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Was Fermat\'s Theorem Really Proven?
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. |
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