AGI-complete in general? Obviously. But still, a lot can be done. See e.g.:
- The Busy Beaver Challenge deciders
Bill Haydon played by Ian Richardson in the 1979 Tinker Tailor Soldier Spy (TV series)
. 
Short for Doctor of Philosophy, it's how some weird places like the University of Oxford say PhD. In Oxford they also analogously say MPHil.
Described at: arxiv.org/pdf/2107.12475.pdf where a relation to the Busy beaver scale is proven, and the intuitive relation to the Collatz conjecture described. Perhaps more directly: demonstrations.wolfram.com/CollatzSequenceComputedByATuringMachine/
- experimentalhistory.substack.com/p/the-rise-and-fall-of-peer-review The rise and fall of peer review by Adam Mastroianni (2022)
One of the most beautiful things is how they paywall even public domain works. E.g. here: www.nature.com/articles/119558a0 was published in 1927, and is therefore in the public domain as of 2023. But it is of course just paywalled as usual throughout 2023. There is zero incentive for them to open anything up.
Given stuff like arxiv.org/pdf/2107.12475.pdf on Erdős' conjecture on powers of 2, it feels like this one will be somewhere close to computer science/Halting problem issues than number theory. Who knows. This is suggested e.g. at The Busy Beaver Competition: a historical survey by Pascal Michel.
There are unlisted articles, also show them or only show them.