Tverberg's theorem

Tverberg's theorem states that if you have enough points in a space (like a plane or higher dimensions), you can always group them into a specific number of clusters so that the convex hulls (the smallest convex shapes containing each group) all overlap at least at one common point. In simple terms, no matter how you arrange a large enough set of points, you can find several groups whose combined "shape areas" intersect at or near the same location, highlighting an inherent overlap structure in large point sets.