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100 pages of dense mathematics created by Claude. It doesn't even have an abstract or a summary. What are we looking at here? Has anyone read this? Please expla

by mr_mitm 25d ago

100 pages of dense mathematics created by Claude. It doesn't even have an abstract or a summary. What are we looking at here? Has anyone read this? Please explain like I'm not a math PhD.

robinhouston 25d ago
I’m pretty sure no one (except perhaps Anthropic insiders who had prior access, and probably not even them) has properly digested this paper yet, and some caution is warranted given the notoriety of this problem and the history of claimed solutions that did not stand up to scrutiny. But if it stands up, it’s a really big deal. Background: https://mathoverflow.net/questions/1973/is-there-a-complex-structure-on-the-6-sphere https://mathoverflow.net/questions/1973/is-there-a-complex-s...
- oliculipolicula 25d ago
  for maybe undergrads, complex structure in S^6 would mean an associative version of octonions (which are non associative "almost complex" versions of their cousins native to S^3, which you may know as (unit) "quaternions"). Also fancy cousins of unit vectors (that you can do a nonzero triple cross product with), ie "non associative vectors" living on S^2, the 2D surface of a sphere "with radius 1" If you haven't quite got the PhD https://ncatlab.org/nlab/show/quaternionic+structure https://ncatlab.org/nlab/show/quaternionic+structure Big enough that Atiyah the godfather of this subfield, in 2016 claimed to have solved it (not sure if it was before or after the dementia) This is not just any math PhD, it's the anthropic guy whom Claude helped find the Jacobian counterexample, which might be quite worthy of a fields medal (for impact if not notoriety or complexity) if it were human Disclaimer: not a pure maths PhD myself, just someone who likes this stuff so..
  - deleted 24d ago
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  - jesuslop 24d ago
    > complex structure in S^6 would mean an associative version of octonions where can one read more about that?
    - oliculipolicula 24d ago
      In TFA itself! The multiplication they call an "alternating [skew-symmetric?] invariant form": Q0 in symbols I think? Basically a polynomial function in the components of the "superoctonions" that go into the product.that how I'd vibesplain to a fellow non-pro, anyways P10, sec 2.4 Lemma 2.8 The complex structure itself is much more complicated.. or else alpoge would have posted a one line verification of the result? But a summary that excites everybody can only be done by a pro... The next relevant thing in the paper though, that I might be able to attempt to vibesplain using my uh consumer knowhow, is "integrability" (starting in the section labelled "Context") Or one could just ask Fable/ChatGPT to ELI10
      - jesuslop 23d ago
        yep I have feet wet with complex geometry/analysis but not to decipher lemma 2.8. But instead of asking ELI10 I asked about S^6 complex structure helping to cure O non-associativity and got open research directions for sibling goals more than clear cut "yes, if the paper pass validation we've got some new associative octonions". That may need some healthy challenging. chat: https://tinyurl.com/4acu6uc3 https://tinyurl.com/4acu6uc3
        oliculipolicula 22d ago
        Well then what are you waiting for :) You've got the tool, you've got the will
cmenge 25d ago
There's an abstract on page 3. But it's quite ... abstract. By the end of the first sentence I'm pretty sure it would take me quite some time to understand what it's about (the first sentence of the abstract, not the whole paper)
deleted 25d ago
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by mr_mitm 25d ago

100 pages of dense mathematics created by Claude. It doesn't even have an abstract or a summary. What are we looking at here? Has anyone read this? Please explain like I'm not a math PhD.

robinhouston 25d ago

I’m pretty sure no one (except perhaps Anthropic insiders who had prior access, and probably not even them) has properly digested this paper yet, and some caution is warranted given the notoriety of this problem and the history of claimed solutions that did not stand up to scrutiny. But if it stands up, it’s a really big deal. Background: https://mathoverflow.net/questions/1973/is-there-a-complex-structure-on-the-6-sphere https://mathoverflow.net/questions/1973/is-there-a-complex-s...

oliculipolicula 25d ago
for maybe undergrads, complex structure in S^6 would mean an associative version of octonions (which are non associative "almost complex" versions of their cousins native to S^3, which you may know as (unit) "quaternions"). Also fancy cousins of unit vectors (that you can do a nonzero triple cross product with), ie "non associative vectors" living on S^2, the 2D surface of a sphere "with radius 1" If you haven't quite got the PhD https://ncatlab.org/nlab/show/quaternionic+structure https://ncatlab.org/nlab/show/quaternionic+structure Big enough that Atiyah the godfather of this subfield, in 2016 claimed to have solved it (not sure if it was before or after the dementia) This is not just any math PhD, it's the anthropic guy whom Claude helped find the Jacobian counterexample, which might be quite worthy of a fields medal (for impact if not notoriety or complexity) if it were human Disclaimer: not a pure maths PhD myself, just someone who likes this stuff so..
- deleted 24d ago
  [deleted]
- jesuslop 24d ago
  > complex structure in S^6 would mean an associative version of octonions where can one read more about that?
  - oliculipolicula 24d ago
    In TFA itself! The multiplication they call an "alternating [skew-symmetric?] invariant form": Q0 in symbols I think? Basically a polynomial function in the components of the "superoctonions" that go into the product.that how I'd vibesplain to a fellow non-pro, anyways P10, sec 2.4 Lemma 2.8 The complex structure itself is much more complicated.. or else alpoge would have posted a one line verification of the result? But a summary that excites everybody can only be done by a pro... The next relevant thing in the paper though, that I might be able to attempt to vibesplain using my uh consumer knowhow, is "integrability" (starting in the section labelled "Context") Or one could just ask Fable/ChatGPT to ELI10
    - jesuslop 23d ago
      yep I have feet wet with complex geometry/analysis but not to decipher lemma 2.8. But instead of asking ELI10 I asked about S^6 complex structure helping to cure O non-associativity and got open research directions for sibling goals more than clear cut "yes, if the paper pass validation we've got some new associative octonions". That may need some healthy challenging. chat: https://tinyurl.com/4acu6uc3 https://tinyurl.com/4acu6uc3
      - oliculipolicula 22d ago
        Well then what are you waiting for :) You've got the tool, you've got the will

cmenge 25d ago

There's an abstract on page 3. But it's quite ... abstract. By the end of the first sentence I'm pretty sure it would take me quite some time to understand what it's about (the first sentence of the abstract, not the whole paper)

deleted 25d ago

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