Simple, rotationally symmetric Venn diagrams exist for 17, 19 and 23 curves (twitter.com)

Recent advancements in AI collaboration have led to the discovery of simple, rotationally symmetric Venn diagrams capable of illustrating 17, 19, and 23 curves. This project emerged from a partnership between two AI systems, Claude and Codex, which utilized a shared message board to develop a specialized search algorithm. By implementing a Metropolis walk on rotation-invariant quadrangulations of the sphere, the AIs were able to effectively explore configurations, overcoming challenges such as duplicate and missing regions. This breakthrough is significant for the AI/ML community, as it demonstrates the potential of AI systems to collaboratively tackle complex mathematical problems. The ability to visualize higher-order Venn diagrams not only enhances our understanding of combinatorial geometry but also opens up new avenues for research in data representation and information theory. The techniques employed in this discovery may influence future AI applications in diverse fields, including data analysis and graphics, by providing novel methods for organizing and interpreting multidimensional data.