Was Fermat's Theorem Really Proven?

David Sklansky · #1 07-22-2005, 01:45 AM

Unlike scientific theories that are sometimes eventually shown to be wrong, generally accepted math proofs have never, to my knowledge, been overturned. Some like the proof that there is no largest prime, or that the harmonic series converges are so obvious that the odds it isn't true are greater than one in a googol (but less than one in a googolplex). More complex accepted proofs might be a quintillion to one favorites to be true.

But Wiles proof is different. It is lenghty, complex, has no obvious connection to the original question, and most importantly has only been double checked by a large handful of people. Furthermore I believe there is a probability argument that would allow Fermat's Theorem to have no counterexamples because of "chance". Also its proof had escaped the best minds for 500 years.

Personally I would take 100,000 to one odds that Wiles proof will eventually be shown to have a flaw. That's an exceedingly low number regarding a math proof, I think. But I am very unknowledgeable in this field. I wonder therefore what professional mathmeticans would make the odds.

Zygote · #2 07-22-2005, 01:51 AM

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But I am very unknowledgeable in this field.

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i wish i was as unknowledgable as you. Being overly modest is both stupid and disgusting. kinda like announcing "answered" prayers.

David Sklansky · #3 07-22-2005, 02:06 AM

"Being overly modest is both stupid and disgusting."

I wasn't being modest regarding this subject. Actually I don't think I'm overly modest about any subject.

Zygote · #4 07-22-2005, 02:37 AM

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"Being overly modest is both stupid and disgusting."

I wasn't being modest regarding this subject. Actually I don't think I'm overly modest about any subject.

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ya, i was joking. maybe i should've used a smiley face. don't forget that you should still value the fact that you know enough to truly know you're unknowledgable.

goofball · #5 07-22-2005, 03:40 AM

[ QUOTE ]
[ QUOTE ]
But I am very unknowledgeable in this field.

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i wish i was as unknowledgable as you. Being overly modest is both stupid and disgusting. kinda like announcing "answered" prayers.

[/ QUOTE ]

From what I've read here, sklansky is many things. Overly modest is not one of them.

awarunn · #6 07-22-2005, 02:03 AM

Just an example of a mathematical theory that has been considered to be refuted is set theory. I don't claim to be a mathematical expert but I just thought I'd throw that out there.

David Sklansky · #7 07-22-2005, 02:07 AM

I'm talking about a proof, not a theory.

wmspringer · #8 07-30-2005, 12:19 AM

Note that, while in science a theory is basically a "best guess", in math a theorem is something which has been proved; if the logic of the proof is sound, the theorem can never be disproved.

Edit: Really I should say, if the logic AND the axioms are sound.

pzhon · #9 07-22-2005, 02:57 PM

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Just an example of a mathematical theory that has been considered to be refuted is set theory.

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As a mathematician, I have no idea what you mean when you say set theory has been refuted. I don't know of any problem with set theory. I suggest that you are remembering something that got garbled.

kpux · #10 07-22-2005, 04:56 PM

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Just an example of a mathematical theory that has been considered to be refuted is set theory. I don't claim to be a mathematical expert but I just thought I'd throw that out there.

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I'm pretty sure set theory is logically consistent. Are you referring to something like Russell's Paradox or the Continuum Hypothesis?