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I think this would count as esoteric if you ignore the drama portion of it. Just to get to the point of understanding what they're talking about would probably

I think this would count as esoteric if you ignore the drama portion of it. Just to get to the point of understanding what they're talking about would probably take months of dedicated uninterrupted work. Neat. I have no idea where to even start. https://en.wikipedia.org/wiki/Anabelian_geometry https://en.wikipedia.org/wiki/Anabelian_geometry

strikelaserclaw 8y ago
I don't profess to understand the mathematics behind these papers but i have been following the debate for a couple years now. It is weird for such eminent mathematicians to not be able to reach a conclusion as to whether mochizukis arguments are true or false. I think this is the first time a really eminent mathematician like scholze has put in his two cents that the proof might not be right. At least it looks like work is being done at a serious level to prove or disprove these papers.
xxpor 8y ago
I think what makes these number theory arguments so interesting to me is how simple the theorems are, but how impenetrable the proofs are. For example, Fermat's last theorem is so easy to understand, but there's no chance in hell I'll ever understand Wiles' paper proving it.
- dagw 8y ago
  You might not understand all the details of the paper, but you can definitely follow the thrust of the argument and see the elegance in it without advanced math skills. The really hard part (and main part of Wile's contribution to the proof) was proving something called the Taniyama–Shimura–Weil conjecture. However if you skip that bit and just accept that the conjecture is true the rest of the steps of the proof are both elegant and relatively easy to follow (if you gloss over some of the details) for anybody with a decent grasp of basic math. The book Fermat's Last Theorem by Simon Singh is a pretty great read and does a good job of outlining the basic structure of the proof for anybody with a decent grasp of high school mat.
throwaway080383 8y ago
Years even. And really, that's kind of the issue at hand. This stuff is so difficult that very few mathematicians really understand it, and Mochizuki's work is so much more esoteric than that, that basically no one understands it, even recent Fields Medallists.

strikelaserclaw 8y ago

I don't profess to understand the mathematics behind these papers but i have been following the debate for a couple years now. It is weird for such eminent mathematicians to not be able to reach a conclusion as to whether mochizukis arguments are true or false. I think this is the first time a really eminent mathematician like scholze has put in his two cents that the proof might not be right. At least it looks like work is being done at a serious level to prove or disprove these papers.

xxpor 8y ago

I think what makes these number theory arguments so interesting to me is how simple the theorems are, but how impenetrable the proofs are. For example, Fermat's last theorem is so easy to understand, but there's no chance in hell I'll ever understand Wiles' paper proving it.

dagw 8y ago
You might not understand all the details of the paper, but you can definitely follow the thrust of the argument and see the elegance in it without advanced math skills. The really hard part (and main part of Wile's contribution to the proof) was proving something called the Taniyama–Shimura–Weil conjecture. However if you skip that bit and just accept that the conjecture is true the rest of the steps of the proof are both elegant and relatively easy to follow (if you gloss over some of the details) for anybody with a decent grasp of basic math. The book Fermat's Last Theorem by Simon Singh is a pretty great read and does a good job of outlining the basic structure of the proof for anybody with a decent grasp of high school mat.

throwaway080383 8y ago

Years even. And really, that's kind of the issue at hand. This stuff is so difficult that very few mathematicians really understand it, and Mochizuki's work is so much more esoteric than that, that basically no one understands it, even recent Fields Medallists.