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Everyone already strongly suspected that the FCT was true. Nobody was surprised by the result, it just took a computer to prove it.
by bjl 9y ago
Everyone already strongly suspected that the FCT was true. Nobody was surprised by the result, it just took a computer to prove it.
- opportune 9y agoThe same is true of P != NP. And yet proving that would be a very big deal indeed (much as the FCT was).
- cestith 9y agoProving the opposite would be even bigger.
- qubex 9y agoYou clearly are not a mathematician (nor am I). There's a huge, unimaginably broad chasm cognitive chasm between "suspected", "conjectured", and "proved".
- Confusion 9y agoThere is, according to quite a few, also a huge etc. chasm between 'proved' and 'proved by a computer'. Especially if it's a proof through exhaustive enumeration.
- qubex 9y agoI disagree wholeheartedly. Proof by enumeration of finite cases is the most iron clad and idiot proof form of proof one can possibly aspire to. Proof by enumeration is fine and dandy. Some might cast a pall of disreputability upon a proof by enumeration by computer, but really it is no different — the computer and its program are merely a formal system somewhat more complicated and thus harder to inspect than mathematicians are used to, but this does not pose any real conceptual disconnect.
- bjl 9y agoI understand the difference between the concepts. Im just saying the FCT result was not a 'surprising one', which the poster I responded to was implying.