Finite algebraic envelopes and the Boone–Higman conjecture
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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100+ reactions to 100+ solutionsProofs and PromptsOct 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…