Finite algebraic envelopes and the Boone–Higman conjecture
Source: github.com/openai/math/tree/main/preprints/Finite-algebraic…
We prove the Boone–Higman conjecture. A finitely generated group has decidable word problem if and only if it embeds in a finitely presented simple group.
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I think he could take some comfort from the Boone-Higman conjecture since he and his colleagues took a big step towards this (proving it for hyperbolic groups). Anyway, as you hint, none of this is established truth yet. Reply Yiftach says: 09/10/2026 at 22:14 It would be even more amusing if they…
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100+ reactions to 100+ solutionsProofs and PromptsMatt ZaremskyOct 8, 2026
It turns out our sufficient condition always works, and the main mechanism we were missing was morally quite similar to the thing that was our 2025 breakthrough (extremely roughly speaking, the key is affine-like actions of things). So, apparently we were really on to something, and it’s…