Uh, no. There’s no indication the person I was responding to was anything but serious. Even if they were joking, they were so bad at it that the concept of the whoosh still doesn’t apply.
It wasn’t very funny, though that doesn’t usually stop me, but I was joking.
Simon Singh moots it in the aforementioned book. I’ve also heard it in discussions.
Did Fermat even have any notion of what would later be called commutative algebra, Dedekind rings, etc.? Mid-17th century math was very primitive; the proofs of Fermat’s I’ve seen for other results have all been clever but elaborate algebraic manipulations and some extremely basic number theory. Some of his techniques were later used and developed further (the height machine, for example, is essentially a hardcore version of infinite descent over an arbitrary number field), but that doesn’t mean that Fermat had any thoughts on, or even conception of, those later results.
It’s almost certain that what happened was Fermat was reading a book and thought of something that appeared to be a proof. He wrote down a note to remind himself later. Then when he subsequently did a more rigorous check of his idea he found a flaw in it and dropped it. There are several false proofs he might have thought of.
Fermat just didn’t bother going back and crossing out the note he had written to himself. There’s no evidence he intended it to be found by history. People forget that Fermat wrote his note in 1637 and he lived until 1665 - if he had found a real proof he would have published it. The note was discovered thirty years after his death and this started the legend of the Lost Proof.
Oh, sure, he certainly didn’t have a valid proof, and I doubt he felt any particular need to retract a comment in the margins of a book. I was just disagreeing with the idea that the failure of unique factorization in O_K for arbitrary number fields K was Fermat’s mistake. I don’t think he was even at that level of sophistication; this was a century before Euler and Gauss, after all.
Just to be pedantic, this isn’t strictly true.
Fermat was only semi-officially a mathematical amateur, by which I mean he never published his work and hardly ever gave proofs and made his primary living as a lawyer. Most of his work is known because of the letters he sent to other mathematicians, but even this work was often without proof.
That’s actually why the idea he may have had an undiscovered proof became so prevalent. He was already known for keeping much of his work to himself and the majority of his proofs (whether or not he actually had them) are lost to history. Only a small fraction of his proofs ever survived even his own lifetime.
That said, even within his own lifetime mathematicians doubted he had proofs to some of the theorems he claimed, especially as he rarely offered proof of them and many of them were eventually proven using techniques he was unlikely to have known. It’s likely he never actually had a proof of his Last Theorem.
Sorry, I guess it requires some context. I remember Asymptotically Fat being mentioning .999… = 1 before, and even posting once or twice in the last big thread on it so to me it was obvious he was joking.
The greatest unsolved mystery in mathematics is “What the hell was he thinking?”
FWIW, I knew you were joking and I chuckled.
Yep - AF posted in that thread the last time it was brought back to life. And so did Derleth, to explain to another poster something that AF had written…
Cool - now I know that 0x5f3759df is a ‘‘magic’’ number and what it’s good for! (from googling the mouse-over)