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I wonder if it bothers someone like Terry Tao that a question of this requires so much machinery to solve. I'd like to believe him that, say, the work to renorm
by ajkjk 9y ago
I wonder if it bothers someone like Terry Tao that a question of this requires so much machinery to solve. I'd like to believe him that, say, the work to renormalize the Hamiltonian there is totally correct and rigorous -- he's the best person to believe that it is, anyway. But why is it... necessary?
It seems so completely unlikely that the universe would require going so far afield from the original question in order to prove something that's relatively simple to state about it!
Of course, it's probably because there's some big piece missing -- if you knew how to prove the RH, this would probably be a comparatively trivial corollary. But it still feels kinda weird that all those conclusions couldn't be 'reduced' to something simpler.
- jules 9y agoMaybe it can be reduced to something simpler, because this is the first proof and proofs are often simplified later, but as far as proofs go this one isn't that complex.
- rwallace 9y agoFor a more accessible example, what about Fermat's Last Theorem? An apparently simple statement about integer arithmetic, whose proof needs to go into wild excursions about arcane functions of continuous curves. Counterintuitive!
- danharaj 9y agoUndecidability basically guarantees the existence of arbitrarily hard to prove but easy to state theorems.
- posterboy 9y agoWhy is the completeness theorem never mentioned in this context? FOL is decidable! And as far as I can see, RH is in FOL.
- zeth__ 9y ago>It seems so completely unlikely that the universe would require going so far afield from the original question in order to prove something that's relatively simple to state about it! There is nothing in the universe that is simple to prove rigorously.