New tetrahedron theorem found with Claude after scanning 1.6M sphere combos
IgorCarron · x · 2026-10-22
A user reports discovering a new solid geometry theorem — the seven-point sphere — with Claude's help: for any tetrahedron, seven notable points (including intersections of the centroid-vertex line with the circumsphere, three tangent-plane intersections, the orthocenter, and inversion points) are concyclic on one sphere.
- Method: Claude ran a brute-force scan of 1,957 notable tetrahedron points, with 1,096 fully cross-checked, yielding 1,622,536 five-plus-point concyclic combinations; filtering out trivial and derivable cases left this new theorem.
- The proof is promised later; another AI-for-Math data point showing AI can surface new theorems even in classical geometry.
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