't see how your statement follows mine....

Your "logic" seems to be "absolutely anything is possible". That 
includes the sky falling down. Which is about as likely as the Halting 
Problem being incorrect - but, obviously, far more serious. I don't know 
about you, but *I* would rather be wrong about some theorum than have 
chunks of sky fall on my head!

> Throughout history, mankind has claimed to have reached the end of 
> knowledge on all manner of topics, saying "there's nothing more to learn 
> here".  In every instance (AFAIK), that's been proven wrong.
> 
> But now here, in the 21st century, we've finally exhausted the base of 
> knowledge?  I don't think that's the case.

In mathematics, learning generally consists of discovering new things, 
and rarely involves finding out that old things were wrong. (Although 
you have to carefully draw a line between *facts* which have been 
proven, and *ideas* about mathematics. The latter can and do change, the 
former are forever.)

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

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