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If there's nothing to be grasped in "Gödel's Wonder", why do you think the man himself, who, we can reasonably conjecture, understood his theorems more than any

If there's nothing to be grasped in "Gödel's Wonder", why do you think the man himself, who, we can reasonably conjecture, understood his theorems more than anybody else, spent the remainder of his life "grasping" at what his theorems meant? I find it much more reasonable to conclude that there was, and is, in fact something significant to be grasped, and thinkpieces like this simply want to declare that there's nothing to be grasped.

Kinnard 8y ago
I meant by people like me :)
throwawaymath 8y ago
Brilliant mathematicians and computer scientists are capable of making mistakes. Atiyah was a titan of his field, but in the twilight of his life he published a superfluous, incoherent "proof” of Riemann. It was so deeply flawed that not a single well known mathematician has commented on it publicly out of respect for the man - the most you can find is a MathOverflow discussion picking apart specific claims. We aren’t flying too close to the Sun if we dare to question their conjectures, even those regarding their previous work. In consideration of this point and the available evidence, I remain deeply unconvinced there is a unrealized, grand philosophical insight to be derived from whatever Gödel’s later, more obscure work had to say about the incompleteness theorems. Likewise Fermat was probably the foremost authority on his most famous conjecture during his life; but the common consensus is that he did not, in fact, have a “truly marvelous proof” of the FLT which he couldn’t fit in the margins. Everyone thinks silly things from time to time, their prior work notwithstanding. I’m inclined to believe Gödel either wasn’t as invested in the philosophical implications of his earlier work as you believe. Or perhaps he was, but I really doubt he actually arrived at a novel, rigorous result from it. Occam’s Razor suggests we would know if he had.
- jeromebaek 8y ago
  The difference between Godel and Atiyah is that Godel's later (and more "philosophical") works are very hard to dismiss, because literally nobody understands it. Though it hasn't stopped people from trying: https://www.andrew.cmu.edu/user/avigad/Papers/dialect.pdf https://www.andrew.cmu.edu/user/avigad/Papers/dialect.pdf
  - throwawaymath 8y ago
    I think you'll find many people actually do understand it. In fact, you generally shouldn't predicate your argument on the idea that "literally nobody understands" a thing, because that implies you're directly aware of the entire scope of literature around the subject and its implications. Aside from that, inability to understand a thing should really count against it. Or do you suppose Miyazaki's Inter-Universal Teichmüller theory is strong because it's borderline incomprehensible? Like I said, Occam's Razor suggests there really isn't much there.
    - jeromebaek 8y ago
      Funny, some suggest Occam's Razor is just a paraphrase of Gödel's theorem.

Kinnard 8y ago

I meant by people like me :)

throwawaymath 8y ago

Brilliant mathematicians and computer scientists are capable of making mistakes. Atiyah was a titan of his field, but in the twilight of his life he published a superfluous, incoherent "proof” of Riemann. It was so deeply flawed that not a single well known mathematician has commented on it publicly out of respect for the man - the most you can find is a MathOverflow discussion picking apart specific claims. We aren’t flying too close to the Sun if we dare to question their conjectures, even those regarding their previous work. In consideration of this point and the available evidence, I remain deeply unconvinced there is a unrealized, grand philosophical insight to be derived from whatever Gödel’s later, more obscure work had to say about the incompleteness theorems. Likewise Fermat was probably the foremost authority on his most famous conjecture during his life; but the common consensus is that he did not, in fact, have a “truly marvelous proof” of the FLT which he couldn’t fit in the margins. Everyone thinks silly things from time to time, their prior work notwithstanding. I’m inclined to believe Gödel either wasn’t as invested in the philosophical implications of his earlier work as you believe. Or perhaps he was, but I really doubt he actually arrived at a novel, rigorous result from it. Occam’s Razor suggests we would know if he had.

jeromebaek 8y ago
The difference between Godel and Atiyah is that Godel's later (and more "philosophical") works are very hard to dismiss, because literally nobody understands it. Though it hasn't stopped people from trying: https://www.andrew.cmu.edu/user/avigad/Papers/dialect.pdf https://www.andrew.cmu.edu/user/avigad/Papers/dialect.pdf
- throwawaymath 8y ago
  I think you'll find many people actually do understand it. In fact, you generally shouldn't predicate your argument on the idea that "literally nobody understands" a thing, because that implies you're directly aware of the entire scope of literature around the subject and its implications. Aside from that, inability to understand a thing should really count against it. Or do you suppose Miyazaki's Inter-Universal Teichmüller theory is strong because it's borderline incomprehensible? Like I said, Occam's Razor suggests there really isn't much there.
  - jeromebaek 8y ago
    Funny, some suggest Occam's Razor is just a paraphrase of Gödel's theorem.