Simple symmetric Venn diagrams with 17, 19 and 23 curves found via AI-assisted search, verified in Lean 4
pickover · x · 2026-10-21
Chris Dzoba's arXiv paper presents the first simple, rotationally symmetric Venn diagrams with 17, 19 and 23 curves — a jump from the previous record of 13 (Mamakani & Ruskey 2014). The post frames it as a discovery by a human working with two AI models that communicated with each other.
- Symmetric Venn diagrams exist for any prime number of curves (Griggs-Killian-Savage 2004) but had many curves through a point; 'simple' ones were known only up to 13 curves.
- Method: a Metropolis walk on rotation-invariant quadrangulations of the sphere, allowing temporarily duplicated regions, starting from the Griggs-Killian-Savage diagram with multiple crossings resolved; yields four 17-curve, twelve 19-curve and six 23-curve diagrams.
- At 23 curves the walk stalled for two weeks on duplicated regions near the poles; the two finishing lineages were the first with all E=92 states duplication-free.
- Every diagram comes with a machine-checkable certificate; one per size verified by formal proofs in Lean 4.
- All diagrams are non-monotone, which is why prior crossing-sequence searches could never have found them.
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