>> 1. Fermat claimed to have a proof, but to this day nobody knows what it was.
> 
>   Some people have the opinion that, regardless of being an exceptionally
> gifted mathematician, Fermat was simply wrong when he wrote that margin
> note.

That seems perfectly plausible to me...

Some have also speculated that Fermat spotted a "simple" proof that has 
eluded the rest of the community for over 300 years. This seems rather 
less plausible.

(The modern day proof could not possibly be the one Fermat had. Well, I 
mean, unless he invented several entire branches of mathematics in his 
head that day...)

Some folks think he might have had a broken proof similar to Cauchy, but 
not realised it was broken. The margin note looks like an off-hand 
remark, so maybe he didn't check it out too much... People certainly 
make mistakes.

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

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