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Nice touch: 4.15 FERMAT’S LAST THEOREM: ... General case when n>2 was proved by Andrew Wiles (1994). The proof is too long to be written here. See: http://www.c

Nice touch: 4.15 FERMAT’S LAST THEOREM: ... General case when n>2 was proved by Andrew Wiles (1994). The proof is too long to be written here. See: http://www.cs.berkeley.edu/~anindya/fermat.pdf http://www.cs.berkeley.edu/~anindya/fermat.pdf

throwawaymath 7y ago
I actually can't tell if that was an intentional "margin" joke, or if the author is just bluntly stating a fact about Wiles' proof... EDIT: Nope, probably intentional. The author doesn't say something similar for any other proof based on a quick CTRL+F :)
- piqufoh 7y ago
  Fermat wrote that in the margin of his book Arithmetica that a proof existed, but there wasn’t space in the margin to write it. It took Wiles 385 years to find a proof, and it won’t fit in a margin. https://en.m.wikipedia.org/wiki/Fermat%27s_Last_Theorem https://en.m.wikipedia.org/wiki/Fermat%27s_Last_Theorem That’s the allure of the theorem; that a simple unknown proof may exist.
  - barking 7y ago
    Yes, I remember when news of his proof broke, being disappointed at how voluminous and obscure (to someone like me) it was. I'd been hoping for something I might be able to get my head around. (Hard as it was, I don't think Wiles spent 385 years coming up with it btw!)
    - nurettin 7y ago
      Whether there is an existing and verified proof or not, there is still a great mystery to be solved by figuring out what Fermat actually meant by what he thought as an elegant solution, whether it is an actual solution or not.
      - EGreg 7y ago
        Well, it could have been like Kempe's chains... they finally realized there is a problem, and then it took like 100 years before Appel and Haken made what is probably the first computer-aided proof. And who can say it's really a "proof" if it doesn't explain "why" it's true.
    - Sharlin 7y ago
      Phrased in a way that doesn't imply Wiles's extreme longevity: it took 385 years of advances in mathematics to invent the tools and frameworks that allowed Wiles to come up with the proof.
  - soVeryTired 7y ago
    There's some speculation that fermat made the same mistake as lamé, who thought he had a proof. However lamé incorrectly assumed unique factorisation of a general number field, which was an easy mistake to make at the time.
  - 0815test 7y ago
    > That’s the allure of the theorem; that a simple unknown proof may exist. Well, Fermat made lots of similar claims wrt. other propositions, and for most of them the proof was found easily, or perhaps they were refuted altogether and shown to be wrong. FLT gets its name because it was a very rare case of a claim that just couldn't be solved, one way or the other. In fact, it seems that Fermat himself may have realized at some point that what he thought of as a proof he had, was in fact wrong - and dropped his claim altogether as a consequence. Which would then explain why it was only found as a margin note in a textbook. It's fascinating because it's such a simple claim to state, and yet the proof is incredibly complex. To be sure, logicians can predict that such cases will occur, in the abstract; it's a bit like having hard-to-solve instances of the SAT. But it's still nice to have such a natural example!
  - throwawaymath 7y ago
    Yeah that's the math lore what I was referencing when I put the word margin in quotes :) I wasn't sure if the author was making an intentional callout to Fermat's lost marvelous proof he couldn't fit in the margin. But indeed, looks like he was, since he doesn't seem to have really mentioned the length of any other proofs.
hatsunearu 7y ago
Link's unfortunately broken :(
- _cereal 7y ago
  You can find it at https://web.archive.org/web/20170414120550/https://people.eecs.berkeley.edu/~anindya/fermat.pdf https://web.archive.org/web/20170414120550/https://people.ee...

throwawaymath 7y ago

I actually can't tell if that was an intentional "margin" joke, or if the author is just bluntly stating a fact about Wiles' proof... EDIT: Nope, probably intentional. The author doesn't say something similar for any other proof based on a quick CTRL+F :)

piqufoh 7y ago
Fermat wrote that in the margin of his book Arithmetica that a proof existed, but there wasn’t space in the margin to write it. It took Wiles 385 years to find a proof, and it won’t fit in a margin. https://en.m.wikipedia.org/wiki/Fermat%27s_Last_Theorem https://en.m.wikipedia.org/wiki/Fermat%27s_Last_Theorem That’s the allure of the theorem; that a simple unknown proof may exist.
- barking 7y ago
  Yes, I remember when news of his proof broke, being disappointed at how voluminous and obscure (to someone like me) it was. I'd been hoping for something I might be able to get my head around. (Hard as it was, I don't think Wiles spent 385 years coming up with it btw!)
  - nurettin 7y ago
    Whether there is an existing and verified proof or not, there is still a great mystery to be solved by figuring out what Fermat actually meant by what he thought as an elegant solution, whether it is an actual solution or not.
    - EGreg 7y ago
      Well, it could have been like Kempe's chains... they finally realized there is a problem, and then it took like 100 years before Appel and Haken made what is probably the first computer-aided proof. And who can say it's really a "proof" if it doesn't explain "why" it's true.
  - Sharlin 7y ago
    Phrased in a way that doesn't imply Wiles's extreme longevity: it took 385 years of advances in mathematics to invent the tools and frameworks that allowed Wiles to come up with the proof.
- soVeryTired 7y ago
  There's some speculation that fermat made the same mistake as lamé, who thought he had a proof. However lamé incorrectly assumed unique factorisation of a general number field, which was an easy mistake to make at the time.
- 0815test 7y ago
  > That’s the allure of the theorem; that a simple unknown proof may exist. Well, Fermat made lots of similar claims wrt. other propositions, and for most of them the proof was found easily, or perhaps they were refuted altogether and shown to be wrong. FLT gets its name because it was a very rare case of a claim that just couldn't be solved, one way or the other. In fact, it seems that Fermat himself may have realized at some point that what he thought of as a proof he had, was in fact wrong - and dropped his claim altogether as a consequence. Which would then explain why it was only found as a margin note in a textbook. It's fascinating because it's such a simple claim to state, and yet the proof is incredibly complex. To be sure, logicians can predict that such cases will occur, in the abstract; it's a bit like having hard-to-solve instances of the SAT. But it's still nice to have such a natural example!
- throwawaymath 7y ago
  Yeah that's the math lore what I was referencing when I put the word margin in quotes :) I wasn't sure if the author was making an intentional callout to Fermat's lost marvelous proof he couldn't fit in the margin. But indeed, looks like he was, since he doesn't seem to have really mentioned the length of any other proofs.

hatsunearu 7y ago

Link's unfortunately broken :(

_cereal 7y ago
You can find it at https://web.archive.org/web/20170414120550/https://people.eecs.berkeley.edu/~anindya/fermat.pdf https://web.archive.org/web/20170414120550/https://people.ee...