alt Hacker NewsI’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-s...
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
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..