In 1985, Danzer has shown that, for any set D of (arbitrary) pairwise intersecting disks in the plane, all the disks can be stabbed by four points, and that there exist 10 pairwise intersecting disks that cannot be stabbed by fewer (i.e., three) points.

The paper is next to impossible to read and understand, the construction and its proof are rather involved, and one part of the analysis requires computer assistance to verify. The number of living people who fully understand the proof (Danzer has passed away several years ago) is non-negative.

In the talk I will describe our attempts to find a simpler and more understandable proof, and will present some partial results.